Computational fluid dynamics investigation of 3d truss based lattice structures submitted in partial fulfilment of the requirements for the degree of bachelor of engineering

Coventry University
Faculty of Engineering, Environment & Computing
Department of Mechanical, Aerospace & Automotive Engineering

324MAE Project Report

Computational Fluid Dynamics Investigation of 3D
truss-based lattice structures
Submitted in partial fulfilment of the requirements for the degree of Bachelor of
Engineering

O. Searle SID: 7651401
Meng Mechanical Engineering
Supervisor: Dr D. Aremu
April 2021

Declaration: The work described in this report is the result of my own
investigations. All sections of the text and results that have been obtained from
other work are fully referenced. I understand that cheating and plagiarism
constitute a breach of University Regulations and will be dealt with accordingly.
Signed: O.Searle

Date: 16/04/21

1


1 Acknowledgements
I would like to thank Dr Deji Aremu for his guidance and support throughout the duration
of this project. I would also like to acknowledge the software support team, with special thanks
to Kyle Panton, who have helped me overcome many difficulties during the early stages of this

project.

2 Table of Contents
1

Acknowledgements ............................................................................................................ 2

2

Table of Contents................................................................................................................ 2

3

Table of Figures .................................................................................................................. 3

4

Table of Tables ................................................................................................................... 4

5

Nomenclature...................................................................................................................... 4

6

Abstract............................................................................................................................... 5

7

Introduction ........................................................................................................................ 5

7.1
Background ................................................................................................................. 5
7.2

Problem Description and Scope .................................................................................. 6

7.3

Aims and Objectives ................................................................................................... 6

7.4
Hypothesis ................................................................................................................... 6
8 Literature Review ............................................................................................................... 6
8.1

Manufacturing Methods and Materials ....................................................................... 6

8.2

Computational Fluid Dynamics .................................................................................. 8

8.3

Existing Heat Exchangers ........................................................................................... 9

8.4
8.5

Industrial Applications ................................................................................................ 9
Existing Truss Lattice Literature ............................................................................... 10

8.6

Literature Review Closing Statements ...................................................................... 10

9

Methodology ..................................................................................................................... 10
9.1

Unit Cell Creation ..................................................................................................... 11

9.2

CFD Model Set-Up ................................................................................................... 12

9.2.1

Geometry............................................................................................................ 13

9.2.2

Regions and Initial Conditions........................................................................... 14

9.2.3

Meshing.............................................................................................................. 15

9.2.4

Physics Models and Governing Equations ........................................................ 18

9.2.5

Exploratory Simulations .................................................................................... 19

9.3

Mesh Independence Study ........................................................................................ 20

9.4

Model Validation....................................................................................................... 20

10

Results and Discussion ................................................................................................. 21

10.1

Pressure Drop ............................................................................................................ 21

10.2

Temperature Change ................................................................................................. 23
2


10.3

Heat Transfer ............................................................................................................. 25

10.4
10.5

Reynolds Number ...................................................................................................... 27
Extended Fin HE ....................................................................................................... 27

10.6

2x2x4 Lattice ............................................................................................................. 27

10.7

Assumptions and Errors ............................................................................................ 28

11
11.1
11.2

Conclusions ................................................................................................................... 29
Considerations to Hypothesis and Aims ................................................................... 29
Future Work .............................................................................................................. 30

12

References ..................................................................................................................... 30

13

Appendix ....................................................................................................................... 32

3 Table of Figures
Figure 1 - Lattice Structure Types: BCC (A), BCCZ (B), FCC (C), FCCZ (D) (Maconachie.
T et al. 2019) .............................................................................................................................. 5
Figure 2 - Nickel Plated Lattice from Maloney et al. (2012) page 2488. .................................. 7
Figure 3 - Scan of SLM Truss Structures Demonstrating Surface Finish from Leary. M et al.
(2016) page ................................................................................................................................ 8
Figure 4 - Extended Surface Heat exchanger (Kwon et al., 2020) page 5. ................................ 9
Figure 5 - Lines of Code from Matlab Script .......................................................................... 11
Figure 6 - BCCZ Truss Lattice Unit Cell Dimensions ............................................................ 12
Figure 7 - Imported Unit Cell .................................................................................................. 13
Figure 8 - United Lattice with Extended Faces ....................................................................... 13
Figure 9 - VOI Dimensions...................................................................................................... 14
Figure 10 - Side View of Volume Mesh with Volumetric Control Applied ........................... 16
Figure 11 - Detailed View of Refined Prism Layers ............................................................... 17
Figure 12 - Wall y+ Monitor Plot ............................................................................................ 17
Figure 13 - Mesh Independence Study .................................................................................... 20
Figure 14 - Typical Extended Surface HE Validation Model.................................................. 20
Figure 15 - Pressure Gradient Contour Plot............................................................................. 21
Figure 16 – Porosity (%) vs Pressure Drop (Pa) ...................................................................... 22
Figure 17 - Velocity Streamline Around 47.5% Porous Lattice .............................................. 22
Figure 18 - Top-Down View of Velocity Streamlines Through A) 94.5% Porous Lattice and
B) 2x2x4 Lattice ...................................................................................................................... 23
Figure 19 - Temperature Contour Plot Across Lattice and Fluid ............................................ 23
Figure 20 – Porosity (%) vs Temperature Change (K) ............................................................ 24
Figure 21 - Velocity Vector Contour Plot at Plane in A) 78.2% Porous, B) 47.5% Porous, C)
94.5% Porous and D) 2x2x4 Lattice ........................................................................................ 25
Figure 22 - Porosity (%) vs Heat Exchange (W) ..................................................................... 26
Figure 23 - Porosity (%) vs Heat Exchange (W) Including 2x2x4 Lattice.............................. 26

Figure 24 – Porosity (%) vs Reynolds Number ....................................................................... 27
Figure 25 - Normalised Heat transfer and Temperature Change ............................................. 28

3


4 Table of Tables
Table 1 - Unit Cell Parameters................................................................................................. 11
Table 2 - Truss Radius and Porosity ........................................................................................ 11
Table 3 – Fluid Inlet Initial Conditions.................................................................................... 14
Table 4 - Lattice Initial Conditions .......................................................................................... 15
Table 5 - Applied Meshing Tools ............................................................................................ 15
Table 6 - Basic Mesh Controls................................................................................................. 16
Table 7 - Applied Fluid Physics Models.................................................................................. 18
Table 8 - Fluid Properties of Air
Table 9 - Solid
Properties of Aluminium.......................................................................................................... 19

5 Nomenclature
CFD – Computational Fluid Dynamics
BCC – Body centred cubic
BCCZ – Body centred cubic with Z
axis struts
FCC – Face centred cubic
FCCZ – Face centred Cubic with Z
axis struts

NSE –Navier Stokes Equations
HE – Heat exchanger
SLM – Selective laser melting

CAD – Computer aided design
VOI – Volume of Interest

4


6 Abstract
Truss lattices are promising structures for a multitude of functions such as energy
absorption, lightweight structural components, and compact heat exchangers. They possess
excellent mechanical strength for their weight and can be used as effective load-bearing
structures. In addition to this, they have large surface areas for their size and, as a result, can
be used as highly efficient compact heat exchangers. The combination of these properties and
advances in modern additive manufacturing techniques leads to the potential for some highly
effective multifunctional structures. This study will detail an investigation into the heat transfer
performance of varying porosity BCCZ truss lattice unit cells to determine the optimum
geometry for heat transfer, as this has not been investigated in the existing literature.
Considerations such as pressure drop, specific heat transfer, flow turbulence and potential
applications are also discussed. It is found that the optimum unit cell porosity is 78.2%, which
performs 4.7% better than a typical extended fin HE, in terms of heat transfer, of the same
external volume, whilst using 15.2% less material and maintaining significantly better
mechanical strength properties.

7 Introduction
7.1 Background
A lattice is defined as a regular repeated three-dimensional arrangement of unit cells;
they can take many forms and are often based on crystalline structures (Zok et al., 2016). Figure
1 shows a selection of typical truss lattice unit cells. This set is based on metallic crystalline
shapes in BCC, FCC and their Z strut variants. A truss lattice is made from unit cells that
consist of truss struts arranged regularly.

Figure 1 - Lattice Structure Types: BCC (A), BCCZ (B), FCC (C), FCCZ (D)
(Maconachie. T et al. 2019)

Trusses are a series of connected beams that create a rigid structure. They are widely
used across all industries in structural applications such as bridges and buildings due to their
excellent structural properties (Lin & Yoda, 2017). Combining truss structures and metallic
crystalline structures produces truss lattices. These structures are known for their high specific
compressive strength, meaning they have various uses within industry where strength and
weight are considerations, particularly within the automotive and aeronautical industries
(Frulloni et al., 2007).
Truss lattices have high specific surface areas due to their complex cylindrical truss
structures. High specific surface area can lead to excellent heat transfer performance. The
combination of these factors justifies the interest in these structures as multifunctional
structural heat exchangers.
Efficient heat transfer is becoming more of a concern as the global energy consumption
is increasing significantly every year. Around 50% of this energy is heat energy meaning
efficient heat transfer is vital. Truss lattice HEs can provide very efficient heat transfer in small
volumes and therefore contribute to improving heat transfer efficiency.

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7.2 Problem Description and Scope
As established, truss lattice structures have excellent heat transfer and structural
properties, leading to the next step of optimising these structures. Optimising these structures
will provide a more appropriate comparison to typical extended surface heat exchangers as
these HEs have had many years of development and optimisation. Existing literature covers
many different unit cell structures, but are no studies optimising any particular unit cell type.
This gap in literature provides an opportunity to further the research in this area and aid the
development of truss lattices.

Due to limited time and access to computational resources, this study will focus on only
one type of truss lattice unit cell, BCCZ. BCCZ has been selected as it is a commonly used
structure with excellent compressive strength and specific surface area, making it a good
candidate for optimisation.

7.3 Aims and Objectives
This project aims to determine the optimum unit cell porosity for heat transfer and
pressure drop performance by studying the flow through various truss lattice unit cells in a Star
CCM+ CFD simulation. A secondary aim is to compare the optimised truss lattice unit cell to
a current typical CPU HE, providing context for the real-world application and if these truss
lattices are viable to replace current designs.
Objectives:
- Create a series of truss lattice unit cells with varying porosities using a Matlab script
- Construct a lattice array using unit cells within Star CCM+
- Create a CFD model in Star CCM+
- Conduct a mesh independence study
- Collect Data from the CFD simulations
- Analyse fluid flow and HE performance
- Validate CFD simulations by comparing results to the existing literature
- Select the most effective truss lattice unit cell for heat transfer and pressure drop
- Compare most effective truss lattice unit cell to typical existing HE

7.4 Hypothesis
It is hypothesised that as the porosity of the unit cell decreases, there will be an increase
in the pressure drop across the lattice. It is thought that as the porosity of the unit cell decreases,
there will be an increase in heat transferred and therefore the temperature change of the fluid.

8 Literature Review
8.1 Manufacturing Methods and Materials
Truss lattice structures are complex, and therefore difficult to manufacture. Traditional

techniques such as brazing can be used to create truss lattices. This process is time-consuming
and labour-intensive as each unit cell is made individually and then assembled. This assembly
process makes creating accurate lattices extremely difficult (Helou & Kara, 2017). Techniques
such as wire-woven metals are quicker to produce but may not yield strong structures as the
bonds between the weaves are often flawed. An investigation by Khoda et al. (2021) uses a
dipped continuous rod technique that claims to improve nodal bonding. It is in the early stages
of research but has produced promising results.

6


In a study by Maloney et al. (2012), nickel plating via electrolysis was used to create
hollow lattice structures. This process uses a polymer lattice scaffold coated in a conductive
seed layer. It is then electroplated in nickel with a thickness of 50µm, and the scaffold is then
etched away. Figure 2 shows the result of this process. An advantage of this manufacturing
method is the hollow truss struts which can be used in a crossflow heat exchanger with fluid
passing through the inner tubes and across the outside of the lattice.

Figure 2 - Nickel Plated Lattice from Maloney et al. (2012) page
2488.

Investment casting is a conventional method that can yield complex and accurate lattice
structures. A sacrificial scaffold is created in a volatile wax or polymer using an injection
moulding or additive manufacturing method. This scaffold is then coated in a ceramic slurry.
Once the ceramic has dried, the volatile scaffold is removed by melting it away, and liquid
metal is then poured into the ceramic mould. This process is costly and time-consuming due to
the number of steps involved (Rashed et al., 2016).
The current preferred method of manufacture is additive manufacture, which covers a
wide range of techniques. One example is SLM, which builds up thin layers of material using
a laser to melt material on top of each layer (Lei et al., 2019). This method means lattices can

be made in one process, and the internal geometry can be highly complex. Due to the novelty
of this method and the expensive machinery used, SLM is an expensive and time-consuming
option. A potential issue with SLM is the surface finish of the product, as it can have a high
roughness value due to the nature of the layer-by-layer build process. This roughness is seen
clearly in Figure 3. However, this may be advantageous for heat transfer applications due to
the increased surface area and boundary layer disruption (Leary et al., 2016).

7


Figure 3 - Scan of SLM Truss Structures Demonstrating Surface Finish
from Leary. M et al. (2016) page

A technique called wire arc additive manufacturing has been investigated by Zhang et al.
(2020), which uses an automated traditional arc welder to build truss lattices. It does this by
melting stainless steel rod feed material with an arc and building spot by spot until the structure
is completed. This process produces structures with good mechanical properties but low
accuracy.
SLM additive manufacturing allows for the use of many different materials, including
aluminium, titanium, steel, tungsten, and copper (Song et al., 2020). Titanium offers excellent
mechanical properties due to its high specific stiffness and strength, making it a good choice
for structural applications (Takezawa et al., 2017). Copper has good conductive properties,
making it a good choice for use as a HE. Aluminium has good mechanical and thermal
properties, making it a good choice for structural HE. Due to these properties, aluminium is the
material selected to be simulated in this study (Leary et al., 2016). Aluminium is also
commonly used in existing HEs, making comparisons between truss lattice HEs and existing
HEs feasible.

8.2 Computational Fluid Dynamics
CFD software packages do not all perform the same. They all calculate the solutions

using slightly different methods meaning the results will differ from each other. Two industry
leaders are Star CCM+ (Multiphysics Computational Fluid Dynamics (CFD) Simulation
Software, 2021) and Ansys Fluent (Ansys Fluent | Fluid Simulation Software, 2020). They both
perform similarly overall, but each has advantages.
A study by Zou et al. (2017) analysed the differences between the two CFD packages.
The same mesh was used for both software packages to make a fair comparison. In this study,
Ansys is less computationally intensive, yielding lower simulation times (14% - 29% lower),
which will be advantageous for running simulations on lower power devices. For large
simulations, small percentage changes in computational efficiency can make a significant
difference in time taken, which can be worth a lot in industrial applications. Ansys can also
yield slightly more accurate results than Star CCM+, mainly when using 'advanced wall
treatment' for heat transfer applications, although the differences are minimal.
Star CCM+ has a significant advantage over Ansys in that it does not have a cell limit
for student use. This means a more refined mesh can be generated, providing results that can
be made mesh independent. It will also allow for more resolution around the boundary layers,
and in the wake, this is key in conjugate heat transfer simulations and will provide more
accurate results (Versteeg & Malalasekera, 2007).

8


The CFD of truss lattices must be carefully considered as the geometry is intricate, and
heat transfer applications typically require more computational power. This complexity will
cause more fluid interactions with the solid structure, meaning the potential for turbulent flow,
which significantly impact heat transfer. Different physics models can be applied to simulations
to improve accuracy. An example of this is 'advanced wall treatment', which will benefit the
turbulence modelling around the boundary layers of the lattice structures (Zou et al., 2017).

8.3 Existing Heat Exchangers
To provide context for the performance of truss lattice HEs, they must be compared to

existing HEs. There are a wide variety of HEs commonly used in industry, such as plate, shell
and tube and extended surface (Aslam Bhutta et al., 2012). They each have different advantages
and optimal use cases. Plate HEs are constructed from thin plates, often with internal
corrugation. These HEs are modular and can easily be changed depending on the required
usage. They can be used for moderate temperatures and pressures applications. Shell and tube
HEs are ubiquitous within industry as they can be used in a wide range of applications. This is
due to their ability to cope with an extensive range of temperatures and pressures. They also
can exchange heat between different fluid phases.
The HE most comparable to a truss lattice is the extended surface HE, as they have
similar use cases. They work by transferring heat from a solid object to a fluid via convection.
Extended surface HEs have relatively simple geometry, as seen in Figure 4. Despite this, they
have high specific surface areas. As a result of their simple geometry, they are easy to
manufacture using traditional techniques, meaning they are low cost and quick to produce
compared to truss lattice made via additive manufacture. This makes them suitable for use in
cars, computers, and other consumer goods.

Figure 4 - Extended Surface Heat exchanger (Kwon et al., 2020)
page 5.

Truss lattice HEs also have large specific surface areas meaning they are comparable to
extended fin HEs. This makes them an ideal candidate for direct comparisons.

8.4 Industrial Applications
Compact HEs have a wide range of industrial uses. An example of this is in the power
cycle application of supercritical carbon dioxide. A study by Kwon et al., (2020) details the
high thermal efficiency and impressive mechanical properties.
During hypersonic flight, the leading edges of the wings experience high levels of
loading and heat due to the air resistance at these velocities. This heat needs to be dissipated;
otherwise, thermal expansion may cause structural damage to the vehicle. The study by Yang
et al. (2019) explains the application of truss lattice HEs as these structures will be able to bear

9


the loads experienced by the wing whilst dissipating the heat away from the leading edge.
Applications such as the nose cone of re-entry vehicles and use in rocket combustion chambers
were also detailed in this study.
The current applications of truss lattice heat exchangers are limited compared to the
potential uses. This is due to high manufacturing costs and a lack of knowledge within the
industry. As manufacturing becomes more economically viable, these structures will be used
more widely.

8.5 Existing Truss Lattice Literature
There are many studies into the heat transfer capabilities of truss lattice, many of which
have both experimental and CFD results. A number of these studies investigate the heat transfer
performance of truss lattices between sandwich panels. A study by Kim et al. (2004)
investigates 93.8% porosity sandwich panels experimentally. This study determines that the
performance of the HE is similar to that of a bank of cylinders but have significantly better
mechanical properties.
An experimental investigation conducted by Chaudhari et al. (2019) tested a range of
aluminium octet truss structures with varying porosities. It determined that these structures
were excellent both structurally and used as a HE. Despite testing a range of porosities, no clear
conclusions and recommendations were made regarding the optimal structure.
Crossflow truss lattice structures are an interesting area of research as they widen the
range of applications in which these structures can be used. A study by Maloney et al. (2012)
details the complex manufacturing methods and the performance of these structures. The
results show these structures are very effective compact HEs but are challenging to
manufacture.
Yang et al. (2019) conducted both an experimental and CFD comparison of Kagome and
tetrahedral lattices, both of which are similar to BCCZ truss lattices. This study analyses the
heat transfer performance and the flow characteristics of these structures. A comparison of the

CFD and experimental results are also made, providing an insight into the accuracy of the CFD
methods and potential advantages and disadvantages.

8.6 Literature Review Closing Statements
Truss lattice HEs are a well-researched field, with many studies investigating these
structures. However, no studies are aiming to optimise these lattices. It is well documented that
these structures are effective HEs and have many potential applications within industry. The
next step is to refine and optimise these lattices. The findings from the research conducted will
act as a basis for understanding these structures and the methods that can be used to analyse
and optimisation.
Results and methodologies from these studies will also provide context and opportunity
for validation of this study.

9 Methodology
The methodology of this project will follow four main stages; Unit cell generation, CFD
model set up, CFD model validation, and unit cell optimisation. This project methodology has
been used across many fields in existing literature, so it forms a solid basis for this study to
follow.

10


9.1 Unit Cell Creation
Truss lattice unit cells are complex. Therefore, creating a wide range of varying
geometries in a CAD package will be very time consuming to produce. To get around this, a
Matlab code produced by Dr D. Aremu can automatically create several unit cell types, each
with varying parameters (see appendix A for complete code). For this project, the code is used
to create BCCZ unit cells. Doing this is a matter of entering the desired parameters into the
code into line (2), as seen in Figure 5. Line (1) in Figure 5 shows the control parameters this
code can control. These are as follows in Table 1.

(1)
(2)
Figure 5 - Lines of Code from Matlab Script

Table 1 - Unit Cell Parameters

Parameter Control
cs
rad

Definition
Unit Cell Size
Truss Radius
Unit Cell Type (eg. BCCZ,
FCCZ etc)
File name of output

axis
Fname

Line (2) in Figure 5 produces a BCCZ unit cell with a unit cell size of 10, a truss radius
of 0.7 in a .stl format. This code produces a unit cell in a .stl format that does not have units.
When the file is imported into CAD or CFD software, then a unit system must be set. For this
study, these units are millimetres. The parameter changed for this study is the truss radius, as
this will change the porosity of the unit cell but will maintain the unit cell size so it can be
compared to an existing HE of the same size.
For this study, unit cells with a truss radius range of 0.5 – 1.8mm with 0.1mm
increments are created. This range covers porosity values from 47.5% to 94.6%, a wide enough
range to discover trends in the heat exchange performance of the structures. Table 2 shows the
unit cells and their corresponding percentage porosity values.

Table 2 - Truss Radius and Porosity

Truss Radius (mm)
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5

Porosity (%)
94.6
92.2
89.6
86.7
83.5
80.0
76.4
72.5
68.5
64.5
60.2
11

1.6
1.7
1.8

56.0
51.8
47.5

The equation below shows the calculation used to calculate the percent porosity of
each unit cell. (equation number)
𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦 (%) = 100 − (

𝐿𝑎𝑡𝑡𝑖𝑐𝑒 𝑉𝑜𝑙𝑢𝑚𝑒
) × 100
𝐵𝑙𝑜𝑐𝑘 𝑉𝑜𝑙𝑢𝑚𝑒

Figure 6 below details the dimensions of a BCCZ truss lattice unit cell. For this study,
the unit cell is symmetric and H=L=W. This is referred to as the unit cell size. The truss radii
in Table 2 above are equal to D/2.

Figure 6 - BCCZ Truss Lattice Unit Cell Dimensions

9.2 CFD Model Set-Up
With the understanding of CFD fundamentals gained from the literature review, the CFD
conjugate heat transfer is set up in Star CCM+ using industry-standard practices. The method
for setting up a conjugate heat transfer model is as follows: Import geometry, repair surface
geometry and create a VOI, assign fluid and solid domains, set initial conditions, mesh both
fluid and solid domains, apply appropriate physics models to solid and fluid domains, and run
exploratory simulations.
This simulation replicates the conditions found in CPU coolers. These conditions will

allow for a comparison between truss lattices as a HE and a typical extended fin HE. The truss
lattice will be simulated assuming it is produced by SLM additive manufacture from
aluminium.

12


9.2.1 Geometry
When importing the unit cells into Star CCM+, the units are set to millimetres and the
Z struts of the BCCZ unit cell are aligned with the Z-axis in the coordinate system of the
software.

Figure 7 - Imported Unit Cell

Figure 7 above shows the imported unit cell. Star CCM+ creates a triangular surface
geometry mesh on the imported geometry, which can be seen clearly in Figure 7. This surface
geometry mesh often has errors and broken surfaces measured by several parameters: Pierced
faces, face quality, face proximity, free edges, non-manifold edges, and non-manifold vertices.
The unit cell is then duplicated, translated 10mm in the X direction and united with the
original unit cell to form a 1x1x2 lattice. When symmetry planes are introduced, this will
become a 2x2x2 lattice. Symmetry planes simplify the geometry and reduce the mesh size and,
therefore, computational time. The surface mesh of this lattice is checked to ensure there are
no surface quality errors. The faces normal the +Y and +Z directions on the lattice are extended
1.5mm, to ensure the VOI generates correctly. Figure 8 shows the completed lattice with
repaired surfaces and extended faces, A) shows the view from the +X axis and B) shows the
view from the +Y axis.
An additional lattice structure will be simulated using the optimum unit cell from the
initial run of simulations. This simulation will contain a 2x2x4 lattice occupying the same
10x10x20 mm volume. This will analyse the effect of the unit cell size on the heat transfer
performance.

A)

B)

Figure 8 - United Lattice with Extended Faces

13


The wind tunnel is made by creating a cuboid around the lattice. It contacts the top and
side faces of the lattice as these will be symmetry planes. Figure 9 shows the dimensions of the
wind tunnel with the lattice in situ. These dimensions allow the fluid to flow freely through and
around the structure. Enough space has been added +X direction behind the lattice to ensure
the wake is fully developed, which improves the accuracy of the simulation.

Figure 9 - VOI Dimensions

The sides of the wind tunnel are separated into individual faces that are assigned names
to identify when setting the inlet, outlet, symmetry planes, and walls later in the setup. A VOI
is created to separate the fluid and solid domains. This is done by subtracting the lattice volume
from the wind tunnel volume. The volume left after the subtraction is the fluid domain, and the
lattice is the solid domain.

9.2.2 Regions and Initial Conditions
Regions are set, so the CFD software knows which area to simulate fluid and which
area to simulate as solid. The VOI is set to be the fluid domain, and the lattice is set to be the
solid domain.
The respective sides of the VOI are set with the appropriate boundary conditions and
initial conditions. The front face in the +X direction is set as a mass flow inlet, and the rear
face from the same direction is set as a pressure outlet. The top and left sides viewed from the

+X direction are set as symmetry planes. The right and bottom sides, viewed from the same
direction, are set as walls.
Table 3 – Fluid Inlet Initial Conditions

Fluid Inlet Initial
Conditions
Velocity
Pressure
Mass Flow Rate
Temperature
Turbulence Intensity

Value
9m/s
Gauge (101.3 KPa)
0.005kg/s
298K
0.01

14


Table 3 above shows the initial conditions of the fluid entering the fluid domain, a
velocity of 9m/s is used as this is a typical exit velocity of CPU cooler fans (Anandakrishnan
& Balaji, 2009). This equates to a 0.005kg/s mass flow rate for a wind tunnel this size. An
initial temperature of 298K is a typical inlet velocity for a CPU cooler as this is room
temperature. The pressure outlet is set to gauge pressure, and the walls are set to have a slip
condition so they will not interfere with the fluid flow.
The solid and fluid domains interact through an interface, allowing for heat transfer
between the two domains. The interface is set between the outer surfaces of the lattice and the

corresponding faces of the VOI. The interface conditions are set to conjugate heat transfer as
this applies to this type of solid to fluid HE. The initial conditions of the solid domain are set
to replicate a section of an aluminium CPU cooler operating at 373K with an overall power
input of 80 W, equating to 5 W per unit cell (Anandakrishnan & Balaji, 2009). Truss lattice
unit cells are likely to be made via additive manufacture, meaning surface roughness will differ
from an extruded aluminium HE. This roughness is accounted for, as shown in Table 4 below.
Table 4 - Lattice Initial Conditions

Lattice Initial Conditions
Material
Temperature
Power Output
Surface Roughness height

Value
Aluminium
373K
5W per unit cell
0.01mm (Udroiu et al., 2019)

9.2.3 Meshing
Meshing is a crucial factor in obtaining accurate results from CFD simulations, and it
is essential to set it up correctly and ensure there is no mesh dependency.
Star CCM+ provides serval meshing tools to create an appropriate mesh for specific
geometries and simulation types.
Table 5 shows the meshing tools applied to this model; these tools are commonly used
in existing literature, meaning they are well suited for this application.
Table 5 - Applied Meshing Tools

Mesher

Surface Remesher
Automatic Surface Repair
Polyhedral Mesher

Setting
Triangle, curve+ proximity refinement
Minimum Quality - 0.05
Post Mesh Optimiser active
Stretch Function - Geometric Progression,
Distribution Mode - Stretch Factor,
Gap-fill – 25%,
Minimum Thickness – 10%,
Layer Reduction - 50%

Prism Layer Mesher

Basic mesh controls are used to tailor the mesh to the specific size and geometry of the
model being simulated. Table 6 show the parameters used for the simulations in this study. In
Star CCM+ mesh parameters can be set to be relative to the base size. This allows for easy
changes in mesh size by changing a single central parameter. These parameters have been set
after conducting a mesh independence study to find the optimum mesh size.
15


Table 6 - Basic Mesh Controls

Default Controls
Base Size
Target Surface Size
Minimum Surface Size

Surface Growth Rate
Number of Prism Layers
Prism Layer Stretching
Prism Layer Total Thickness
Volume Growth Rate
Maximum Tet Size
Core Mesh optimisation

Setting
1.2 mm
75% of Base
1% of Base
1.3
6
1.2
0.18 mm
1.2
10,000% of Base
1 Cycle, Quality Threshold – 0.4

Advanced controls are used to refine the mesh in critical areas, for example,
surrounding the lattice and in the wake behind the lattice. Prism layer control is applied to the
walls, which removes prism layer refinement on the walls. This control reduces the mesh count
and does not affect accuracy as there is a slip condition applied to the walls meaning they will
not interfere with the flow. For this simulation, volumetric control is added around the lattice
and in the wake. The volumetric control has a size of 10% of the base size. This dramatically
increases the cell count and the accuracy of the simulation. The refined mesh can be seen in
Figure 10.

Figure 10 - Side View of Volume Mesh with Volumetric Control Applied

16


A key part of a volume mesh are the prism layers, these are small, structured cells
around the interface between the solid and the fluid, as shown in Figure 11.

Figure 11 - Detailed View of Refined Prism Layers

During initial exploratory runs, the wall y+ values are monitored, and the prism layers
are adjusted until the wall y+ are within 0-3, the acceptable range. Figure 12 shows the wall y+
monitor after prism layer refinement has been carried out. The prism layers are then set to these
absolute values, so when if the mesh size is changed, the prism layers will not be affected by
the change in base size.

Figure 12 - Wall y+ Monitor Plot

17


9.2.4 Physics Models and Governing Equations
When conducting a study in CFD software, assumptions must be made to simulate the
flow as replicating a real-world flow is impossible. The assumptions made in this study follow
practices used in the existing literature.
Assumptions:
- Three Dimensional
- Steady State
- Adiabatic Walls
- Constant Fluid Properties
- No Heat Loss Due to Radiation

Table 7 - Applied Fluid Physics Models

Physics Model

Setting

Constant Density

On

Coupled Energy

On

Coupled Flow

Implicit, 2nd Order

Gravity

On (9.81m/s2 in -Z)

K-Epsilon Turbulence

On

Realisable K-Epsilon
Two-Layer

2nd Order, Shear Driven

Reynolds-Averaged
Navier-Stokes

On

Steady

On

Three Dimensional

On

Turbulent

On

Justification
For the fluid velocities in this
simulation, constant densities can be
used. This is commonly used in
literature
This is a conjugate heat transfer model,
so coupled energy must be used as there
is energy transfer
Coupled solver works better with fine
meshes
Applied to more accurately simulate a
realistic environment

Performs well in simulations with
internal fluid flows, and low pressure
gradients. More stable than K-Omega
Improves accuracy in turbulent mixing
flows, which will benefit these
simulations
Widely used existing literature as is one
of the more accurate methods for
solving turbulence
A transient simulation is not required for
obtaining results. Steady simulations use
far less computational time than
transient
The geometry used in this model is three
dimensional
Complex internal geometries cause
turbulent flow

Table 7 details the physics models applied to the fluid and the justification for each. As
this is a conjugate heat transfer simulation, the critical aspect of this flow is at the boundary
between the solid and fluid. This boundary requires a refined mesh and appropriate physics
models to obtain accurate results. The K-Omega model can yield better results, so it was tested
on a range of simulations but could not be made reliable across all simulations, so K-Epsilon
is used.

18


The governing equations for the CFD model produced for this study are NSE, and these
equations solve the flow and energy transfer. The following equations are solved during the

CFD simulations, in order, they are the continuity equation, X momentum equations (repeated
for both Y and Z directions), and the Energy equation.
𝜕𝜌 𝜕(𝜌𝑢) 𝜕(𝜌𝑣) 𝜕(𝜌𝑤)
+
+
+
=0
𝜕𝑡
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕𝜌 1 𝜕𝜏𝑥𝑥 𝜕𝜏𝑥𝑦 𝜕𝜏𝑥𝑧
𝜕(𝜌𝑢) 𝜕(𝜌𝑢 2 ) 𝜕(𝜌𝑢𝑣) 𝜕(𝜌𝑤)
+
+
+
+
=− +
[
+
]
𝜕𝑦
𝜕𝑡
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕𝑥 𝑅𝑒 𝜕𝑥
𝜕𝑧
𝜕𝑞𝑦
𝜕𝑞

𝜕𝑞
1
𝜕(𝜌𝑤𝐸)
𝜕(𝜌𝑣𝐸)
𝜕(𝜌𝑢𝐸)
𝜕(𝜌𝑢)
𝜕(𝜌𝑣)
𝜕(𝜌𝑤)
𝜕𝜌𝐸
− 𝑅𝑒𝑃𝑟 [ 𝜕𝑥𝑥 + 𝜕𝑦 + 𝑧 ] +
+ 𝜕𝑥 + 𝜕𝑦 +
=
−
−
−
𝜕𝑧
𝜕𝑡
𝜕𝑧
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕
𝜕
1 𝜕
(𝑢𝜏
+
𝑣𝜏
+
𝑤𝜏
)

+
(𝑢𝜏
+
𝑣𝜏
+
𝑤𝜏
)
+
[
(𝑢𝜏
+
𝑣𝜏
+
𝑤𝜏
𝑥𝑦
𝑦𝑦
𝑦𝑧
𝑥𝑥
𝑥𝑦
𝑥𝑧
𝑥𝑧
𝑦𝑧
𝑧𝑧 )]
𝜕𝑦
𝑅𝑒 𝜕𝑥
𝜕𝑧

Where t = Time, 𝜌 = Density, E = Total Energy, 𝜏 = Stress, Re = Reynolds number and Pr =
Prandtl Number (Navier-Stokes Equations, 2015).
Table 8 - Fluid Properties of Air

Fluid Properties (Air)
Density
Dynamic Viscosity
Specific Heat
Thermal Conductivity
Turbulent Prandtl
Number

Table 9 - Solid Properties of Aluminium

Solid Properties
(Aluminium)
Density
Specific Heat
Thermal
Conductivity

Value
1.18415 kg/m3
1.85508e-5 PaS
1003.62 J/kgK
0.0260305 W/mK
0.9

Value
2702.0 kg/m3
903.0 J/kgK
237.0 W/mK

Table 8 and 9 above detail the properties of the fluid and solid domains used in this
model.
The physics conditions applied to the solid domain are Constant density and Coupled
solid energy. This model simulates conjugate heat transfer meaning that energy will be
transferred into the fluid. For this to occur, an energy model needs to be applied.

9.2.5 Exploratory Simulations
Exploratory simulations are run to troubleshoot and refine the model until results are
reliable and consistent. A simulation is said to have run successfully when the residuals
converge below 10-5. Adjustments are made to prism layers, mesh size, and physics models
until a final model converges and runs reliably.
Once a final model is settled on, it is used as a basis for all subsequent simulations to
ensure results are comparable and conclusions can be drawn.

19


9.3 Mesh Independence Study
A mesh independence study verifies that the results obtained by a simulation are not
dependent on the mesh size. Mesh independence is crucial in obtaining usable and reliable
results. Mesh independence is reached when increasing the mesh size does not affect the results
of the simulations. In this model, the mesh parameters, except prism layers, are set relative to
the base size meaning that this is the only parameter that needs changing to conduct this study.
Figure 13 shows the study results. This study covers a mesh size range of 373,295 to
3,925,897cells.

Heat Transfer Vs Cell Count
0

1000000

2000000

3000000

4000000

5000000

-5.82
-5.84

Heat Transfer (W)

-5.86
-5.88
-5.9
-5.92

-5.94
-5.96
-5.98
-6

Cell Count
Figure 13 - Mesh Independence Study

For this model, the results become independent around 1,200,000 cells, which
corresponds to a base size of 1.2mm. This base size will be used throughout the study.

9.4 Model Validation
Model validation is essential to trust the results obtained from CFD simulations. The
methodology of the study is compared to that of existing literature, such as the study conducted
by Yang et al. (2019) and the tutorials set in the Star CCM+ user guide (Multiphysics
Computational Fluid Dynamics (CFD) Simulation Software, 2021). The comparison to existing
literature validates the methodology of this study.
A Baseline model of a typical extended surface HE was also created from the same set
up as the lattice model. The geometry and results are compared to existing literature to validate
the setup of this model. A percentage temperature difference of 0.16% was found in the study

Figure 14 - Typical Extended Surface HE Validation Model

20


by Freegah et al., (2020). The extended surface HE validation simulation for this study yields
a percentage temperature difference of 0.2%, a 25% difference between the studies. This
disparity may be due to the slight difference in the model set up and initial conditions. However,
these are close enough to validate the model and all subsequent simulations produced from this
baseline model. Figure 14 shows the wall y+ plot of the typical extended fin HE, which was
used to validate the CFD model.

10 Results and Discussion
The metrics used to measure the heat exchange performance of the truss lattice HE are
Pressure drop across the length of lattice, Temperature change in the fluid between the front
and rear of the lattice, and Heat energy exchanged. A typical CPU fan would not be able to
pass enough air through the HE if the pressure drop is excessive, so this needs to be measured.
The temperature change and heat exchange are measures of how effective the structure is as a
HE. From these metrics, the optimum unit cell can be found. The optimum unit cell will have
high heat transfer and temperature change values with minimal pressure drop.

10.1 Pressure Drop
The pressure drop across the lattice is measured by creating inspection planes in front
and behind the lattice structure and finding the difference between them.

Figure 15 - Pressure Gradient Contour Plot

Figure 15 above displays the pressure gradient across the surface area of the lattice
structures. The arrow shows the direction of flow in the +X direction. Red indicates a higherpressure region, whilst blue indicates regions of pressures below gauge pressure. This colour
gradient allows for easy visualisation of the pressure acting on the lattice structures. Images B)
and C) are the lattices with the largest and smallest truss radius, respectively. Image B) shows
a large area of high pressure on the leading face, with a maximum of 120.17 Pa above gauge
21


pressure. This is supported in Figure 16 as this unit cell has the highest pressure drop of 47.5
Pa. Image A) is the unit cell with a truss radius of 1.05 mm, which performs best in heat
transfer. It has a middling performance in terms of pressure drop, which fits the trend shown
in Figure 16 below.

Porosity vs Pressure Drop
50

Pressure Drop (Pa)

45
40
35
30
25

20
15
10
5

1x2 BCCZ Lattice

2x2x4 Lattice

0
0

20

40

60

80

100

Porosity (%)
Figure 16 – Porosity (%) vs Pressure Drop (Pa)

Figure 16 shows the relationship between percentage porosity and pressure drop, the
black line on the right shows the results for the 1x1x2 lattice, and the blue point is the result
for the 2x2x4 lattice. This relationship supports the hypothesis until around 60% porosity,
where the pressure drop begins to plateau. It is thought the plateau is close to the value of a
solid block, where fluid is diverted around the object. This case would be the maximum

pressure drop value.
Figure 17 shows a top-down view of velocity streamlines passing over the 47.5% porous
lattice. It supports this theory as it shows the fluid flow passing above, below and around the
lattice. It also shows the development of turbulence which contributes to pressure loss.

Figure 17 - Velocity Streamline Around 47.5% Porous Lattice

The lattice with the best pressure drop performance, of 16.4Pa, is the 94.5% porous
lattice. This result supports the hypothesis and is visualised in image A) of Figure 18 below. It

22


shows the velocity streamlines pass through the lattice with little change in velocity or
direction.

Figure 18 - Top-Down View of Velocity Streamlines Through A) 94.5% Porous Lattice and B) 2x2x4 Lattice

An interesting result from this investigation is the pressure drop of the 2x2x4 lattice, with
a porosity of 21.8%, which would be expected to have the highest pressure drop, based on the
hypothesis. The pressure drop is 38.7 Pa, which is comparable to a lattice with a porosity of
68.5%. This result may be due to the unit cells having a porosity of 78.2% and the numerous
routes for the fluid to take. Image B) in Figure 18 supports this theory as the velocity
streamlines can be seen passing evenly through the inside of the lattice.

10.2 Temperature Change
The temperature change was calculated by taking the average temperature on the two
planes used for the pressure drop calculation and calculating the temperature change between
them.

Figure 19 - Temperature Contour Plot Across Lattice and Fluid

Figure 19 shows temperature contour plots of the lattice structure to aid the visualisation
of the temperature throughout the fluid and solid domains. The highest temperatures are
indicated in red, whilst blue indicates areas of fluid at inlet temperature.
23


The hypothesis states that as the porosity increases, the temperature change will decrease,
Figure 20 partially supports this hypothesis as there is a general trend between 68.6% and
94.5% porosity of temperature change decreasing. From 68.6% to 47.5% porosity, there is a
general trend in decreasing temperature change. This result directly contradicts the hypothesis.

Porosity vs Temperature Change
12

Temperature Change (K)

10

8
6
4
2

1x2 BCCZ Lattice
2x2x4 Lattice

0
0

20

40

60

Porosity (%)

80

100

Figure 20 – Porosity (%) vs Temperature Change (K)

As the porosity of the lattice increases, there is less surface area which may explain the
decrease in temperature change as there is less surface area for heat exchange to occur. There
will be less turbulence on high porosity lattices (as seen in Figure 21 image C), which will
decrease heat exchange as there will be less flow mixing and a larger boundary layer that will
inhibit heat transfer.
The 2x2x4 lattice has the largest temperature change by a significant margin at 10.2 K,
a 35% improvement over the best 1x1x2 lattice. This result supports the hypothesis as this
lattice has the lowest porosity and the highest temperature change. Image D) in Figure 19 above
aids in visualising this as the wake behind the lattice has a significantly higher temperature than
seen in images A), B), and C). This lattice has the largest surface area, and therefore the largest
area for heat exchange to occur. Image D) in Figure 21 below visualises the turbulence within
the structure. This structure has the most turbulent flow, which will improve heat transfer
significantly.
The unit cells with porosities smaller than 68.6% have lower temperature differences.
This result may be explained by larger pressure drop and minimal fluid contact time. As

discussed previously, a large proportion of the fluid passes around these structures rather than
through them, meaning there is less fluid in contact with the surface for heat transfer to occur.
The 68.6% porosity or truss radius of 1.3 mm, unit cell has the largest temperature
difference of 7.55 K. A large temperature difference suggests this is the most effective heat
exchanger. This unit cell balances too much and too little flow interference, meaning it causes
turbulence but allows the fluid to flow through the structure instead of around it.
Figure 19 on page 23 above shows the temperature distribution throughout the solid
structure. This figure provides insight into the cooling effect of the fluid on the lattice. Image
C) shows the largest temperature variation throughout the solid with a peak temperature
significantly larger than other lattices. As the fluid passes through the lattice, its temperature
increases, because of this, the temperature difference between the solid and fluid is smaller,
and therefore heat transfer will be slower. This temperature gradient explains why the peak
temperature on all lattices is located on the external trailing edge.

24


Figure 21 - Velocity Vector Contour Plot at Plane in A) 78.2% Porous, B) 47.5% Porous, C) 94.5% Porous and D) 2x2x4
Lattice

10.3 Heat Transfer
The heat transfer is measured by extracting the total heat transferred for the whole
system. Star CCM+ has an extraction tool for this.
The results for porosity vs heat transfer are shown in Figure 22 below. It is hypothesised
that as the porosity decreases, heat transfer will increase. As with the temperature difference,
the results partially support this hypothesis. From 94.5% to 78.2% porosity, there is a clear
trend in increasing heat transfer, supporting the hypothesis. However, from 78.2% to 47.5%
porosity, there is a clear trend of decreasing heat transfer, directly contradicting the hypothesis.

25