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 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 Table of Contents Acknowledgements 2 Table of Contents Table of Figures Table of Tables Nomenclature Abstract Introduction 7.1 Background 7.2 Problem Description and Scope 7.3 Aims and Objectives 7.4 Hypothesis Literature Review 8.1 Manufacturing Methods and Materials 8.2 Computational Fluid Dynamics 8.3 Existing Heat Exchangers 8.4 8.5 Industrial Applications Existing Truss Lattice Literature 10 8.6 Literature Review Closing Statements 10 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 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 Table of Figures Figure - Lattice Structure Types: BCC (A), BCCZ (B), FCC (C), FCCZ (D) (Maconachie T et al 2019) Figure - Nickel Plated Lattice from Maloney et al (2012) page 2488 Figure - Scan of SLM Truss Structures Demonstrating Surface Finish from Leary M et al (2016) page Figure - Extended Surface Heat exchanger (Kwon et al., 2020) page Figure - Lines of Code from Matlab Script 11 Figure - BCCZ Truss Lattice Unit Cell Dimensions 12 Figure - Imported Unit Cell 13 Figure - United Lattice with Extended Faces 13 Figure - 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 Table of Tables Table - Unit Cell Parameters 11 Table - Truss Radius and Porosity 11 Table – Fluid Inlet Initial Conditions 14 Table - Lattice Initial Conditions 15 Table - Applied Meshing Tools 15 Table - Basic Mesh Controls 16 Table - Applied Fluid Physics Models 18 Table - Fluid Properties of Air Table - Solid Properties of Aluminium 19 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 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 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 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 - 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 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 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 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 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 - 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 However, this may be advantageous for heat transfer applications due to the increased surface area and boundary layer disruption (Leary et al., 2016) Figure - 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 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) 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 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 - Extended Surface Heat exchanger (Kwon et al., 2020) page 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 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 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 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 𝜕𝜏𝑥𝑥 𝜕𝜏𝑥𝑦 𝜕𝜏𝑥𝑧 𝜕(𝜌𝑢) 𝜕(𝜌𝑢 ) 𝜕(𝜌𝑢𝑣) 𝜕(𝜌𝑤) + + + + =− + [ + ] 𝜕𝑦 𝜕𝑡 𝜕𝑥 𝜕𝑦 𝜕𝑧 𝜕𝑥 𝑅𝑒 𝜕𝑥 𝜕𝑧 𝜕𝑞𝑦 𝜕𝑞 𝜕𝑞 𝜕(𝜌𝑤𝐸) 𝜕(𝜌𝑣𝐸) 𝜕(𝜌𝑢𝐸) 𝜕(𝜌𝑢) 𝜕(𝜌𝑣) 𝜕(𝜌𝑤) 𝜕𝜌𝐸 − 𝑅𝑒𝑃𝑟 [ 𝜕𝑥𝑥 + 𝜕𝑦 + 𝑧 ] + + 𝜕𝑥 + 𝜕𝑦 + = − − − 𝜕𝑧 𝜕𝑡 𝜕𝑧 𝜕𝑥 𝜕𝑦 𝜕𝑧 𝜕 𝜕 𝜕 (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 - Fluid Properties of Air Fluid Properties (Air) Density Dynamic Viscosity Specific Heat Thermal Conductivity Turbulent Prandtl Number Table - 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 and 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 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 1x2 BCCZ Lattice 2x2x4 Lattice 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 1x2 BCCZ Lattice 2x2x4 Lattice 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 ... 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. .. 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. .. 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