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
This article presents a selection of typical truss lattice unit cells, specifically focusing on metallic crystalline structures in Body-Centered Cubic (BCC), Face-Centered Cubic (FCC), and their Z strut variants A truss lattice is composed of unit cells featuring regularly arranged truss struts.
Trusses are interconnected beams that form a rigid structure, commonly utilized in various industries for structural applications like bridges and buildings due to their superior structural properties When truss structures are combined with metallic crystalline structures, they create truss lattices, which are recognized for their high specific compressive strength This characteristic makes them valuable in industries where both strength and weight are critical factors, especially in the automotive and aeronautical sectors.
Truss lattices feature intricate cylindrical structures that result in high specific surface areas, enhancing their heat transfer performance This unique combination of attributes makes truss lattices an attractive option for multifunctional structural heat exchangers.
As global energy consumption rises significantly each year, efficient heat transfer has become increasingly important, with approximately 50% of this energy being heat energy Truss lattice heat exchangers (HEs) offer a compact solution for achieving highly efficient heat transfer, thereby enhancing overall heat transfer efficiency.
Figure 1 - Lattice Structure Types: BCC (A), BCCZ (B), FCC (C), FCCZ (D)
Problem Description and Scope
Truss lattice structures are known for their superior heat transfer and structural properties, prompting the need for their optimization By optimizing these structures, we can create a more relevant comparison with traditional extended surface heat exchangers, which have undergone extensive development and refinement over the years Although existing literature explores various unit cell structures, there is a notable lack of studies focused on optimizing specific unit cell types This gap in research presents a valuable opportunity to advance the understanding and development of truss lattice systems.
This study will concentrate on the BCCZ truss lattice unit cell due to constraints in time and computational resources The BCCZ structure is widely utilized for its remarkable compressive strength and specific surface area, positioning it as a strong candidate for optimization efforts.
Aims and Objectives
This project focuses on identifying the ideal unit cell porosity for enhanced heat transfer and reduced pressure drop by analyzing flow through different truss lattice unit cells using Star CCM+ CFD simulations Additionally, it seeks to evaluate the performance of the optimized truss lattice unit cell against a conventional CPU heat exchanger, assessing the practical implications and potential of these truss lattices as alternatives to existing designs.
- Create series of truss lattice unit cells with varying porosities using a Matlab script a
- Construct a lattice array using unit cells within Star CCM+
- Create CFD model in Star CCM+ a
- Collect Data from the CFD simulations
- Analyse fluid flow and HE performance
- Validate CFD simulations by comparing sults to the existing literature re
- 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
Hypothesis
As the porosity of the unit cell decreases, it is hypothesized that the pressure drop across the lattice will increase This reduction in porosity is also believed to enhance heat transfer, resulting in a greater temperature change of the fluid.
Manufacturing Methods and Materials
Truss lattice structures are inherently complex, making their manufacturing challenging Traditional methods like brazing, while effective, are labor-intensive and time-consuming due to the individual assembly of each unit cell, which complicates achieving precise lattice configurations (Helou & Kara, 2017) Although quicker alternatives, such as wire-woven metals, exist, they often result in weaker structures due to flawed bonds between the weaves Recent research by Khoda et al (2021) explores a dipped continuous rod technique that shows potential for enhancing nodal bonding, although it remains in the early stages of development with promising preliminary outcomes.
In a study by Maloney et al (2012), electrolysis was employed for nickel plating to fabricate hollow lattice structures This innovative process involves a polymer lattice scaffold that is first coated with a conductive seed layer and then electroplated with nickel to a thickness of 50 µm After the electroplating, the scaffold is etched away, resulting in hollow truss struts These struts are particularly advantageous for use in crossflow heat exchangers, allowing fluid to flow through the inner tubes while circulating around the outer lattice.
Investment casting is a traditional technique known for producing intricate and precise lattice structures The process begins with the creation of a sacrificial scaffold made from a volatile wax or polymer, utilizing either injection molding or additive manufacturing This scaffold is subsequently coated with a ceramic slurry, and after the ceramic dries, the scaffold is melted away to leave a mold Finally, liquid metal is poured into the ceramic mold However, this method can be expensive and time-consuming due to its multi-step nature (Rashed et al., 2016).
Additive manufacturing is currently the preferred method of production, encompassing various techniques, including Selective Laser Melting (SLM) SLM constructs intricate lattices by melting material layer by layer with a laser, allowing for complex internal geometries However, the process is costly and time-consuming due to the advanced machinery required A notable challenge of SLM is the surface roughness of the finished product, which can be significant due to its layer-by-layer construction Despite this, the increased surface area and boundary layer disruption caused by the roughness may benefit heat transfer applications.
Figure 2 - Nickel Plated Lattice from Maloney et al (2012) page
A technique called wire arc additive manufacturing has been investigated by Zhang et al
In 2020, an automated traditional arc welder was utilized to construct truss lattices by melting stainless steel rod feed material with an arc, creating the structure incrementally While this method yields structures with strong mechanical properties, it suffers from low accuracy in the final build.
SLM additive manufacturing enables the utilization of various materials, including aluminum, titanium, steel, tungsten, and copper (Song et al., 2020) Among these, titanium is favored for its exceptional mechanical properties, characterized by high specific stiffness and strength, which makes it suitable for structural applications (Takezawa et al., 2017) Copper's excellent conductivity positions it as a viable option for heat exchangers (HEs), while aluminum is recognized for its favorable mechanical and thermal properties, making it ideal for structural HEs This study focuses on simulating aluminum due to its prevalent use in existing HEs, allowing for effective comparisons between truss lattice HEs and traditional designs (Leary et al., 2016).
Computational Fluid Dynamics
CFD software packages vary in performance and methodology, leading to differences in their calculated results Among the industry leaders, Star CCM+ stands out for its advanced capabilities in 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) compared two CFD packages using the same mesh for a fair evaluation The findings revealed that Ansys is less computationally intensive, resulting in simulation times that are 14% to 29% shorter, making it advantageous for use on lower power devices In large simulations, even small improvements in computational efficiency can lead to significant time savings, which is crucial in industrial applications Additionally, Ansys tends to provide slightly more accurate results than Star CCM+, particularly when utilizing 'advanced wall treatment' for heat transfer scenarios, although the differences in accuracy are minimal.
Star CCM+ offers a distinct advantage over Ansys for student users by not imposing a cell limit, enabling the generation of a more refined mesh This capability enhances mesh independence, allowing for improved resolution around boundary layers and wakes, which is crucial for accurate conjugate heat transfer simulations (Versteeg & Malalasekera, 2007).
Figure 3 - Scan of SLM Truss Structures Demonstrating Surface Finish from Leary M et al (2016) page
When conducting CFD analysis of truss lattices, it is essential to account for their intricate geometry, as heat transfer applications often demand higher computational resources This complexity increases fluid interactions with the solid structure, leading to potential turbulent flow that can significantly affect heat transfer efficiency To enhance simulation accuracy, various physics models can be employed, such as advanced wall treatment, which improves turbulence modeling around the boundary layers of lattice structures (Zou et al., 2017).
Existing Heat Exchangers
To understand the performance of truss lattice heat exchangers (HEs), it's essential to compare them with various existing types, including plate, shell and tube, and extended surface HEs Each type offers distinct advantages and is suited for specific applications Plate HEs, made from thin plates with internal corrugation, are modular and adaptable for moderate temperature and pressure applications In contrast, shell and tube HEs are widely used in the industry due to their versatility in handling a broad range of temperatures and pressures, as well as their capability to facilitate heat exchange between different fluid phases.
Extended surface heat exchangers (HEs) are highly comparable to truss lattice designs, as both serve similar functions in transferring heat from solid objects to fluids through convection With their straightforward geometry, extended surface HEs boast high specific surface areas, facilitating efficient heat transfer Their simple design allows for easy manufacturing using traditional methods, resulting in lower costs and quicker production times compared to truss lattices created through additive manufacturing This efficiency makes extended surface HEs ideal for applications in automobiles, computers, and various consumer products.
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.
Industrial Applications
Compact heat exchangers (HEs) are utilized in various industrial applications, notably in the power cycle process involving supercritical carbon dioxide Research conducted by Kwon et al (2020) highlights their exceptional thermal efficiency and remarkable mechanical characteristics.
During hypersonic flight, the wings' leading edges face intense loading and heat from air resistance, necessitating effective heat dissipation to prevent thermal expansion and potential structural damage Yang et al (2019) discuss the use of truss lattice heat exchangers (HEs) as a solution, highlighting their capability to withstand these extreme conditions.
Figure 4 - Extended Surface Heat exchanger (Kwon et al., 2020) page 5
The study examined the loads on the wing while effectively dissipating heat from the leading edge, highlighting applications in the nose cone of re-entry vehicles and rocket combustion chambers.
Truss lattice heat exchangers have significant potential applications that remain largely untapped due to high manufacturing costs and limited industry knowledge However, as manufacturing processes become more cost-effective, the adoption of these innovative structures is expected to increase, unlocking their widespread use in various industries.
Existing Truss Lattice Literature
Numerous studies have explored the heat transfer capabilities of truss lattices, utilizing both experimental and computational fluid dynamics (CFD) results Many of these investigations focus on the heat transfer performance of truss lattices within sandwich panels Notably, a study conducted by Kim et al (2004) examines sandwich panels with 93.8% porosity, revealing that their heat transfer performance is comparable to that of a bank of cylinders, while also demonstrating significantly improved mechanical properties.
An experimental study by Chaudhari et al (2019) examined various aluminum octet truss structures with different porosities, revealing their strong structural performance and potential as heat exchangers However, the investigation did not yield definitive conclusions or recommendations on the optimal structure for these applications.
Crossflow truss lattice structures represent a significant advancement in engineering, expanding their potential applications across various fields Research conducted by Maloney et al (2012) highlights the intricate manufacturing processes and performance characteristics of these structures The findings indicate that while crossflow truss lattice structures serve as highly efficient compact heat exchangers, their manufacturing poses considerable challenges.
In their 2019 study, Yang et al compared the heat transfer performance and flow characteristics of Kagome and tetrahedral lattices, which are analogous to BCCZ truss lattices, using both experimental methods and computational fluid dynamics (CFD) The research highlights the accuracy of CFD techniques by juxtaposing the results with experimental data, revealing both the strengths and weaknesses of these modeling approaches.
Literature Review Closing Statements
Truss lattice heat exchangers (HEs) have been extensively studied, highlighting their effectiveness and potential industrial applications Despite the wealth of research, there is a notable gap in efforts to optimize these lattice structures The next phase of research will focus on refining and enhancing the performance of truss lattice HEs The insights gained from this research will provide a foundational understanding of these structures and the analytical methods necessary for their optimization.
Results and methodologies from these studies will also provide context and opportunity for validation of this study
This project will be structured around four key stages: unit cell generation, CFD model setup, CFD model validation, and unit cell optimization This established methodology, widely utilized in various fields within existing literature, provides a robust foundation for the study that follows.
Unit Cell Creation
Truss lattice unit cells are intricate structures, making the generation of diverse geometries in CAD software a time-consuming task To streamline this process, Dr D Aremu developed a MATLAB code that can automatically generate various unit cell types with different parameters (refer to Appendix A for the complete code) For this project, the code is utilized to create Body-Centered Cubic Zigzag (BCCZ) unit cells by simply inputting the desired parameters into line (2) of the code, as illustrated in Figure 5 The control parameters available for manipulation are displayed in line (1) of Figure 5 and detailed in Table 1.
Parameter Control Definition cs Unit Cell Size rad Truss Radius axis Unit Cell Type (eg BCCZ,
Fname File name of output
Line (2) in Figure 5 generates a BCCZ unit cell with a size of 10 and a truss radius of 0.7 in stl format, which lacks defined units Upon importing this file into CAD or CFD software, it is essential to establish a unit system, with millimeters being used for this study The primary variable adjusted in this research is the truss radius, which affects the porosity of the unit cell while keeping the unit cell size constant for comparison with an existing HE of the same dimensions.
This study investigates unit cells featuring a truss radius ranging from 0.5 to 1.8 mm, with increments of 0.1 mm, resulting in porosity values between 47.5% and 94.6% This extensive range allows for the identification of trends in the heat exchange performance of the structures Refer to Table 2 for the unit cells and their associated percentage porosity values.
Table 2 - Truss Radius and Porosity
Figure 5 - Lines of Code from Matlab Script
The equation below shows the calculation used to calculate the percent porosity of each unit cell quation number) (e
The dimensions of a symmetric BCCZ truss lattice unit cell, where height (H), length (L), and width (W) are equal, are illustrated in Figure 6 This configuration is known as the unit cell size, and the truss radii, as indicated in Table 2, are equivalent to D/2.
CFD Model Set- Up
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
The imported unit cell, illustrated in Figure 7, is processed by Star CCM+, which generates a triangular surface geometry mesh However, this mesh may exhibit errors and broken surfaces, assessed through various parameters including pierced faces, face quality, face proximity, free edges, non-manifold edges, and non-manifold vertices.
The unit cell is duplicated and translated 10mm in the X direction to create a 1x1x2 lattice, which transforms into a 2x2x2 lattice upon introducing symmetry planes These symmetry planes enhance geometric simplicity, reduce mesh size, and decrease computational time A thorough check of the surface mesh ensures there are no quality errors To ensure correct generation of the Volume of Interest (VOI), the faces normal to the +Y and +Z directions are extended by 1.5mm Figure 8 illustrates the completed lattice with repaired surfaces and extended faces, with views from both the +X axis (A) and +Y axis (B).
A new lattice structure will be simulated based on the optimal unit cell identified in the initial simulations This simulation will feature a 2x2x4 lattice within a 10x10x20 mm volume, allowing for an analysis of how unit cell size influences heat transfer performance.
Figure 8 - United Lattice with Extended Faces
The wind tunnel is designed as a cuboid surrounding the lattice, with contact points on the top and side faces to serve as symmetry planes As illustrated in Figure 9, the dimensions of the wind tunnel facilitate unobstructed fluid flow around the structure Additionally, ample space has been allocated in the +X direction behind the lattice to ensure the wake is fully developed, enhancing the accuracy of the simulation.
The wind tunnel's sides are divided into distinct faces, each labeled for easy identification during the setup of inlets, outlets, symmetry planes, and walls A Volume of Interest (VOI) is established to differentiate between the fluid and solid domains by subtracting the lattice volume from the total wind tunnel volume The remaining space after this subtraction represents the fluid domain, while the lattice constitutes the solid domain.
Regions and Initial Conditions
In computational fluid dynamics (CFD) simulations, defining regions is crucial for accurately modeling fluid and solid areas The volume of interest (VOI) is designated as the fluid domain, while the lattice represents the solid domain, ensuring that the software effectively distinguishes between the two for precise analysis.
In the VOI, the boundary and initial conditions are established appropriately, with the front face in the +X direction designated as a mass flow inlet and the rear face as a pressure outlet The top and left sides, when viewed from the +X direction, are configured as symmetry planes, while the right and bottom sides are defined as walls.
Table 3 Fluid Inlet Initial Conditions –
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
In a wind tunnel with a mass flow rate of 0.005 kg/s, an initial temperature of 298K, which represents room temperature, is typical for CPU cooler inlet velocities The pressure outlet is configured to gauge pressure, while the walls are designed with a slip condition to ensure they do not disrupt the fluid flow.
The interaction between solid and fluid domains occurs at an interface, facilitating heat transfer between them This interface is positioned between the outer surfaces of the lattice and the corresponding faces of the volume of interest (VOI), with conjugate heat transfer conditions applied to the solid-to-fluid heat exchanger (HE) The solid domain's initial conditions mimic an aluminum CPU cooler operating at 373K with a total power input of 80 W, translating to 5 W per unit cell (Anandakrishnan & Balaji, 2009) Additionally, truss lattice unit cells are typically produced through additive manufacturing, resulting in varying surface roughness compared to extruded aluminum heat exchangers, which is taken into account as detailed in Table 4.
Power Output 5W per unit cell
Surface Roughness height 0.01mm (Udroiu et al., 2019)
Meshing
Meshing is a crucial factor in obtaining accurate results from CFD simulations, and it is essential to set up correctly and ensure there is no mesh dependency it
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 a well suitre ed for this application
Surface Remesher Triangle, curve+ proximity refinement
Automatic Surface Repair Minimum Quality - 0.05
Polyhedral Mesher Post Mesh Optimiser active
Stretch Function - Geometric Progression, Distribution Mode - Stretch Factor ,
Gap-fill 25%, – Minimum Thickness 10%, – Layer Reduction - 50%
Basic mesh controls are essential for customizing the mesh to fit the specific size and geometry of the model being simulated As outlined in Table 6, the parameters used for the simulations in this study were carefully selected In Star CCM+, mesh parameters can be adjusted relative to a base size, enabling straightforward modifications by altering a single central parameter These settings were established following a mesh independence study to determine the optimal mesh size for accurate results.
Target Surface Size 75% of Base
Minimum Surface Size 1% of Base
Prism Layer Total Thickness 0.18 mm
Maximum Tet Size 10,000% of Base
Core Mesh optimisation 1 Cycle, Quality Threshold 0.4 –
Advanced controls are implemented to enhance mesh refinement in critical areas, particularly around the lattice and its wake By applying prism layer control to the walls, unnecessary refinement is eliminated, resulting in a reduced mesh count without compromising accuracy, as a slip condition is maintained on the walls to prevent flow interference For this simulation, volumetric control is introduced around the lattice and in the wake, with a size set to 10% of the base size, significantly increasing cell count and simulation accuracy The refined mesh is illustrated in Figure 10.
Figure 10 - Side View of Volume Mesh with Volumetric Control Applied
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
In the initial exploratory runs, wall y+ values are carefully monitored and prism layers are adjusted to ensure they fall within the acceptable range of 0-3 Following the refinement of the prism layers, as illustrated in Figure 12, these layers are established at absolute values This approach guarantees that any subsequent changes in mesh size will not impact the prism layers.
Figure 12 - Wall y+ Monitor Plot Figure 11 - Detailed View of Refined Prism Layers
Physics Models and Governing Equations
In computational fluid dynamics (CFD) studies, certain assumptions are necessary to simulate flow, as accurately replicating real-world conditions is not feasible This study adopts assumptions that align with established practices found in existing literature.
- No Heat Loss Due to Radiation
Table 7 - Applied Fluid Physics Models
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 Flow Implicit, 2 Order nd Coupled solver works better with fine meshes Gravity On (9.81m/s in - 2 Z) Applied more accurately simulate a to realistic environment
Performs well in simulations with internal fluid flows, and low pressure gradients More stable than K-Omeg a
Two-Layer 2 nd Order, Shear Driven
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 Three Dimensional On The geometry used in this model is three dimensional
Turbulent On Complex internal geometries cause turbulent flow
Table 7 outlines the physics models utilized in the fluid analysis and their justifications In this conjugate heat transfer simulation, the key focus is on the boundary between the solid and fluid, necessitating a refined mesh and suitable physics models for precise outcomes Although the K-Omega model demonstrated potential for improved results in various simulations, it lacked reliability across all scenarios, leading to the decision to employ the K-Epsilon model instead.
The CFD model developed for this study is based on the Navier-Stokes equations (NSE), which govern fluid flow and energy transfer The simulations solve a series of equations, starting with the continuity equation, followed by the X momentum equations, and similarly for the Y and Z directions, concluding with the Energy equation.
Where t Time, = Density, E Total Energy, = Stress, Re = Reynolds number and Pr = = 𝜌 = 𝜏 Prandtl Number (Navier-Stokes Equations, 2015)
Table 8 - Fluid Properties of Air Table 9 - Solid Properties of Aluminium
Table 8 and 9 above detail the properties of the fluid and solid domains used in this model
The solid domain in this model operates under constant density and coupled solid energy conditions, facilitating conjugate heat transfer This process enables energy transfer into the fluid, necessitating the application of an energy model to effectively simulate these interactions.
Exploratory Simulations
Exploratory simulations are conducted to troubleshoot and enhance the model's reliability and consistency A simulation is deemed successful when the residuals converge below 10 To achieve this, adjustments are made to prism layers, mesh size, and physics models until a final model is established that converges and operates 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
Density 2702.0 kg/m 3 Specific Heat 903.0 J/kgK Thermal
Mesh Independence Study
A mesh independence study is essential for ensuring that simulation results are not influenced by mesh size, which is critical for obtaining reliable and usable outcomes Mesh independence is achieved when variations in mesh size do not impact simulation results In this study, all mesh parameters, apart from prism layers, are adjusted relative to a base size, making it the sole parameter that requires modification for the analysis The results, illustrated in Figure 13, demonstrate the study's coverage of a mesh size range from 373,295 to 3,925,897 cells.
For this model, the results become independent around 1,200,000 cel , which ls corresponds to a base size of 1.2mm This base size will be used throughout the study.
Model Validation
Model validation is crucial for ensuring the reliability of results from CFD simulations This study's methodology is evaluated against established literature, including the research by Yang et al (2019) and the tutorials provided in the Star CCM+ user guide on Multiphysics.
Computational Fluid Dynamics (CFD) Simulation Software, 2021) The comparison to exist g in literature validates the methodology of this study
A baseline model of a typical extended surface heat exchanger was developed using the same configuration as the lattice model The geometry and results were compared with existing literature to ensure the validity of the model setup The study revealed a minimal percentage temperature difference of 0.16%.
Heat Transfer Vs Cell Count
Figure 14 - Typical Extended Surface HE Validation Model
The validation simulation of the extended surface heat exchanger (HE) conducted by Freegah et al (2020) reveals a minimal temperature difference of 0.2%, indicating a 25% variance compared to previous studies This discrepancy may arise from slight variations in model setup and initial conditions Nevertheless, the results are sufficiently close to validate the model, allowing for reliable subsequent simulations based on this baseline Figure 14 illustrates the wall y+ plot of the typical extended fin HE utilized for validating the CFD model.
The performance of the truss lattice heat exchanger (HE) is evaluated using key metrics, including the pressure drop across the lattice length, the temperature change in the fluid from the front to the rear, and the total heat energy exchanged An excessive pressure drop can hinder a typical CPU fan's ability to move sufficient air through the heat exchanger, making it crucial to measure this parameter Additionally, the temperature change and heat exchange metrics indicate the effectiveness of the lattice structure in thermal management.
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.
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
The pressure gradient across the surface of the lattice structures is illustrated in Figure 15, where the flow direction is indicated by an arrow pointing in the +X direction The color gradient, with red representing higher pressure regions and blue indicating areas below gauge pressure, facilitates the visualization of pressure effects on the lattice Images B) and C) depict the lattices with the largest and smallest truss radius, respectively Notably, Image B) reveals a significant high-pressure area on the leading face, reaching a maximum of 120.17 Pa above gauge pressure.
Figure 15 - Pressure Gradient Contour Plot
22 pressure This is supported in Figure 16 as this unit cell has the highest pressure drop of 47.5
The unit cell depicted in Image A, featuring a truss radius of 1.05 mm, exhibits optimal heat transfer performance while demonstrating average pressure drop results, consistent with the trends illustrated in Figure 16 below.
Figure 16 illustrates the correlation between percentage porosity and pressure drop, with the black line representing the 1x1x2 lattice and the blue point indicating the 2x2x4 lattice results The data supports the hypothesis up to approximately 60% porosity, beyond which the pressure drop starts to level off This plateau is believed to approach the pressure drop value of a solid block, where fluid is diverted around the object, indicating the maximum pressure drop achievable.
Figure 17 illustrates a top-down view of velocity streamlines over a 47.5% porous lattice, demonstrating fluid flow dynamics as it navigates above, below, and around the lattice structure This visual evidence supports the theory of fluid behavior in porous materials and highlights the development of turbulence, which plays a significant role in pressure loss.
The lattice with the best pressure drop performance, of 16.4Pa, is the 94.5% porous lattice This resu supports the hypothesis and is visualised in image A) of Figure 18 below Ilt t
Figure 16 Porosity (%) vs Pressure Drop (Pa) –
Figure 17 - Velocity Streamline Around 47.5% Porous Lattice
23 shows the velocity streamlines pass through the lattice with little change in velocity or direction
The investigation revealed an unexpected pressure drop of 38.7 Pa in the 2x2x4 lattice with a porosity of 21.8%, which contradicts the hypothesis that it would exhibit the highest pressure drop This pressure drop is similar to that of a lattice with a porosity of 68.5% The findings suggest that the unit cells, possessing a porosity of 78.2%, and the multiple pathways available for fluid flow contribute to this outcome Supporting this theory, Image B in Figure 18 illustrates the even distribution of velocity streamlines throughout the lattice.
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 presents temperature contour plots of the lattice structure, visually illustrating temperature distribution across both fluid and solid domains Red areas represent the highest temperatures, while blue signifies regions of fluid at the inlet temperature.
Figure 19 - Temperature Contour Plot Across Lattice and Fluid Figure 18 - Top-Down View of Velocity Streamlines Through A) 94.5% Porous Lattice and B) 2x2x4 Lattice
The hypothesis suggests that increased porosity leads to a decrease in temperature change Figure 20 provides partial support for this idea, showing a general trend of decreasing temperature change between 68.6% and 94.5% porosity However, from 68.6% to 47.5% porosity, the results indicate a contrary trend, with temperature change decreasing, which directly contradicts the original hypothesis.
Increased lattice porosity results in reduced surface area, leading to diminished temperature changes due to limited heat exchange High porosity lattices experience lower turbulence, as illustrated in Figure 21 image C, which further decreases heat transfer by reducing flow mixing and creating a larger boundary layer that inhibits effective thermal exchange.
The 2x2x4 lattice demonstrates a remarkable temperature change of 10.2 K, marking a 35% improvement over the optimal 1x1x2 lattice This finding supports the hypothesis that lower porosity correlates with higher temperature changes As illustrated in Image D) of Figure 19, the wake behind the lattice exhibits a significantly elevated temperature compared to images A), B), and C) With the largest surface area, this lattice facilitates the most effective heat exchange Additionally, Image D) in Figure 21 highlights the turbulence within the structure, which enhances heat transfer significantly.
Unit cells with porosities below 68.6% exhibit reduced temperature differences due to increased pressure drops and shorter fluid contact times This phenomenon occurs because a significant amount of fluid flows around the structures rather than through them, resulting in limited surface contact for effective heat transfer In contrast, the unit cell with 68.6% porosity and a truss radius of 1.3 mm achieves the highest temperature difference of 7.55 K, indicating its superior performance as a heat exchanger This specific design optimally balances flow interference, creating turbulence while facilitating fluid passage through the structure, enhancing overall heat exchange efficiency.
Figure 19 illustrates the temperature distribution within the solid structure, highlighting the cooling effect of the fluid on the lattice Image C reveals the most significant temperature variation, with a peak temperature notably higher than that of other lattices As the fluid flows through the lattice, its temperature rises, resulting in a reduced temperature difference between the solid and fluid, which slows down heat transfer This temperature gradient accounts for the peak temperature observed on all lattices being situated at the external trailing edge.
T em p er at u re C h an g e (K )
Figure 20 Porosity (%) vs Temperature Change – (K)
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
Figure 22 illustrates the relationship between porosity and heat transfer, suggesting that decreased porosity correlates with increased heat transfer The data supports this hypothesis for porosity levels ranging from 94.5% to 78.2%, where heat transfer increases However, from 78.2% to 47.5% porosity, a notable decrease in heat transfer is observed, contradicting the initial hypothesis.
Figure 21 - Velocity Vector Contour Plot at Plane in A) 78.2% Porous, B) 47.5% Porous, C) 94.5% Porous and D) 2x2x4
The initial analysis indicated that the optimal heat transfer occurred at a porosity of 80% To verify this finding, additional inspection points were established around this peak Subsequent simulations conducted at porosities of 78.2% and 81.8% revealed a slightly higher peak heat transfer of 11.01W at a porosity of 78.2%.
A possible explanation for the decrease in heat exchange between 78.2% and 47.5% porosity is the increased pressure drop and reduced contact time, as described in section 10.2
The porosity vs heat transfer graph in Figure 23 illustrates that the 2x2x4 lattice achieves a heat transfer rate of 18.7 W, representing a significant 69.7% improvement compared to the top-performing 1x1x2 lattice This finding aligns with the hypothesis, as the 2x2x4 lattice exhibits the lowest porosity at 21.8% while achieving the highest heat transfer This enhanced performance can be attributed to the increased surface area and the turbulent flow characteristics within the structure, as discussed in section 10.2.
Figure 22 - Porosity (%) vs Heat Exchange (W)
Figure 23 - Porosity (%) vs Heat Exchange (W) Including 2x2x4 Lattice
Reynolds Number
Figure 24 below shows the relationship between porosity and Reynolds number This graph confirms that as porosity increases, so does the turbulence verifying the explanations , made in sections 10.1, 10.2 and 10.3.
Extended Fin HE
The extended fin heat exchanger (HE) serves as a baseline for comparing the performance of truss lattice structures, achieving a total heat transfer of 10.5 W This performance is comparable to that of the 89.6% and 60.2% porous unit cells, though it is 4.6% less efficient than the top-performing unit cell Notably, the extended fin HE features a significantly lower pressure drop of 4.7 Pa, making it an ideal choice for applications with limited airflow where minimizing pressure drop is crucial.
For a fair comparison to be made, the material efficiency of the HE is considered This
The specific heat transfer of HE is measured at 10.52 W/gram, which is comparable to that of similar porous truss lattice unit cells However, it falls short by 43.7% when compared to the most efficient truss lattice, which boasts a specific heat transfer of 18.7 W/gram.
This lattice was simulated to determine what effect varying the unit cell size has on the heat transfer performance of the unit cell
The 2x2x4 lattice emerged as the most effective heat exchanger (HE) in this study, transferring 18.7 W of heat energy—69.69% more than the top-performing 1x1x2 lattice However, it also experienced a pressure drop of 38.7 Pa, which is 22.9% higher than that of the 1x1x2 lattice When compared to extended surface heat exchangers, the 2x2x4 lattice exhibited an astonishing 837% increase in pressure drop This phenomenon can be attributed to its low porosity of 21.8% and the high turbulence generated by its intricate internal structures Despite its superior heat transfer capabilities, the specific heat transfer performance of the 2x2x4 lattice is significantly lower than that of the 1x1x2 lattice unit cells, recording just 8.86 W/gram—52.6% less than the 78.2% porosity unit cell.
The findings indicate that reducing the unit cell size enhances overall heat transfer performance, aligning with the hypothesis that decreased porosity leads to improved heat transfer However, due to time and computational constraints, only one variation was explored in this study.
Figure 24 Porosity (%) vs Reynolds Number –
28 has been tested More variations will need to be tested if trends and optimum unit cell sizes are to be found.
Assumptions and Errors
CFD simulations rely on various assumptions due to the challenges of accurately replicating real-world environments, particularly regarding fluid properties and material characteristics Ideal conditions, such as constant density and thermal conductivity for solid regions, often do not reflect the inconsistencies found in additive manufacturing Additionally, geometrical and surface roughness assumptions can lead to inaccuracies in simulation results Errors in CFD software can arise from physical approximation errors linked to the chosen physics models, discretization errors from coarse meshes, and minor variations during the iterative convergence process Furthermore, inexperienced users may introduce setup errors, underscoring the importance of thorough model validation and error analysis in CFD simulations.
Heat transfer and temperature change are theoretically expected to correlate directly; however, normalized graph comparisons reveal a lack of direct correlation This discrepancy may arise from the plane averaging method employed in Star CCM+ for temperature change calculations, which averages values at a cellular level across the mesh Consequently, this mesh-dependent averaging can lead to inaccuracies in the results.
The pressure drop results utilize the same averaging method, allowing for the observation of general trends but compromising accuracy While this averaging approach does not invalidate the findings, it indicates that the temperature change and pressure drop results should not be deemed precise Consequently, the averaging method is likely the most significant source of error in this project.
N o rm al is ed V al u es
Normalised HT Normalised Temperature Change
Figure 25 - Normalised Heat transfer and Temperature Change
The findings from the heat transfer analysis reveal the total heat energy transferred into the fluid, providing a comprehensive understanding rather than an average measurement across a plane.
This study investigates the heat exchange performance of BCCZ truss lattice unit cells with varying porosity to identify the optimal unit cell design It evaluates overall heat transfer, pressure drop, and specific heat transfer performance The findings reveal that the 78.2% porosity unit cell exhibits the highest overall heat transfer performance, achieving a 4.6% improvement over the baseline extended fin heat exchanger (HE) However, this enhancement results in a pressure drop that is 26.8 Pa greater than that of the extended fin HE, making it less suitable for applications with low power fans.
The simulation of the 2x2x4 lattice indicates a significant potential for enhanced heat transfer in compact volumes, achieving 78.1% greater heat transfer compared to the baseline extended fin heat exchanger within a 10x10x20mm space This finding is particularly relevant for applications requiring high-performance compact heat exchangers, although considerations regarding mass, cost, and pressure drop are essential Notably, this lattice design has 524% more mass than a 78.2% porous unit cell of the same external volume, resulting in higher manufacturing costs Further research is necessary to comprehensively explore the impact of unit cell size on heat exchange performance, as the current study lacks the breadth to fully address this complex topic.
As a result of this study and comparisons to existing literature, recommended uses for each
For applications where cost and pressure drop are critical, but structural performance is not a priority, extended fin heat exchangers (HE) are the ideal choice These heat exchangers are produced through a cost-effective and rapid extrusion process, making them more affordable than truss lattice designs created through additive manufacturing A prime example of their application is in consumer electronics, where minimizing costs is essential.
For optimal heat exchange performance, the 78.2% porosity unit cell lattice is recommended, as it outperforms other designs in this study It offers a slight advantage in heat transfer over the extended fin heat exchanger while maintaining a significantly lower mass and superior structural integrity.
For applications where weight is a critical factor, particularly in the wing leading edges of supersonic aircraft, the 94.5% porous unit cell is highly recommended due to its impressive specific heat transfer of 70 W/kg This performance is 3.7 times greater than that of the 78.2% porous unit cell and 6.7 times higher than the extended fin heat exchanger Additionally, the 94.5% porous unit cell offers excellent specific strength and a relatively low pressure drop when compared to the 78.2% porous unit cell.
Considerations to Hypothesis and Aims
The findings of this study validate the hypothesis, demonstrating a linear correlation between pressure drop and porosity However, a plateau is observed at 60% porosity, which contradicts the initial hypothesis A detailed examination of the fluid flow reveals that the fluid behaves similarly to that around a solid cube, circulating around the outer structure.
The investigation into heat exchange and temperature changes confirms the hypothesis regarding porosity levels from 94.5% to 78.2%, but contradicts it for the range of 78.2% to 47.5% This discrepancy is attributed to fluid movement occurring around the exterior of the structure rather than passing through it.
This study successfully achieved its overall aim by systematically fulfilling the established objectives, leading to the identification of the optimal unit cell lattice within the defined scope.
Future Work
This study is limited by time and computational resources, focusing solely on one type of truss lattice To advance this research and identify the optimal truss lattice unit cell across various types, it is essential to simulate additional unit cell types and a broader range of parameters.
A range of physical experiments would be beneficial to validate this study further, as CFD software has limitations and errors associated, which ideally would be compared to real-world data
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Matlab code for unit cell creation, written by D Aremu: function [f,v] = cylin8a(cs,rad,axis,Fname)
%%%% Strut-based lattice unit cell generator
%%%% rad - radius of the struts in the unit cells
%%%% Fname - file name of the stl file to export
%%%% axis - is the axis for the strut please see the Axis.mat library
%%% for sample axis You can define you own custom axis by
%%% specifying the Cartesian coordinates of the strut in the
%%% cell in a three dimensional space Please check Axis.mat
%%% for the structure of the axis array.
%%% Example usage: cylin8a(10,1,bccz,'Unit_Cell.stl') a = 0:0.15:cs;
B = Base - Cent; u = ((sum(A.^2,2).*sum(B.^2,2)-(sum(A.*B,2)).^2)./sum(B.^2,2)) - rad^2; u = min(u,[],3); u = reshape(u,[Sq,Sq,Sq]);
[f1,v1] = isocaps(-u,0); f1 = f1 + size(v,1); f1 = [f1(:,2),f1(:,1),f1(:,3)]; f = [f;f1]; v = [v;v1]; sc = cs/(max(v(:,1))- min(v(:,1))); v=v*sc;
Fvx(:,:,3) = [v(f(:,3),1), v(f(:,3),2), v(f(:,3),3)]; tr = TriRep(f, v(:,1),v(:,2),v(:,3)); fn = faceNormals(tr);
WRITE_stlbinary(Fname,Fvx,fn) end
% - function WRITE_stlbinary(fileOUT,coordVERTICES,coordNORMALS)
%filePREFIX = fileOUT(1:end-4); % Get the prefix of the output filename