+ All Categories
Home > Documents > LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Date post: 12-Dec-2021
Category:
Upload: others
View: 4 times
Download: 0 times
Share this document with a friend
81
The Pennsylvania State University The Graduate School LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER WICKING STRUCTURES FOR HEAT PIPES AND VAPOR CHAMBERS A Thesis in Additive Manufacturing and Design by Adnen Mezghani 2020 Adnen Mezghani Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2020
Transcript
Page 1: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

The Pennsylvania State University

The Graduate School

LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF

COPPER WICKING STRUCTURES FOR HEAT PIPES AND

VAPOR CHAMBERS

A Thesis in

Additive Manufacturing and Design

by

Adnen Mezghani

2020 Adnen Mezghani

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Master of Science

May 2020

Page 2: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

The thesis of Adnen Mezghani was reviewed and approved by the following:

Abdalla R. Nassar Head of Process Physics, Analytics, and Engineering Department, and Associate

Research Professor, The Applied Research Laboratory, Pennsylvania State University.

Thesis Advisor

Edward W. Reutzel Director of Center for Innovative Materials Processing Through Direct Digital

Deposition Lab (CIMP-3D), and Associate Professor, The Applied Research Laboratory, Pennsylvania State University.

Judith A. Todd Department Head of Engineering Science and Mechanics, and Professor of

Engineering Science and Mechanics, Pennsylvania State University.

Timothy W. Simpson Paul Morrow Professor in Engineering Design and Manufacturing, Pennsylvania

State University. Head of the Additive Manufacturing and Design Graduate Program.

Page 3: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

III

ABSTRACT

An integral component in two-phase thermal management systems, namely, heat pipes

(HP) and vapor chambers (VC), is a porous wicking structure. Traditional methods for

manufacturing wicking structures within HPs and VCs involve secondary manufacturing and

assembly processes and are generally limited to simple pipe-like or plate-like geometries. More

complex geometries may, however, be possible with laser powder bed fusion (LPBF) additive

manufacturing (AM), which permits high level of geometric complexity, part consolidation, and

customization. The work presented in this thesis aims to leverage the unprecedented level of

customization and geometric complexity permitted through LPBF AM to produce copper HPs

and VCs with integrated wicking structures. Several copper wicking structures were successfully

fabricated via partial sintering and via the formation of square, hexagonal, and rectangular

arrangements of micro-pins and micro-grooves. These represent the first published reports on

LPBF AM of copper wicking structures for HPs/VCs applications. The copper wicks were also

successfully fabricated in multiple build directions. The fabricated wicks were then characterized

by measuring porosity and permeability as well as conducting capillary rate-of-rise analysis.

Results are compared with recently published works on AM for fabricated wicking structures in

316L stainless steel and AlSi12 aluminum material systems. The porosity of fabricated sintered-

powder wicks ranged from 0.31 to 0.37, while the measured porosity for micro-pin and micro-

groove wicks ranged from 0.55 to 0.85. Capillary performance K/reff achieved ranged from 0.186

µm to 1.79 µm, with the rectangular-arrangement micro-pin wick presenting the highest capillary

performance. The results of this work indicate the viability of fabricating copper wicking

structures via LPBF and provide foundational knowledge and experimental validation necessary

for additively manufacturing complete assemblies of copper HPs and VCs.

Page 4: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

IV

TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................................. VI

LIST OF TABLES ................................................................................................................... VIII

ACKNOWLEDGEMENTS ..................................................................................................... IX

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

1.1 Motivation and research goal ...................................................................................... 1 1.2 Thesis outline .............................................................................................................. 2

Chapter 2 Literature review ............................................................................................ 3

2.1 Operation of HPs and VCs .......................................................................................... 3 2.2 Types of wicking structures used in VCs ................................................................... 5 2.3 The LPBF AM Process ............................................................................................... 9 2.4 LPBF AM of wicks ..................................................................................................... 10

Chapter 3 Preliminary experiment: Investigating the printability of sintered-powder and micro-pin wicks ......................................................................................................... 14

3.1 Build preparation and sample geometry ..................................................................... 14 3.2 Sample preparation and characterization .................................................................... 18

3.2.1Porosity measurement ...................................................................................... 18 3.2.2Qualitative wickability assessment .................................................................. 19

3.3 Results and discussion ................................................................................................ 20

Chapter 4 Secondary experiment: Improving on sintered-powder and micro-structured wicks ............................................................................................................... 23

4.1 Sample geometry and build preparation ..................................................................... 23 4.2 Wick characterization and data analysis ..................................................................... 28

4.2.1Porosity measurement ...................................................................................... 28 4.2.2Permeability measurement ............................................................................... 28 4.2.3Capillary rate-of-rise testing ............................................................................. 30 4.2.4Data reduction .................................................................................................. 32

4.3 Results and discussion ................................................................................................ 34

Chapter 5 Conclusions .................................................................................................... 40

References ........................................................................................................................ 42

Appendix A Preliminary experiment sample images ...................................................... 44

Appendix B Secondary experiment sample images ........................................................ 47

Appendix C MATLAB script for rate-of-rise analysis ................................................... 50

Page 5: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

V

Appendix D Experimental setup images ......................................................................... 54

Appendix E Permeability measurements ........................................................................ 56

Appendix F Rate-of-rise water mass vs. time plots ........................................................ 61

Page 6: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

VI

LIST OF FIGURES

Figure 1: An illustration of the operation of a HP/VC system ................................................. 3

Figure 2: Illustration of a cross-section of a commercially available vapor chamber showing the utilization of sintered powder and wire mesh wicks for working liquid transport. .......................................................................................................................... 6

Figure 3: An illustration of cycle of operation of a laser powder bed fusion (LPBF) system. ............................................................................................................................. 9

Figure 4: Image of the fabricated aluminum cylindrical heat pipe with an octahedral lattice-structure wick [4]. ................................................................................................. 11

Figure 5: Image of the manufactured stainless steel primary wick [5]. ................................... 11

Figure 6: Image of the internal structure of the manufactured stainless steel primary wicks [6]: (a) large (280–300 µm), (b) small (70–90 µm). .............................................. 12

Figure 7: Image of the fabricated a stainless steel octahedral lattice-structure wick [7]. (a) Unit cell, (b) a photo of the 3D-printed sample of 1×20×40mm3, (c) proposed CAD model, (d) scanning electron microscope image and (e) optical microscopic image. ...... 13

Figure 8: The build plate of the preliminary experiment showing the sintered-powder samples and micro-pin samples. ...................................................................................... 16

Figure 9: Schematic of capillary rate-of-rise setup used to capture wicked water mass vs. time data. .......................................................................................................................... 19

Figure 10: capillary rate-of-rise data: water mass vs. time of three samples processed with different laser power levels, where P=power level, S=scanning speed level, and H=hatch spacing level. ..................................................................................................... 21

Figure 11: capillary rate-of-rise data: water mass vs. time of a sample in the vertical direction (perpendicular to build plate) and horizontal direction (parallel to build plate). ............................................................................................................................... 22

Figure 12: Optical images of some of the fabricated micro-pin and micro-groove wick samples: (a) square arrangement "P-S-400-H", (b) groove "G-600-H", (c) rectangular arrangement "P-R-350-600-H", (d) hexagonal arrangement "P-H-400-H" .. 24

Figure 13: A schematic of the permeability test setup. ............................................................ 30

Figure 14: A schematic of the rate-of-rise test setup. .............................................................. 31

Figure 15: Snapshots of the rate-of-rise IR video at different time stamps. Wicking sample: P-R-450-600-H. Working fluid: DI water. ......................................................... 33

Page 7: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

VII

Figure 16: Plot of the capillary performance parameter K/reff vs. porosity of the sintered-powder wicks fabricated through laser powder bed fusion additive manufacturing (current study) as well as some traditionally sintered wicks. ........................................... 37

Figure 17: Plot of the difference between porosity measurements performed using density and Archimedes methods vs. Linear energy density of laser process parameters used to fabricate the sintered-powder samples. ........................................................................ 38

Figure 18: Plot of the difference between porosity measurements performed using density and Archimedes methods vs. porosity of the fabricated micro-structured wicking samples. ............................................................................................................................ 39

Page 8: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

VIII

LIST OF TABLES

Table 1: Types of wicking structures typically used in vapor chambers, listing some examples and comparing capillary performance characteristics. [8] ............................... 7

Table 2: Specifications of the LPBF instrument used. ............................................................. 14

Table 3: Specifications of the metal powder used. .................................................................. 15

Table 4: Experimental processing parameters (i.e., Laser power, laser scanning speed, and hatch spacing) used to fabricate the samples of the preliminary experiment. ........... 17

Table 5: Measured sample porosity using the density method. ............................................... 20

Table 6: The selected micro-structure arrangements implemented in the wick samples and the selected pin and groove spacing. ................................................................................ 25

Table 7: (Cont.) The selected micro-structure arrangements implemented in the wick samples and the selected pin and groove spacing. ........................................................... 26

Table 8: Processing parameters for the sintered wick samples ................................................ 27

Table 9: Room-temperature properties of the working fluid. .................................................. 31

Table 10: Porosity, permeability, K/reff, and Pc·K, of successfully tested samples, with comparison to capillary performance of other AM wicks................................................ 35

Table 11: (Cont.) Porosity, permeability, K/reff, and Pc·K, of sintered-powder and micro-pin wicks fabricated through sintering and electroplating, respectively. ......................... 36

Page 9: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

IX

ACKNOWLEDGEMENTS

This work was supported by SET Group, LLC though prime contract number

80NSSC18C0125 from the National Aeronautics and Space Administration under FY 2017 SBIR

topic S3.03. The views and conclusions contained in this document are those of the authors and

should not be interpreted as necessarily representing the official policies, either expressed or

implied, of the Government.

I wish to express my sincere appreciation to my advisor, Dr. Abdalla R. Nassar, who

provided substantial guidance and was a tremendous source of knowledge and valuable advice,

and for providing the opportunity to work at the Applied Research Laboratory as a graduate

research assistant.

I would like to acknowledge Corey Dickman and Ed Good from The Applied Research

Laboratory and SET Group engineers for the great technical support and helpful input throughout

the project.

Many thanks go to CIMP-3D students, researchers, and staff for creating a friendly and

supportive environment.

Finally, my deep and sincere gratitude go to my parents for their unconditional support,

tremendous encouragement, and endless patience.

Page 10: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Chapter 1

Introduction

1.1 Motivation and research goal

Thermal management of high heat-flux electronic devices poses a significant engineering

challenge, especially in the context of electronics used in space, where volume and weight

considerations are non-trivial. As an alternative to conventional heat exchangers, heat pipes and

vapor chambers have gained significant attention in the past several decades [1]–[3]. The

primary advantages of heat pipes and vapor chambers, over single-phase, surface-mounted heat

dissipation technologies, are (1) very high thermal conductance and (2) passive cooling.

Conventional heat pipes (HP) and vapor chambers (VC) are limited in geometry and

complexity to pipe-like or plate-like geometries and involve secondary manufacturing processes

for porous wick production and assembly (e.g., sintering, welding, or vapor and chemical

deposition). Additive manufacturing (AM) offers the potential for great complexity and

customization in HP and VC geometries, as well as eliminating the secondary wick

manufacturing step.

Wick production and integration into an additively manufactured component is, however,

non-trivial. Several resent works have focused on this problem. Ameli et al. [4] investigated

LPBF of an aluminum HP. The researchers investigated different lattice arrangements and sizes

and were able to successfully manufacture a simple HP assembly in one step. Richard et al. [5]

experimentally demonstrated the capability of LPBF to produce 316L stainless steel wicks with

controlled pore size to be used in loop HPs. Esarte et al. [6] also manufactured, via LPBF, a 316L

stainless steel primary wick used in a loop HP. Jafari et al. [7] successfully manufactured, via

LPBF, and characterized octahedral lattice-structure wicks from 316L stainless steel.

Page 11: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

2

To date, however, no work has sought to investigate LPBF AM of pure copper wicking

structures for applications in HPs/VCs. Copper is an attractive material for thermal management

in general and HPs/VCs in particular due to its high thermal conductivity, high operating

temperature, and range of compatible working fluids. Unfortunately, due to the difficulties

associated with AM of pure copper and other highly reflective, highly thermally conductive

materials, laser powder bed fusion (LPBF) of pure copper is rarely pursued. This work aims to

validate the manufacturability of copper wicking structures to be used in two-phase thermal

management systems (i.e., HP/VC), VCs in particular, as well as characterize the manufactured

wicks and conduct performance comparison to other AM wicks.

1.2 Thesis outline

In this thesis, Chapter 2 presents a review of the literature pertinent to wicking structures

used in VC and recent research in LPBF of wicking structures are presented.

Chapter 3 presents a preliminary experiment, the objective of which is to investigate the

printability of copper sintered-powder and micro-pin structures. Sample production, preparation,

porosity measurement, and wickability assessment are detailed.

Chapter 4 presents a secondary experiment, the objective of which is to further tweak

LPBF laser processing parameters used in the preliminary experiment, with the objective of

increasing porosity and improving wickability of sintered-powder samples as well as fabricating

several arrangements of micro-structured wicks, namely, micro-pins and micro-groove structures.

Sample design, build preparation, wick characterization, and results and discussions are detailed.

Chapter 5 presents a summary and conclusions of the work done, as well as the

contributions of the research and potential future work.

Page 12: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

3

Chapter 2

Literature review

2.1 Operation of HPs and VCs

HPs/VCs are two-phase thermal management systems that transport heat or transform

heat flux from an evaporator to a condenser through the cyclic evaporation and condensation of a

liquid. These systems are widely used in cooling high-heat flux electric components,

isothermalization, temperature control, and heat flux transformation [1], [3]. Figure 1 illustrates

the operational cycle of a conventional tube HP.

Figure 1: An illustration of the operation of a HP/VC system

The outer surface of a HP or VC is a solid, dense shell enclosing a conformal porous

wick and an inner hollow cavity. The porous wick transports the condensed liquid from the

condenser to the evaporator via capillary pressure, while the hollow cavity transports the

evaporated liquid from the evaporator to the condenser. The selection of an appropriate working

fluid depends on the compatibility and working temperature range suitable for the intended

Page 13: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

4

application. Here, we utilize deionized water as the working fluid for its high merit number, great

compatibility with copper, and wide range of application temperatures of 30-200˚C [1].

In a wick, a pressure gradient is generated in the direction of lower liquid saturation,

resulting in the liquid transport. Constructing a momentum balance at the liquid front of a liquid

rising through a wick, three pressure sources are found to be in balance:

𝑃𝑃𝑐𝑐 = 𝑃𝑃ℎ + 𝑃𝑃𝑓𝑓 (1)

where the capillary pressure, 𝑃𝑃𝑐𝑐, driving the liquid transport is counteracted by the hydrostatic

pressure, 𝑃𝑃ℎ, and the pressure generated from viscous friction, 𝑃𝑃𝑓𝑓.

The capillary pressure, 𝑃𝑃𝑐𝑐, is found from a force balance across a curved liquid surface

through:

𝑃𝑃𝑐𝑐 =2𝜎𝜎𝑅𝑅

(2)

where 𝜎𝜎 is the surface tension of the liquid and 𝑅𝑅 is the radius of curvature of the liquid meniscus.

The radius of liquid curvature, 𝑅𝑅, can be replaced with the effective radius, 𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓, which is related

to the actual pore radius in a wick structure, 𝑟𝑟𝑝𝑝, and wetting angle, 𝜃𝜃, through 𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓 = 𝑟𝑟𝑝𝑝cos (𝜃𝜃)

,

reducing Equation (2) to:

𝑃𝑃𝑐𝑐 =

2𝜎𝜎𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓

(3)

The hydrostatic pressure is expressed as:

𝑃𝑃ℎ = 𝜌𝜌𝜌𝜌ℎ (4)

𝑃𝑃ℎ = 𝜌𝜌𝜌𝜌where 𝜌𝜌 is the density of the rising liquid, 𝜌𝜌 is the gravitational acceleration (= 9.81

m/s2), and ℎ is the height of the liquid front rising through the wick. The pressure generated from

viscous friction is expressed by a form of Darcy’s law as:

𝑃𝑃𝑓𝑓 =

𝜇𝜇𝜇𝜇𝐾𝐾ℎ𝑑𝑑ℎ𝑑𝑑𝑑𝑑

(5)

Page 14: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

5

where 𝜇𝜇 is the dynamic viscosity of the working fluid, 𝜇𝜇 is the porosity of the wicking structure, ℎ

is the liquid rise height, 𝑑𝑑ℎ𝑑𝑑𝑑𝑑

is the liquid rise velocity, and 𝐾𝐾 is the permeability of the wicking

structure. Substituting Equations (3, 4, &5) into Equation (1) yields:

2𝜎𝜎𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓

= 𝜌𝜌𝜌𝜌ℎ +𝜇𝜇𝜇𝜇𝐾𝐾ℎ𝑑𝑑ℎ𝑑𝑑𝑑𝑑

(6)

Equation (6) relates the effective pore radius (which is related to capillary pressure), permeability,

and porosity to the rate of rise, 𝑑𝑑ℎ/𝑑𝑑𝑑𝑑, and height, ℎ, of a rising meniscus of a liquid through a

porous wicking structure.

In order to achieve high capillary pressure, the pore radius of the wicking structure needs

to be as small as possible. Generally, however, the smaller the pore radius is, the lower the

permeability and the higher the viscous friction becomes. An ideal wicking structure is, thus, one

which exhibits high capillary pressure as well as high permeability. Therefore, in order to capture

the effects of these two opposing parameters and to characterize and compare wicking structures,

capillary performance parameters that combine capillary pressure and permeability such as

𝐾𝐾/𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓 and 𝑃𝑃𝑐𝑐 ∙ 𝐾𝐾 are typically used. The calculation steps for these parameters are presented in

Chapter 4.

2.2 Types of wicking structures used in VCs

Wicks used in commercial VC are typically sintered powder or wire mesh that provide

uniform capillary pressure along all directions. Figure 2 shows an illustration of the cross-section

of a commercially available VC that utilizes sintered powder and wire mesh wicks for working

fluid transport. Other wick structures that can be used in vapor chambers include micro-pin arrays

and micro grooves.

Page 15: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

6

Table 1 lists the different types of wicks that can be used in thin HPs and VCs [8]. This

section provides a review of the typical wick structures considered for VC and recent research

done on the optimization and performance comparisons of such wicks.

Figure 2: Illustration of a cross-section of a commercially available vapor chamber showing the utilization of sintered powder and wire mesh wicks for working liquid transport.

Page 16: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

7

Table 1: Types of wicking structures typically used in vapor chambers, listing some examples and comparing capillary performance characteristics. [8]

Wick structure Examples Attributes

Sintered porous

structure

Sintered powder, sintered

mesh, and sintered fiber.

• High capillary pressure and low

permeability.

• Great in anti-gravity applications

Micro-grooves

Rectangular, v-shaped

(triangular), and trapezoidal.

Arrangements: Parallel,

radial.

• Low capillary pressure and high

permeability.

• Great in space applications.

Micro-pin

Round or square shape.

Arrangements: square,

rectangular, and hexagonal.

• High capillary pressure and moderate

permeability.

• Great in space applications.

Composite Sintered grooves or grooves

with sintered powder/mesh.

• Can achieve high capillary pressure and

high permeability.

• Higher cost and more complex

manufacturing process.

Micro-pin arrays can provide uniform capillary pressure as well as directional capillary

pressure depending on the arrangement. Three different pin array arrangements were studied by

Cho et al. [8]: (1) square, (2) hexagonal, and (3) rectangular, with different porosities ranging

from 0.45 to 0.8. The experimental results show that the rectangular arrangement provided the

highest permeability and comparable capillary pressure to the other arrangements, resulting in the

highest capillary performance. However, rectangular arrangement showed higher sensitivity of

capillary performance against gravity. The rectangular arrangement also showed directionality in

fluid flow (highest permeability along widest tracks). Hexagonal arrangement showed slightly

Page 17: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

8

higher capillary pressure than the other arrangement, similar permeability to the square

arrangement, and higher isotropy in fluid flow, making it the closest in similarity to sintered

powder wicks. Hale et al. studied the effect of micro-pin geometric ratios in square [9] and

rectangular [10] arrangement on the capillary pressure and permeability for heat pipe

applications. The rectangular arrangement provided higher capillary performance than the square

arrangement due to higher permeability with similar capillary pressure. Capillary pressure

showed strong dependency on porosity regardless of arrangement.

Micro grooves can generate capillary pressure with high permeability and are suitable for

directional flow. Despite their comparatively high capillary performance, micro-groove wicks are

better suited for heat pipes and flat heat pipes in space applications, e.g., satellite electronics

cooling, since gravity forces can significantly affect the fluid flow in micro-groove wicks, which

leads to poor performance in applications requiring fluid flow against gravity [1]. Deng et al. [11]

experimented with micro v-grooves (where the groove cross-section is triangular instead of

rectangular) and composite micro v-grooves with a sintered powder layer. They showed that the

composite wick provided higher capillary pressure due to the sintered powder layer, while the

non-composite wick exhibited significantly higher permeability, leading to much higher capillary

performance. Tang et al. [12] experimented with aluminum micro v-groove wicks and were able

to achieve high capillary performance. Further improvement by up to 200% of the capillary

performance was achieved through controlled corrosion of the wick. Zhang et al. [13] and Zeng et

al. [13] characterized the capillary performance of similar v-groove wicks with an addition of

reentrant structures on the v-groove channels, which increased the surface roughness of the top

surface of the grooves, leading to increased capillary pressure.

Page 18: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

9

2.3 The LPBF AM Process

In a LPBF AM process, illustrated in Figure 3, three-dimensional, layered components

are manufactured through the selective melting and consolidation of metal powder by laser

scanning over sequential layers. The process starts by spreading a thin layer of metal powder

using a recoater onto the build plate. A laser is then used to melt and consolidate the powder

according to a specific two-dimensional geometry. Another layer is then laid over the previous

layer and consolidated similarly. The process is repeated until a complete three-dimensional

geometry is made. After that, the build typically undergoes heat treatment (e.g., stress relieving,

aging, hot isostatic pressing, etc.), and fabricated parts are removed from the build plate using a

mechanical saw or wire-electrical-discharge machine (wire-EDM).

Figure 3: An illustration of cycle of operation of a laser powder bed fusion (LPBF) system.

Page 19: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

10

2.4 LPBF AM of wicks

Recently, AM has been considered for manufacturing two-phase thermal management

systems including heat pipes [4], loop heat pipes [5], [6], pulsating heat pipes [14], and the

manufacturing of different porous structures to be used as wicking structures [4]–[7]. Jafari and

Wits [15] recently published a review paper on the utilization of LPBF technology on thermal

management devices, including HPs and VCs. Research carried out in this area concludes that a

complete assembly of HPs can be manufactured through LPBF with good control over the shape

and porosity of the wicking structure and vapor channels. The AM technology used in all of the

relevant research was LPBF, while the materials considered include aluminum, titanium, and

stainless steel, but no research was found on the AM of copper HPs/VCs or wicks.

The first published work on the manufacturing of an AM heat pipe was conducted by

Ameli et al. [4] in 2013, where a cylindrical heat pipe with an octahedral lattice-structure wick,

shown in Figure 4, was designed, manufactured, and tested utilizing ammonia as the working

fluid. The researchers experimented with the manufacturability of wicks with different lattice

arrangements and sizes, and the manufacturability of the heat pipe assembly with the wick and

end caps in one step. Richard et al. [5] successfully manufactured and tested a primary wick,

shown in Figure 5, used in a loop heat pipe for electronics cooling. The researchers

experimentally demonstrated the capability of LPBF to produce wicks with controlled pore size.

However, they could not control the pore size (design = 6 µm, while built = 44 µm) of the full-

sized wick used in the loop heat pipe. This was thought to be due to the dependence of the

thermal cycle on the geometry and size of the produced parts in a LPBF process. An empirical

formula relating permeability to pore size was established for the characterized wicking

structures. Esarte et al. [6] also manufactured a primary wick, shown in Figure 6, used in a loop

heat pipe for the cooling of light-emitting diodes. Jafari et al. [7] designed, manufactured, and

Page 20: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

11

characterized an octahedral lattice-structure wick, shown in Figure 7, with two unit cell sizes. The

researchers assessed the reliability of various wick characterization techniques and reported the

capillary performance of their wicks.

Figure 4: Image of the fabricated aluminum cylindrical heat pipe with an octahedral lattice-structure wick [4].

Figure 5: Image of the manufactured stainless steel primary wick [5].

Page 21: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

12

Figure 6: Image of the internal structure of the manufactured stainless steel primary wicks [6]: (a) large (280–300 µm), (b) small (70–90 µm).

Page 22: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

13

Figure 7: Image of the fabricated a stainless steel octahedral lattice-structure wick [7]. (a) Unit cell, (b) a photo of the 3D-printed sample of 1×20×40mm3, (c) proposed CAD model, (d)

scanning electron microscope image and (e) optical microscopic image.

As discussed above, several recent studies have sought to validate the printability of

viable wicking structures in 316L stainless steel and AlSi12 aluminum material systems via

LPBF AM. The fabrication of pure-copper wicking structures for HPs/VCs applications via LPBF

AM has yet to be investigated. The objective of this work, consequently, is to validate the

printability of copper wicking structures and, if validated, compare the performance of fabricated

wicks to the other additively manufactured wicks and traditionally fabricated wicks.

Page 23: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Chapter 3

Preliminary experiment: Investigating the printability of sintered-powder and micro-pin wicks

3.1 Build preparation and sample geometry

An EOS 280 LPBF system, with specifications listed in Table 2, was used to fabricate the

samples of the preliminary experiment and the secondary experiment (presented in Chapter 4).

Feedstock copper powder was procured from Elementum 3D, with the specifications listed in

Table 3. All processing occurred in an Argon environment with a maximum oxygen

concentration less than 1000 ppm. A constant layer thickness of 40 μm was used together with a

flexible silicon recoater blade.

Table 2: Specifications of the LPBF instrument used.

PBF Instrument EOS 280

Laser system Yb doped fiber laser

wavelength ~1070 nm

Laser max. power 400 W

Laser max. scan speed 7000 mm/s

Laser spot size (diameter) 100 μm

Layer thickness 40 μm

Shielding gas used Argon

Build volume 250(9.8) x 250(9.8) x 300(11.8) mm3 (in.3)

Chamber atmosphere Argon

Recoater Flexible silicon

Page 24: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

15

Table 3: Specifications of the metal powder used.

Supplier Elementum 3D

Chemical composition 99.6% Cu

Apparent density 4.56 g/cm3

Particle size distribution [(mesh size) %] (-325) 82.8%, (+325) 15.4%, (+200) 1.7%

The selected sample geometry was a simple prismatic shape with the dimensions 6.35

mm × 25.4 mm × 25.4 mm. Figure 8 shows the samples successfully built on a copper build plate.

Two other samples were added to assess the printability of micro-pin structures using a Penn

State Applied Research Laboratory (ARL) proprietary design methodology, with which

significant reduction in file size and computational load is made possible. Sintered-powder

samples were produced via experimental laser processing parameters. Three levels (low, medium,

and high) of laser power, laser scanning speed, and hatch spacing, including proprietary nominal

parameters, were selected to produce 27 parameter combinations. Table 4 lists the experimental

processing parameter combinations used to fabricate the samples.

Page 25: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

16

Figure 8: The build plate of the preliminary experiment showing the sintered-powder samples and micro-pin samples.

Page 26: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

17

Table 4: Experimental processing parameters (i.e., Laser power, laser scanning speed, and hatch spacing) used to fabricate the samples of the preliminary experiment.

Sample

Parameters Power (W)

Scanning Speed (mm/s)

Hatch spacing (mm)

1 Nominal, proprietary parameters 2 370 320 0.24 3 370 320 0.32 4 370 400 0.16 5 370 400 0.24 6 370 400 0.32 7 370 480 0.16 8 370 480 0.24 9 370 480 0.32 10 277.5 320 0.16 11 277.5 320 0.24 12 277.5 320 0.32 13 277.5 400 0.16 14 277.5 400 0.24 15 277.5 400 0.32 16 277.5 480 0.16 17 277.5 480 0.24 18 277.5 480 0.32 19 185 320 0.16 20 185 320 0.24 21 185 320 0.32 22 185 400 0.16 23 185 400 0.24 24 185 400 0.32 25 185 480 0.16 26 185 480 0.24 27 185 480 0.32

Page 27: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

18

3.2 Sample preparation and characterization

After successfully fabricating the samples, excess powder was removed from the build

plate and samples were stress relieved at 650˚C for 2 hours and cooled in a nitrogen atmosphere.

After which, samples were removed from the build plate via wire-EDM.

Samples were cleaned and dried prior to testing, following established procedures

presented in [1], [16], [17] with minor adjustments. Samples were submerged in 2M hydrochloric

acid for 1 minute, followed by a deionized (DI) water rinse to remove carbon and oxides residue

from the wire-EDM process. Afterwards, samples were agitated in an ultrasonic acetone bath for

30 minutes to remove oils, loose powder, and further clean samples. Following the acetone bath,

samples were rinsed in an ultrasonic DI water bath for 10 minutes to remove the acetone.

Samples were finally dried in a furnace at 150˚C for 30 minutes, followed by air cooling for 5

minutes. Samples were subsequently tested for rate-of-rise, and porosity was measured.

3.2.1 Porosity measurement

Porosity measurement of the fabricated porous structures was done using the common

method of comparing the density of the material used to construct the wick to the apparent

density of the structure. For this technique to be accurate, the pores need to be completely

interconnected. By measuring the mass and apparent volume of the wick, the porosity is found

through:

𝜇𝜇 = 1 −𝑚𝑚𝑤𝑤

𝑉𝑉𝑤𝑤𝜌𝜌𝑠𝑠 (7)

where 𝜇𝜇 is the porosity, 𝑚𝑚𝑤𝑤 and 𝑉𝑉𝑤𝑤 are the mass and the total apparent volume of the wick,

respectively, and 𝜌𝜌𝑠𝑠 is the density of the wick’s material.

Page 28: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

19

3.2.2 Qualitative wickability assessment

In order to assess the wickability of the fabricated samples, a qualitative wickability test

setup, illustrated in Figure 9, was constructed. A scale was used to measure the weight of the

rising water in the fabricated sintered-powder and micro-pin structures. The test is done by

dipping the samples in a water reservoir while simultaneously measuring the mass of the water

that is wicked into the sample over time. Since all of the samples have the same shape and size,

an equitable qualitative comparison of mass of wicked water vs. time data can be done. The best

wicking sample would, therefore, be one that wicks the most amount of water the fastest.

Figure 9: Schematic of capillary rate-of-rise setup used to capture wicked water mass vs. time data.

Page 29: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

20

3.3 Results and discussion

The experiment validated the printability of copper sintered-powder and micro-structured

wicks. Several plots of water mass vs. time were generated for qualitative comparison. Notably,

Figure 10 presents a comparison of the capillary rate-of-rise plots for samples fabricated using

three different laser power levels: High (370 W), medium (277.5 W) , and low level (185 W),

showing increased wicking capability as porosity is increased via the reduction of laser power.

The maximum measured porosity of the produced sintered-powder structures was 0.26, which is

less than the typical porosity of conventional sintered powder wicks of 0.3-0.35 [1]. Measured

porosities of the samples are listed in Table 5. Cross-sectioning the most porous sintered structure

(sample 27), presented in Appendix A, revealed the formation of anisotropic micro-channels that

allowed better wickability in the vertical direction than in the horizontal direction, where the

vertical direction is the direction perpendicular to the build plate, while horizontal direction is the

direction parallel to the build plate. Capillary rate-of-rise data, presented in Figure 11 of vertical

and horizontal wicking directions confirmed the anisotropy in the porosity of the fabricated

sintered samples. The above-mentioned findings indicate that laser energy should be further

reduced in order to reduce melting to achieve higher porosity and a more homogeneous wick

structure.

Table 5: Measured sample porosity using the density method.

Sample porosity Sample porosity Sample porosity Sample porosity 1 0.13 8 0.13 15 0.21 22 0.19 2 0.14 9 0.16 16 0.16 23 0.21 3 0.15 10 0.16 17 0.19 24 0.25 4 0.12 11 0.18 18 0.22 25 0.20 5 0.13 12 0.21 19 0.19 26 0.22 6 0.15 13 0.16 20 0.21 27 0.26 7 0.12 14 0.18 21 0.23

Page 30: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

21

Figure 10: capillary rate-of-rise data: water mass vs. time of three samples processed with different laser power levels, where P=power level, S=scanning speed level, and H=hatch spacing

level.

Page 31: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

22

Figure 11: capillary rate-of-rise data: water mass vs. time of a sample in the vertical direction (perpendicular to build plate) and horizontal direction (parallel to build plate).

Page 32: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Chapter 4

Secondary experiment: Improving on sintered-powder and micro-structured wicks

4.1 Sample geometry and build preparation

Unlike the samples fabricated for the preliminary experiment, the geometry of the

samples designed for the secondary experiment was selected to closely resemble a cross-section

of a vapor chamber with thin wicking structures. The samples needed to be large enough to allow

for successful rate-of-rise and permeability testing, yet small enough to allow the inclusion of as

many samples as possible on one build plate. The selected overall dimensions of the samples

were 25.4 mm × 25.4 mm × 2 mm. Samples consisted of a 1 mm-thick porous structure printed

atop a 1mm-thick solid base.

Two strategies were pursued for creating the wicking samples. The first is mimicking

conventional sintered powder wicks by lowering laser energy input in order to sinter, rather than

melt, the powder layer. The sintered structures fabricated in the preliminary experiment indicated

that delamination was likely to occur at the transition from melting to sintering. In order to create

a better bond between the sintered structure and the sample’s base, micro-pins with a 1 mm

spacing were superimposed onto the sintered structure. The second strategy is fabricating pattered

micro-structures, namely, micro-pins and micro-grooves. Table 6 and Table 7 list the selected

micro-structure arrangements implemented and the selected pin and groove spacing. Figure 12

presents optical images of some of the fabricated micro-pin and micro-groove wick samples,

showing morphology and scale of the fabricated micro-structures.

The printability of micro-pin samples in several build orientations was investigated by

fabricating square-arrangement micro-pins: (1) horizontally, (2) vertically (samples P-S-400-V

and P-SX-400-V), (3) inclined at 45˚ with the pins facing upwards (sample P-S-400-IU), and (4)

Page 33: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

24

inclined at 45˚ with the pins facing downwards (sample P-SX-400-ID). In order to be able to print

pins that are facing downwards, an “X” pattern, connecting all the pins, was added at the tips of

the pins, creating a printable self-supporting scaffold structure.

Figure 12: Optical images of some of the fabricated micro-pin and micro-groove wick samples: (a) square arrangement "P-S-400-H", (b) groove "G-600-H", (c) rectangular arrangement "P-R-

350-600-H", (d) hexagonal arrangement "P-H-400-H"

Page 34: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

25

Table 6: The selected micro-structure arrangements implemented in the wick samples and the selected pin and groove spacing.

Sample Micro-structure

arrangement unit size (μm)

Build

orientation Illustration

P-S-350-H

Square (S)

l=350 Horizontal (H)

P-S-400-H l=400 Horizontal

P-S-450-H l=450 Horizontal

P-S-400-V l=400 Vertical (V)

P-S-400-IU l=400 Inclined 45˚ up

(IU)

P-SX-400-V

Square with X on

top (SX)

l=400 Vertical

P-SX-400-ID l=400 Inclined 45˚

down (ID)

P-H-350-H

Hexagonal (H)

l=350 Horizontal

P-H-400-H l=400 Horizontal

P-H-450-H l=450 Horizontal

Page 35: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

26

Table 7: (Cont.) The selected micro-structure arrangements implemented in the wick samples and the selected pin and groove spacing.

Sample Micro-structure

arrangement unit size (μm)

Build

orientation Illustration

P-R-350-400-H

Rectangular (R)

l=350; s=400 Horizontal

P-R-350-600-H l=350; s=600 Horizontal

P-R-400-600-H l=400; s=600 Horizontal

P-R-450-600-H l=450; s=600 Horizontal

P-R-350-800-H l=350; s=800 Horizontal

P-R-400-800-H l=400; s=800 Horizontal

P-R-450-800-H l=450; s=800 Horizontal

G-350-H

Grooves (G)

l=350 Horizontal

G-400-H l=400 Horizontal

G-600-H l=600 Horizontal

G-800-H l=800 Horizontal

Page 36: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

27

Sintered-powder samples with experimental laser processing parameters were fabricated

using five combinations of laser power and scanning speed, presented in Table 8. Sintered regions

were built atop a dense base that was built using proprietary parameters. Linear energy density

(LED = power/speed) was used as a guide to select parameter levels. With the laser power

drastically reduced and made constant at 100 W, the laser scan speed was varied to accomplish

LED reductions by 2, 4, 6, and 8 times the nominal value. These samples were built in three build

directions: (1) horizontal (e.g., sample S-100-84-H), (2) vertical (e.g., sample S-100-84-V), and

(3) inclined at 45˚ degrees (e.g., sample S-100-84-I). After fabrication, samples were post

processed and prepared following the sample preparation procedure detailed in Chapter 3.

Table 8: Processing parameters for the sintered-powder wick samples

Sample

Processing Parameters LED

(J/mm)

LED

reduction

multiplier Power

(W)

Scanning Speed

(mm/s)

Hatch spacing

(mm)

Build

orientation

S-100-84-H 100 84 0.16 Horizontal (H) 1.190 1

S-100-84-V 100 84 0.16 Vertical (V) 1.190 1

S-100-84-I 100 84 0.16 Inclined 45˚ (I) 1.190 1

S-100-168-H 100 168 0.16 Horizontal 0.595 2

S-100-168-V 100 168 0.16 Vertical 0.595 2

S-100-168-I 100 168 0.16 Inclined 45˚ 0.595 2

S-100-336-H 100 336 0.16 Horizontal 0.298 4

S-100-336-V 100 336 0.16 Vertical 0.298 4

S-100-336-I 100 336 0.16 Inclined 45˚ 0.298 4

S-100-504-H 100 504 0.16 Horizontal 0.198 6

S-100-504-V 100 504 0.16 Vertical 0.198 6

S-100-504-I 100 504 0.16 Inclined 45˚ 0.198 6

S-100-672-H 100 672 0.16 Horizontal 0.149 8

S-100-672-V 100 672 0.16 Vertical 0.149 8

S-100-672-I 100 672 0.16 Inclined 45˚ 0.149 8

Page 37: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

28

4.2 Wick characterization and data analysis

Wick performance characterization utilized measurement of porosity, permeability, and

rate-of-rise. Following these tests, data analysis was conducted to determine capillary

performance.

4.2.1 Porosity measurement

Porosity was measured using the same density method detailed in Chapter 3. Porosity

measurements obtained from the density method were juxtaposed with the Archimedes method,

in which the wick is saturated with a wetting liquid. By measuring the mass before and after

infiltration, the porosity is found through:

𝜇𝜇 =1

1 + 𝑚𝑚𝑤𝑤𝜌𝜌𝑙𝑙𝑚𝑚𝑙𝑙𝜌𝜌𝑠𝑠

(8)

where 𝑚𝑚𝑙𝑙 and 𝜌𝜌𝑙𝑙 are the mass and density of the infiltrating liquid, respectively.

4.2.2 Permeability measurement

Permeability was measured experimentally by using a form of Darcy’s law describing the

pressure drop for steady-state laminar fluid flow through porous media [1] through:

∆𝑃𝑃 =

𝜇𝜇𝜇𝜇�̇�𝑚𝜌𝜌𝐾𝐾𝜌𝜌

(9)

where 𝜇𝜇 is the viscosity, 𝜌𝜌 is the density of the flowing liquid, 𝐾𝐾 is the permeability, 𝜇𝜇 is the

length of the wick along the fluid flow, 𝜌𝜌 is the cross-sectional area of the wick perpendicular to

fluid flow, and �̇�𝑚 is the fluid mass flowrate. While this so called forced-flow method, is widely

used [4], [6], [7], [11], [16], [18]–[20] for measuring permeability, one caveat is that high fluid

Page 38: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

29

flow velocities lead to failure of Darcy’s law and result in unreliable permeability measurements.

Transition velocities found in similar studies varied from ≈ 0.07 to 0.1 m/s [7], [21]. Flow

velocities lower than the transition velocity are suitable for permeability measurement using

Darcy’s law.

We note that for conventionally sintered-powder wicks and wire mesh wicks [17],

relations such as the Kozeny-Carman equation, which relates the pressure drop across a porous

structure to porosity and pore size, are often used. Other models are also well established to

estimate permeability of wicks, including micro-pin arrays [8]–[10], [22], [23] and micro grooves

[24], [25]. Despite the availability of such models, they were not pursued in the current work

since applying them on additively manufactured wicks can prove to be challenging due to the

high surface roughness, inherent anisotropy of AM structures, and build defects, which

collectively can render such models unreliable.

In this work, a test setup, schematically shown in Figure 13, was utilized to calculate

permeability. The actual test setup is presented in Appendix D. A sample is placed in the flow

housing with thin silicone rubber strips placed around the sample to ensure a water-tight fit and

eliminate any flow bypassing the sample. Before pressure and flow rate measurements are taken,

the sample is flushed with water for 5 minutes to remove air bubbles and ensure accurate

measurements. A scale was occasionally used to validate the flowrate measured using the

flowmeter.

Page 39: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

30

Figure 13: A schematic of the forced-flow permeability test setup.

4.2.3 Capillary rate-of-rise testing

The capillary rate-of-rise test setup discussed in Chapter 3 was upgraded by utilizing an

infrared (IR) camera to visualize and directly capture the rising water meniscus following the

method introduced by Tang et al. [26]. In this method, the IR camera is able to differentiate

between dry and wet regions of the wick due to the difference in emissivity between the surface

of the copper wick and the wetting liquid. The test was conducted with elevated humidity in the

range of 70-95% in order to reduce unwanted passive evaporation of the water from the reservoir

and the wick sample. Figure 14 presents a schematic of the rate-of-rise setup built and used for

the rate-of-rise test. The actual test setup is presented in Appendix D.

Page 40: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

31

Figure 14: A schematic of the rate-of-rise test setup.

DI water, with the relevant room-temperature properties shown in Table 9, was used in

rate-of-rise and permeability tests. Acetone was used in the rate-of-rise test for one sample due to

poor wettability of DI water.

Table 9: Room-temperature properties of the working fluid.

Property Deionized water Acetone

Viscosity 0.001002 Pa·s 0.000306 Pa·s

Density 0.000998 g/mm3 0.000792 g/mm3

Surface tension 72.75 g/s2 23.7 g/s2

Page 41: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

32

4.2.4 Data reduction

After liquid height is measured and plotted against time from the IR camera videos of the

rate-of-rise test, capillary performance parameters, i.e., 𝐾𝐾/𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓 and 𝑃𝑃𝑐𝑐 ∙ 𝐾𝐾, can be found. Figure

15 presents snapshots that exemplify the rate-of-rise videos obtained, showing the capillary rise

of the wetting liquid. In order to evaluate the capillary performance parameters, equation (6) can

be rearranged to yield:

𝑑𝑑ℎ𝑑𝑑𝑑𝑑

=2𝜎𝜎𝜇𝜇𝜇𝜇

𝐾𝐾𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓

1ℎ−𝜌𝜌𝜌𝜌𝐾𝐾𝜇𝜇𝜇𝜇

(10)

By replacing the rate of rise (velocity),𝑑𝑑ℎ/𝑑𝑑𝑑𝑑, with 𝑦𝑦 and the inverse of liquid height, 1/ℎ, with

𝑥𝑥, equation (10) becomes a linear equation:

𝑦𝑦 =

2𝜎𝜎𝜇𝜇𝜇𝜇

𝐾𝐾𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓

𝑥𝑥 −𝜌𝜌𝜌𝜌𝐾𝐾𝜇𝜇𝜇𝜇

(11)

with the slope 2𝜎𝜎𝜇𝜇𝜇𝜇

𝐾𝐾𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒

, containing the capillary performance 𝐾𝐾/𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓, which is determined after

substituting for the wetting liquid properties and porosity of the wick.

An explicit solution to the differential equation (10) can be found by fitting the height

and time data into a natural log curve of the form: ℎ = 𝑎𝑎 ln(𝑑𝑑) + 𝑏𝑏. From this, the inverse height,

𝑥𝑥 = 1/ℎ, and rate of rise, 𝑦𝑦 = 𝑑𝑑ℎ/𝑑𝑑𝑑𝑑, are calculated for the initial capillary rise duration. Finally,

the slope of a linear fit to equation (11) is determined and the capillary performance 𝐾𝐾/𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓 is

calculated. Similarly, the slope 2𝜎𝜎𝜇𝜇𝜇𝜇

𝐾𝐾𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒

can be rewritten as 𝑃𝑃𝑐𝑐 ∙𝐾𝐾𝜇𝜇𝜇𝜇

. From that, 𝑃𝑃𝑐𝑐 ∙ 𝐾𝐾 is found.

Finally, after permeability 𝐾𝐾 is measured, 𝑟𝑟𝑒𝑒𝑓𝑓𝑓𝑓, and subsequently, the capillary pressure 𝑃𝑃𝑐𝑐 can be

found.

Page 42: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

33

Figure 15: Snapshots of the rate-of-rise IR video at different time stamps. Wicking sample: P-R-450-600-H. Working fluid: DI water.

Page 43: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

4.3 Results and discussion

Liquid height was measured and plotted against time from the IR camera videos of the

rate-of-rise test. Afterwards, the data was fitted to a natural log curve with a coefficient of

determination (R2) of 0.98-0.99. Porosity, permeability, K/reff, and Pc·K, of successfully tested

samples are provided with comparison to capillary performance of other AM wicks in Table 10

and traditionally sintered-powder wicks and electroplated micro-pin wicks in Table 11.

In some cases, samples could not be tested due to overbuilding; that is, the samples

exceeded the maximum height of the permeability testing chamber. This was a byproduct of the

use of a flexible recoater blade. While a flexible blade was found to increase the chances for a

successful build, the blade is also easily deflected and damaged, causing nonuniformity in the

thickness of the powder layers which subsequently caused powder buildup and greater than

expected thickness. Several micro-pin samples were damaged by the wire-EDM process and

showed poor wettability. Some sintered-powder wick samples (namely samples processed under

higher LED) showed poor wettability and were, consequently, not tested for rate-of-rise.

Page 44: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

35

Table 10: Porosity, permeability, K/reff, and Pc·K, of successfully tested samples, with comparison to capillary performance of other AM wicks

* Acetone was used as wetting liquid

Ref. Matl. Mfg. method/

Wick type ε

reff K Pc Pc·K K/reff

× 10-6

m

× 10-11

m2

× 103

Pa

× 10-8

N

× 10-6

m

Current

study Cu

S-100-672-H 0.37 208 4.453 0.701 3.121 0.215

S-100-672-V 0.34 - - - 3.596 0.247

S-100-504-I 0.32 - - - 2.700 0.186

S-100-672-I 0.31 163 4.002 0.892 3.571 0.245

P-S-400-H 0.74 - - - 20.251 1.392

P-S-400-V 0.62 177 21.21 0.823 17.462 1.200

P-S-400-IU 0.75 274 1.941 0.531 10.304 0.708

P-H-350-H* 0.55 - - - 4.754 1.003

G-600-H 0.63 - - - 11.902 0.818

G-800-H 0.78 - - - 7.716 0.530

P-R-450-600-H 0.84 697 124.4 0.209 25.972 1.785

P-R-450-800-H 0.85 - - - 15.498 1.065

[7] 316L SS

LPBF/ octahedral

lattice (500 µm

unit cell)

0.46 104 13.05 - - 1.04

[4]

AlSi12

LPBF/ octahedral

lattice (300 µm

unit cell)

0.17 60 0.047 - - 0.008

AlSi12

LPBF/ octahedral

lattice (500 µm

unit cell)

0.58 140 28.6 - - 2.04

[6] 316L SS LPBF/ scaffold

structure 0.17 80 0.125 - - 0.016

[5]

316L SS LPBF/ adjusting

laser parameters 0.47 94.1 28.4 - - 3.02

316L SS LPBF/ adjusting

laser parameters 0.093 6.3 0.037 11 0.407 0.09

Page 45: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

36

Table 11: (Cont.) Porosity, permeability, K/reff, and Pc·K, of sintered-powder and micro-pin wicks fabricated through sintering and electroplating, respectively.

The micro-pin and micro-groove wicks exhibited larger porosity and better capillary

performance in comparison to the sintered-powder wicks. This is thought to be due to the

presence of larger flow channels in micro-pin and grooved wicks that result in larger permeability

to liquid flow. Another possible reason is thought to be high laser power and high linear energy

density levels used to fabricate the sintered structures, resulting in unwanted excess melting of the

powder. The micro-pin wick with rectangular arrangement and 450 µm - 600 µm spacing showed

the best capillary performance and permeability compared to other pin arrangements. This is in

line with results from Cho et al. [8] where pillar structures with rectangular arrangement were

found to perform better than pillar structures with square and hexagonal arrangements. Micro-

pins in a rectangular arrangement exhibit higher permeability, compared to other pin

Ref. Matl. Mfg. method/

Wick type ε

reff K Pc Pc·K K/reff

X 10-6

m

X 10-11

m2

X 103

Pa

X 10-8

N

X 10-6

m

[8]

Cu

Electroplating/

micro-pin, square

arrangement

0.8 222 10 - - 0.4

Cu

Electroplating/

hexagonal

arrangement

0.8 187 11 - - 0.51

Cu

Electroplating/

rectangular

arrangement

0.8 159 18 - - 1.15

[11] Cu Sintering/

Sintered powder 0.57 - 0.671 4.1 2.751 0.603

[19] Cu Sintering/

Sintered powder 0.28 0.24 11.5 2.76 0.192

[16] Cu Sintering/

Sintered powder 0.45 15-Dec 0.721 8.08 5.83 0.405

Page 46: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

37

arrangements, due to the presence of larger channels aligned along the direction of fluid flow,

while generating comparable capillary pressure due to the presence of small pin-to-pin spacing,

thus, resulting in a higher overall capillary performance.

The sintered-powder porous samples of the secondary experiment exhibited capillary

performance K/reff, ranging from 0.186 to 0.247, similar to traditionally sintered-powder wicks,

namely, K/reff = 0.192 µm [19], K/reff = 0.405 µm [16], K/reff = 0.603 µm [11]. A positive

correlation seems to exist between the porosity of additively manufactured as well as traditionally

manufactured sintered-powder wicks and their capillary performance, as shown in Figure 16.

Figure 16: Plot of the capillary performance parameter K/reff vs. porosity of the sintered-powder wicks fabricated through laser powder bed fusion additive manufacturing (current study) as well

as some traditionally sintered wicks.

The achieved porosities of the wick samples ranged from 0.31 to 0.85. By comparing the

porosity measurements of the two porosity measurement methods, the interconnectedness of the

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

K/r e

ff (µ

m)

Porosity

Current study

Singh et al.

Semenic et al.

Deng et al.

Page 47: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

38

pores in a wicking structure can be inferred. For the sintered-powder samples, the difference

between porosity measurements performed using density and Archimedes methods increases with

LED, as presented in Figure 17. Additionally, micro-structured porous samples showed a

negative correlation between the discrepancy in porosity measurement methods and the porosity

of the wicking structure, as presented in Figure 18. Therefore, reducing LED (i.e., reducing laser

power or increasing laser scanning speed) when fabricating sintered-powder wicks via LPBF AM

will result in more porosity with more pore interconnectedness, leading to better capillary

performance. Adding to that, selecting arrangements of micro-structured wicks exhibiting

porosities ≥ 0.5 will result in more interconnected porosity and are, hence, more favorable.

Figure 17: Plot of the difference between porosity measurements performed using density and Archimedes methods vs. linear energy density of laser process parameters used to fabricate the

sintered-powder samples.

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

% d

iffer

ence

LED (J/mm)

Page 48: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

39

Figure 18: Plot of the difference between porosity measurements performed using density and Archimedes methods vs. porosity of the fabricated micro-structured wicking samples.

Build direction (horizontal, vertical, or inclined at 45˚) had varying effects on the

porosity and capillary performance of the wicks. Sintered samples showed slightly better

performance when printed inclined than otherwise, while square-arrangement micro-pins showed

better performance when printed horizontally than otherwise. This can be due to the difference in

the thermal cycle of the different build orientations during fabrication. The capillary performance

K/reff for almost all samples, nonetheless, were comparable to the maximum values reported in

previously published work on AM wicks, e.g. K/reff = 1.04 µm [7], K/reff = 2.04 µm [4], and K/reff

= 3.02 µm [5].

-5

0

5

10

15

20

25

0.30 0.40 0.50 0.60 0.70 0.80 0.90

% d

iffer

ence

Porosity (Archimedes method)

Square arrangementMicro-grooveHexagonal arrangementRectangular arrangement

Page 49: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Chapter 5

Conclusions

This work has demonstrated the feasibility of additively manufacturing copper wicking

structures via two sets of experiments and analyses. A preliminary experiment was designed to

investigate the printability of sintered powder and micro-structured copper wicks via LPBF AM.

Sintered powder samples were produced using experimental laser exposure parameters that

included three levels (low, medium, and high) of laser power, laser scanning speed, and hatch

spacing. The wickability of the produced samples were qualitatively validated through capillary

rate-of-rise testing. The maximum achieved porosity of the sintered-powder wicks was measured

to be 0.26, which is less than the typical porosity of sintered copper powder wicks of 0.3-0.35 [1].

Qualitative wickability testing and sample cross-sectioning revealed anisotropy in the porosity of

the wicks, which lead to unwanted anisotropy in the wickability of these samples. Low porosity

and anisotropy of porosity indicated that further reduction in laser energy was required in order to

reduce melting to achieve higher porosity and a more homogeneous wick structure. The

fabricated sintered-powder wicks also indicated that delamination was likely to occur at the

transition from melting to sintering.

Taking into account the results and observations of the preliminary experiment, a

secondary experiment was designed to further improve on the processing parameters of sintered-

powder wicks and investigate the printability of several arrangements of micro-structured wicks.

The achieved porosities of successfully tested sintered-powder structures ranged from 0.31 to

0.37, while the measured porosity for micro-pin and micro-groove wicks ranged from 0.55 to

0.85. Capillary performance parameters K/reff and Pc·K were calculated through the capillary rate-

of-rise testing method and permeability was measured through the forced-flow permeability

measurement test method. Calculated capillary performance K/reff ranged from 0.186 µm to 1.79

Page 50: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

41

µm. The micro-pin wick with rectangular arrangement and 450 µm - 600 µm pin spacing showed

the best capillary performance and permeability compared to other pin arrangements. Capillary

performance for almost all samples, nonetheless, were comparable to the maximum performance

reported in previously published work on AM wicks, e.g. K/reff = 1.04 µm [7], K/reff = 2.04 µm

[4], and K/reff = 3.02 µm [5]. Sintered-powder and micro-pin wicks were printed vertically and

inclined at 45˚ without additional support structures, indicating the possibility of fabricating

VCs/HPs assemblies in various orientations and inclination angles without requiring additional

support structures. Sintered samples showed slightly better performance when printed inclined

than otherwise, while square-arrangement micro-pins showed better performance when printed

horizontally than otherwise. This is thought to be due to the difference in the thermal cycle of

these build orientations during fabrication.

Novel sintered-powder, micro-pins, and micro-groove copper wicking structures were

successfully fabricated via LPBF, indicating the feasibility of additively manufactured copper

HPs and VCs with integrated wicking structures. Ongoing work sees to further optimize

processing parameters. Wicks composed of sintered powder and micro pins are of active interest.

In particular, the determination of ideal parameters and ranges, as functions of wick orientation

and structure is an appropriate area of future research, as well as the investigation of other self-

supporting micro-structured wick designs.

Page 51: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

References

[1] D. Reay, P. A. Kew, and R. J. McGlen, in Heat Pipes: Theory, Design, and Applications, Sixth., Elsevier, 2014, pp. 1–91.

[2] S. Lips, V. Sartre, F. Lefevre, S. Khandekar, and J. Bonjour, “Overview of heat pipe studies during the period 2010-2015,” Interfacial Phenom. Heat Transf., vol. 4, no. 1, pp. 33–53, 2016, doi: 10.1615/InterfacPhenomHeatTransfer.2016016345.

[3] M. Elnaggar and E. Edwan, in Heat pipes for computer cooling applications, Intech, 2016, pp. 52–77.

[4] M. Ameli et al., “A novel method for manufacturing sintered aluminium heat pipes (SAHP),” Appl. Therm. Eng., vol. 52, no. 2, pp. 498–504, 2013, doi: 10.1016/j.applthermaleng.2012.12.011.

[5] B. Richard, D. Pellicone, and B. Anderson, “Loop Heat Pipe Wick Fabrication via Additive Manufacturing,” presented at the 47th International Conference on Environmental Systems, 2017, pp. 1–10.

[6] J. Esarte, J. M. Blanco, A. Bernardini, and J. T. San-José, “Optimizing the design of a two-phase cooling system loop heat pipe: Wick manufacturing with the 3D selective laser melting printing technique and prototype testing,” Appl. Therm. Eng., vol. 111, pp. 407–419, 2017, doi: 10.1016/j.applthermaleng.2016.09.123.

[7] D. Jafari, W. W. Wits, and B. J. Geurts, “Metal 3D-printed wick structures for heat pipe application: Capillary performance analysis,” Appl. Therm. Eng., vol. 143, no. July, pp. 403–414, 2018, doi: 10.1016/j.applthermaleng.2018.07.111.

[8] S. Cho, R. Tummala, and Y. Joshi, “Capillary Performance of Micropillar Arrays in Different Arrangements,” Nanoscale Microscale Thermophys. Eng., vol. 22, no. 2, pp. 97–113, 2018, doi: 10.1080/15567265.2018.1431749.

[9] R. S. Hale, R. T. Bonnecaze, and C. H. Hidrovo, “Optimization of capillary flow through square micropillar arrays,” Int. J. Multiph. Flow, vol. 58, pp. 39–51, 2014, doi: 10.1016/j.ijmultiphaseflow.2013.08.003.

[10] R. S. Hale, R. Ranjan, and C. H. Hidrovo, “Capillary flow through rectangular micropillar arrays,” Int. J. Heat Mass Transf., vol. 75, pp. 710–717, 2014, doi: 10.1016/j.ijheatmasstransfer.2014.04.016.

[11] D. Deng, Y. Tang, G. Huang, L. Lu, and D. Yuan, “Characterization of capillary performance of composite wicks for two-phase heat transfer devices,” Int. J. Heat Mass Transf., vol. 56, no. 1–2, pp. 283–293, 2013, doi: 10.1016/j.ijheatmasstransfer.2012.09.002.

[12] H. Tang, Y. Tang, W. Yuan, R. Peng, L. Lu, and Z. Wan, “Fabrication and capillary characterization of axially micro-grooved wicks for aluminium flat-plate heat pipes,” Appl. Therm. Eng., vol. 129, pp. 907–915, 2018.

[13] J. Zeng, L. Lin, Y. Tang, Y. Sun, and W. Yuan, “Fabrication and capillary characterization of micro-grooved wicks with reentrant cavity array,” Int. J. Heat Mass Transf., vol. 104, no. January, pp. 918–929, 2017, doi: 10.1016/j.ijheatmasstransfer.2016.09.007.

[14] S. M. Thompson, Z. S. Aspin, N. Shamsaei, A. Elwany, and L. Bian, “Additive manufacturing of heat exchangers: A case study on a multi-layered Ti-6Al-4V

Page 52: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

43

oscillating heat pipe,” Addit. Manuf., vol. 8, pp. 163–174, 2015, doi: 10.1016/j.addma.2015.09.003.

[15] D. Jafari and W. W. Wits, “The utilization of selective laser melting technology on heat transfer devices for thermal energy conversion applications: A review,” Renew. Sustain. Energy Rev., vol. 91, no. March, pp. 420–442, 2018, doi: 10.1016/j.rser.2018.03.109.

[16] R. Singh, A. Akbarzadeh, and M. Mochizuki, “Effect of Wick Characteristics on the Thermal Performance of the Miniature Loop Heat Pipe,” J. Heat Transf., vol. 131, no. 8, p. 082601, 2009, doi: 10.1115/1.3109994.

[17] Y. Tang, H. Tang, J. Li, S. Zhang, B. Zhuang, and Y. Sun, “Experimental investigation of capillary force in a novel sintered coppermesh wick for ultra-thin heat pipes,” Appl. Therm. Eng., vol. 115, pp. 1020–1030, 2017.

[18] J. Choi, W. Sano, W. Zhang, Y. Yuan, Y. Lee, and D. A. Borca-Tasciuc, “Experimental investigation on sintered porous wicks for miniature loop heat pipe applications,” Exp. Therm. Fluid Sci., vol. 51, pp. 271–278, 2013.

[19] T. Semenic, Y.-Y. Lin, and I. Catton, “Thermophysical Properties of Biporous Heat Pipe Evaporators,” J. Heat Transf., vol. 130, no. 2, p. 022602, 2008, doi: 10.1115/1.2790020.

[20] F. A. D. Espinosa, T. B. Peters, and J. G. Brisson, “Effect of facrication parameters on the thermophysical properties of sinters wicks for heat pipe appliction,” Int. J. Heat Mass Transf., vol. 55, pp. 7471–7486, 2012.

[21] K. Boomsma and D. Poulikakos, “The Effects of Compression and Pore Size Variations on the Liquid Flow Characteristics in Metal Foams,” J. Fluids Eng., vol. 124, no. 1, p. 263, 2002, doi: 10.1115/1.1429637.

[22] K. Yazdchi, S. Srivastava, and S. Luding, “Microstructural effects on the permeability of periodic fibrous porous media,” Int. J. Multiph. Flow, vol. 37, no. 8, pp. 956–966, 2011, doi: 10.1016/j.ijmultiphaseflow.2011.05.003.

[23] C. Byon and S. J. Kim, “Study on the capillary performance of micro-post wicks with non-homogeneous configurations,” Int. J. Heat Mass Transf., vol. 68, pp. 415–421, 2014, doi: 10.1016/j.ijheatmasstransfer.2013.09.064.

[24] S.-W. Chen, J.-C. Hsieh, C.-T. Chou, H.-H. Lin, S.-C. Shen, and M.-J. Tsai, “Experimental investigation and visualization on capillary and boiling limits of micro-grooves made by different processes,” Sens. Actuators A, vol. 139, pp. 78–87.

[25] L. Xibing, W. Shigang, G. Jianhua, and L. Dongsheng, “A mathematical modeling method on micro heat pipe with a trapezium-grooved wick structure Li Xibing,” Appl. Mech. Mater., pp. 1686–1694, 2010, doi: 10.4028/www.scientific.net/AMM.29-32.1686.

[26] Y. Tang, D. Deng, L. Lu, M. Pan, and Q. Wang, “Experimental investigation on capillary force of composite wick structure by IR thermal imaging camera,” Exp. Therm. Fluid Sci., vol. 34, no. 2, pp. 190–196, 2010, doi: 10.1016/j.expthermflusci.2009.10.016.

Page 53: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

44

Appendix A

Preliminary experiment sample images

1. Build plate:

Page 54: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

45

2. Sample 27 top surface close up:

3. Micro-pin sample close up:

Page 55: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

46

4. Horizontal cross section of the corner of sample 27 showing anisotropic micro-

channels aligned along the Z-axis:

Page 56: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Appendix B

Secondary experiment sample images

1. Build plate:

Page 57: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

48

2. Sample S-100-672-H close up:

3. Sample G-600-H close up:

Page 58: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

49

4. Sample P-R-450-600-H close up:

5. Samples S-100-504-I and S-100-504-V:

Page 59: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Appendix C

MATLAB script for rate-of-rise analysis

% Loading video file and measuring pixel width and height and frame rate raw = VideoReader('B--45 x 6 RS-000001-282_17_03_45_017.wmv'); height = raw.Height; width = raw.Width; reset_time = raw.CurrentTime; fps = raw.FrameRate; duration = raw.Duration; numFrames = 0; while hasFrame(raw) readFrame(raw); numFrames = numFrames + 1; end raw.CurrentTime = reset_time; %% reading individual video frames i = 1; while hasFrame(raw) s(i).frames = readFrame(raw); i = i+1; end %% selecting cropping dimensions to fit the sample in the video xStart = 189; yStart = 298; cropWidth = 145; cropHeight = 149; %% Showing imbedded time stamp of the first frame frame = 1; startFrame = 2; % starting frame for height calculations test = imcrop(s(frame).frames, [xStart, yStart, cropWidth, cropHeight]); imshowpair(s(frame).frames, test, 'montage'); %% showing time stamp of last frame frame = numFrames; test = imcrop(s(frame).frames, [xStart, yStart, cropWidth, cropHeight]); imshowpair(s(frame).frames, test, 'montage'); %% Calculating actual time per frame (SPF) % Time stamp of first frame

Page 60: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

51

h1 = 17; m1 = 3; s1 = 50.018; time1 = h1*3600+m1*60+s1; % Time stamp of last frame h2 = 17; m2 = 4; s2 = 28.115420; time2 = h2*3600+m2*60+s2; % Optional frame skipping for slow wicking samples frameSkip = 1; % Calculating actual duration time = time2-time1; SPF = time/numFrames; t = [0:SPF*frameSkip:time-SPF*frameSkip]; %% cropping all frames after confirming cropping dimensions raw.CurrentTime = reset_time; k = 1; while hasFrame(raw) s(k).crop = imcrop(readFrame(raw), [xStart, yStart, cropWidth, cropHeight]); k = k+1; end %% Previewing the first 20 frames k = 1; while k<10*frameSkip imshow(s(k).crop); k = k+frameSkip; pause(0.001); end %% viewing relevant frames and enabling image tools for pixel measurements

Page 61: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

52

k = 1; while k<10*frameSkip imtool(s(k).crop); k = k+frameSkip; %pause; end %% Manually counting and inputting pixel heights for each frame PixelHeight = [0 35 61 74 84 97 108 115 121 122 126 128]; size_PixelHeight = size(PixelHeight); %Calculating length (mm) per pixel (MMPP) MMPP = 25.4/cropHeight; height = PixelHeight*MMPP; %% Plotting rate-of-rise height vs time plot(t(1:size_PixelHeight(2)), height, '.'); title('Height (mm) vs. time (seconds)'); xlabel('time (seconds)'); ylabel('height (mm)'); %% limiting range to appropriate time window by defining time boundaries x_values = t; limit_start = 0.09; limit_end = 1; range_limit = find((x_values >= limit_start) & (x_values <= limit_end)); x_limited = x_values(range_limit); h_limited = height(range_limit); %% fitting data to a natural log curve h_fitted = polyfit(log(x_limited),h_limited,1); h_fitted2 = h_fitted(1).*log(x_limited) + h_fitted(2); plot(x_limited,h_fitted2,x_limited,h_limited, '.'); dh_fitted = diff(h_fitted2)/SPF; dh_instances = size(dh_fitted); %% Calculating R-squared (coefficient of determination) mdl = fitlm(h_fitted2, h_limited); R_square = mdl.Rsquared.Ordinary %% Generating several plots of height vs time and velocity vs time to ensure proper analysis figure(3)

Page 62: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

53

plot(x_limited, h_limited,'.'); title(sprintf('height vs. time limited %.1f to %d seconds', limit_start, limit_end)) figure(2) plot(x_limited(1:dh_instances(2)), dh_fitted, '.'); title(sprintf('rise velocity (dh/dt) vs. time limited %.1f to %d seconds', limit_start, limit_end)) y = dh_fitted; x = 1./h_fitted2; figure(1) plot(x(1:dh_instances(2)),y, '.') title(sprintf('velocity (dh/dt) vs. reciprocal of height (1/h) limited between %.1f to %d seconds with linear fit', limit_start, limit_end)) hold on slope = polyfit(x(1:dh_instances(2)), y, 1); plot(x, x*slope(1)+slope(2)) hold off %% Calculating capillary parameters from fitted data % Defining constants and liquid properties g = 9.81*1000; density = 0.998e-3; viscosity = 10.02e-4; s_tension = 72.75e-3; s_tension = s_tension*1000; % Reading porosity, permeability, and area values stored in excel sheets filename_porosity = 'Build 2_Measured porosity.xlsx'; filename_permeability = 'Build 2_Measured Permeability.xlsx'; porosity = xlsread (filename_porosity, 'Results', 'D36'); area = xlsread (filename_porosity, 'Calculation sheet', 'AG38')./xlsread (filename_porosity, 'Calculation sheet', 'AE38'); % Calculating Capillary performance parameters P_cap_dot_K = slope(1)*viscosity*porosity/1000000 K_r_eff = P_cap_dot_K/2/(s_tension/1000)*1000000 K = xlsread(filename_permeability,'Results','B34'); P_cap = P_cap_dot_K/K r_eff = 2*s_tension/P_cap

Page 63: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

Appendix D

Experimental setup images

1. Permeability test setup, detailed in Chapter 4, showing air pressure source, water tank,

flowmeter, pressure gauges, and sample holder:

2. Permeability sample holder fabricated from 6061 aluminum and acrylic, showing sealing

O-ring, flow inlet and outlet, and pressure gauge ports:

Page 64: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

55

3. Permeability sample holder showing the placement of the samples:

4. Rate-of-rise test setup detailed in Chapter 4

Page 65: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

56

Appendix E

Permeability measurements

1. Permeability measurements and relative standard error:

Sample K Relative Standard Error

(%) × 10-11 m2

S-100-672-H 4.453 5.2 S-100-672-I 4.002 12.9 P-S-400-V 21.21 3.3 P-S-400-IU 1.941 8.7

P-R-450-600-H 124.4 7.5

2. Sample S-100-672-H:

Page 66: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

57

Sample S-100-672-I:

Page 67: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

58

3. Sample P-S-400-V:

Page 68: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

59

4. Sample P-S-400-IU:

Page 69: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

60

5. Sample P-R-450-600-H:

Page 70: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

61

Appendix F

Rate-of-rise water height vs. time plots

1. Sample S-100-504-I:

Page 71: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

62

2. Sample S-100-672-H:

Page 72: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

63

3. Sample S-100-672-I:

Page 73: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

64

4. Sample S-100-672-V:

Page 74: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

65

5. Sample P-R-450-600-H:

Page 75: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

66

6. Sample P-R-450-800-H:

Page 76: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

67

7. Sample B-350-HS:

Page 77: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

68

8. Sample P-S-400-H:

Page 78: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

69

9. Sample P-S-400-IU:

Page 79: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

70

10. Sample P-S-400-V:

Page 80: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

71

11. Sample G-600-H:

Page 81: LASER POWDER BED FUSION ADDITIVE MANUFACTURING OF COPPER …

72

12. Sample G-800-H:


Recommended