Complex 3D-Printed Heat Transfer Surfaces: An Assessment and Comparison of Tools for Implicit Geometry Modelling

Complex 3D-Printed Heat Transfer Surfaces: An Assessment and Comparison of Tools for Implicit Geometry Modelling ZÁLEŠÁK, M.; KLIMEŠ, L.; CHARVÁT, P.; ŠPILÁČEK, M. Chemical Engineering Transactions 2024, vol. 114, iss. 1, pp. 229-234 ISSN: 2283-9216 DOI: https://doi.org/10.3303/CET24114039 Final Published version Published by The Italian Association of Chemical Engineering. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/) dspace.vutbr.cz DOI: 10.3303/CET24114039 Paper Received: 24 May 2024; Revised: 4 October 2024; Accepted: 26 November 2024 Please cite this article as: Zálešák M., Klimeš L., Charvát P., Špiláček M., 2024, Complex 3D-Printed Heat Transfer Surfaces: An Assessment and Comparison of Tools for Implicit Geometry Modelling, Chemical Engineering Transactions, 114, 229-234 DOI:10.3303/CET24114039 CHEMICAL ENGINEERING TRANSACTIONS VOL. 114, 2024 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Petar S. Varbanov, Min Zeng, Yee Van Fan, Xuechao Wang Copyright © 2024, AIDIC Servizi S.r.l. ISBN 979-12-81206-12-0; ISSN 2283-9216 Complex 3D-Printed Heat Transfer Surfaces: An Assessment and Comparison of Tools for Implicit Geometry Modelling Martin Zálešáka,*, Lubomír Klimeša, Pavel Charváta, Michal Špiláčekb aDepartment of Thermodynamics and Environmental Engineering, Brno University of Technology, Technická 2896/2, 61669 Brno, Czech Republic bDepartment of Power Engineering, Brno University of Technology, Technická 2896/2, 61669 Brno, Czech Republic [email protected] In the design of heat exchangers (HXs), an obvious effort is to maximise the heat transfer efficiency and performance while keeping the dimensions and costs of HXs as low as possible. Extended surfaces are a common technique for heat transfer enhancement, leading to an enlarged surface for the interaction of heat transfer fluids. Fins represent the most frequent extended surfaces used in the HX design. In the past, the shape of fins used in HXs was rather simple due to the limited capabilities of the available production technology. However, the rapid development of additive manufacturing (AM) and 3D printing has opened new possibilities in design and production. The AM allows for the production of HXs comprising heat transfer surfaces with a complex topology, which can possess a very high surface-to-volume ratio. In this respect, triply periodic minimal surfaces (TPMS) seem to be very promising. Gyroids and lidinoids are typical examples of such TPMS. Computer simulations are a common approach in the design of HXs. Simulations of HXs with such complex surfaces are, however, challenging. In the case of computational fluid dynamics (CFD) tools, the necessary input is the computational mesh, which is closely related to the domain geometry. The creation of the domain geometry adopting TMPS is rather demanding as TMPS are defined by implicit mathematical relationships and standard computer-aided design (CAD) modellers cannot be utilised for this purpose. The study presents an assessment and comparison of available computer tools for the implicit modelling and preparation of the TPMSbased geometry with implicit modelling. The results indicate that both commercial as well open-source tools exist for this purpose, enabling different levels of flexibility and user-friendliness. 1. Introduction Heat exchangers (HXs) play crucial roles across many industries, serving to regulate temperatures and recuperate energy (Picón-Núñez et al., 2023). They are not just confined to industrial settings; they are integral to the functionality of various commercial devices, aiding in heat dispersion. Take, for instance, the cooling water systems in industrial setups, where the temperatures of both incoming hot and outgoing cold streams are of interest (Reynolds et al., 2023). On the other hand, consider the scenario of a car radiator, where optimizing the performance of the coolant (water) is paramount, while the airflow is maximized. Nevertheless, practical constraints often dictate the dimensions of these HXs. The compact design of car radiators illustrates such limitations. Improving heat exchanger efficiency can reduce their size, while saving space for additional components in compact assemblies and potentially reducing costs. This study explores innovative heat transfer geometries using triply periodic minimal surfaces (TPMS), made feasible by advancements in 3D printing technology. Through the fusion of additive manufacturing (AM) and HX design, a range of bioinspired configurations— namely, TPMS structures—emerge as promising contenders for enhancing the efficiency of HXs. TPMS trace their origins as far back as 1865, introduced by H. A. Schwarz. Presently, there exist approximately 45 distinct types of minimal surfaces (Li et al., 2022). Among these, the Schoen-Gyroid, Schwarz-Diamond, SchwarzPrimitive, and lidinoids are particularly significant in engineering applications. The geometry of select TPMS is shown in Figure 1. These structures, characterized by their periodic geometry, have been identified as highly effective in increasing surface area within a given volume, which is a critical factor in the effectiveness of heat 229 exchangers. The gyroid, a type of TPMS, for instance, offers a complex network of interconnected channels, allowing fluids to transfer heat more effectively due to increased surface contact with the material. An extensive review study by Nazir et al. (2019) revealed that the range of software packages offering design and optimization tools for AM in connection to implicit geometries is quite limited. The available tools typically feature restricted finite element analysis (FEA) capabilities, minimal options for mesh refinement, and a structure library with only a few cell topologies. A general lack of comparative analysis between different design and optimization methods was reported. In particular, there is an absence of FEA methods specifically tailored for analysing cellular structures. The study presented by Mahmoud et al. (2023) investigates the application of laser powder bed fusion (LPBF) for producing heat exchangers with gyroid-shaped channels. The research aims to leverage the complex geometrical capabilities of AM to enhance the thermal performance of HXs beyond conventional designs. The authors adopted nTopology software during the prototype development. Prototypes were fabricated using LPBF with AlSi10Mg alloy and tested to validate their performance against traditional HX designs. The findings demonstrate that gyroid-based HXs significantly outperform conventional models, highlighting the potential of AM to innovate thermal management systems. Parittothok et al. (2022) presented a study focused on the integration of TPMS structures such as Schwarz Diamond and Schwarz Primitive to optimize the flow rate and temperature distribution across a glass microfiber membrane. Analogically to the study presented by Mahmoud et al. (2023), the authors also utilised the nTopology software when creating the TPMS structures. In the research, TPMS were characterized by key parameters including the ratio of solid material to the volume of a TPMS unit cell, the length of each unit cell, the diameter of the largest sphere that fits within a TPMS unit cell, and the average thickness of the TPMS sheet structures. Reynolds et al. (2023) focused on evaluating the performance of 3D-printed HXs designed with TPMS, specifically the sheet gyroid configurations. Researchers explored the influence of design variables such as porosity, hydraulic diameters, and wall thickness on the thermal efficiency and pressure drops of these HXs. The authors adopted an in-house software package called TPMS Studio during the mesh creation process. The study demonstrated that TPMS designs, particularly those based on the sheet gyroid, significantly enhanced heat transfer capabilities as reflected by improved Nusselt numbers compared to conventional straight tube exchangers. Zheng et al. (2022) investigated 3D-printed titanium scaffolds for mandibular repair using TPMS to mimic natural bone structure, enhancing osseointegration and mechanical compatibility. Employing reverse engineering and selective laser melting, the team developed personalized scaffolds with gyroid structures, optimized through sandblasted, large-grit, and acid-etched (SLA) surface treatments. These scaffolds matched natural bone's mechanical properties, making them suitable for surgical use. The design process utilized MSLattice and Materialise software. Figure 1: Geometry of (a) Schoen-Gyroid, (b) Schwarz Diamond, and (c) Schwarz Primitive visualised in MATLAB TPMS Designer This paper focuses on assessing and comparing various tools and techniques for modelling implicit geometries that are crucial for 3D printing applications. A critical analysis of the current technologies available for designing and fabricating complex 3D-printed heat transfer surfaces is provided. This work strictly focuses on the TPMS geometry, and the tools used for its generation, without considering the effects and constraints of the manufacturing process and the material properties 230 2. Methods The mathematical description of TPMS is simple and straightforward. However, before CAD, AM, and 3D printing became available, the HXs comprising TPMS were difficult to design and manufacture. The TPMS gained popularity with the development of AM as they minimize the use of material needed for manufacturing of the structure/component. Light structures with high load-bearing capacity can be produced when utilizing TPMS (Veloso et al., 2022). These advantages of TPMS can be exploited in design of HXs produced with AM. 2.1 TPMS TPMS partition the design space into two isolated domains, each operating independently. Mathematically, this surface can be represented using implicit equations. The following equation is utilized to produce a gyroid surface: sin(2π𝑥 𝑎)cos(2π𝑦 𝑎)+sin(2π𝑦 𝑎)cos(2π𝑧 𝑎)+sin(2π𝑧 𝑎)cos(2π𝑥 𝑎)= 𝑐 , (1) where 𝑎 represents the unit cell size of the gyroid structure, and 𝑐 stands for the level constant. The parameter 𝑎 directly influences the sizes of the pores and struts, whereas the value of 𝑐 governs the relative density of the gyroids. Eq. (1) is called the level-set surface equation defined implicitly as 𝑓(𝑥,𝑦,𝑧)= 𝑐. Other combinations of period functions can be utilised to produce TPMS of different complexity. The level-set equations for various commonly used TPMS are summarised in Table 1. Table 1: Level-set equations for select TPMS TPMS Level-set equation of TPMS 𝑓(𝑥,𝑦,𝑧)= 𝑐 Schoen-Gyroid cos(𝑥)sin(𝑦)+cos(𝑦)sin(𝑧)+cos(𝑧)sin(𝑥)= 0 Schoen-IWP 2[cos(𝑥)cos(𝑦)+cos(𝑦)cos(𝑧)+cos(𝑧)cos(𝑥)]−[cos(2𝑥)+cos(2𝑦)+cos(2𝑧)]= 0 Schwarz Primitive cos(𝑥)+cos(𝑦)+cos(𝑧)= 0 Schwarz Diamond sin(𝑥)sin(𝑦)sin(𝑧)+sin(𝑥)cos(𝑦)cos(𝑧)+cos(𝑥)sin(𝑦)cos(𝑧)+ cos(𝑥)cos(𝑦)sin(𝑧)= 0 Lidinoid 0.5[sin(2𝑥)cos(𝑦)sin(𝑧)+sin(2𝑦)cos(𝑧)sin(𝑥)+sin(2𝑧)cos(𝑥)sin(𝑦)]− 0.5[cos(2𝑥)cos(2𝑦)+cos(2𝑦)cos(2𝑧)+cos(2𝑧)cos(2𝑥)]= −0.15 Fisher-Koch S cos(2𝑥)sin(𝑦)cos(𝑧)+cos(𝑥)cos(2𝑦)sin(𝑧)+sin(𝑥)cos(𝑦)cos(2𝑧)= 0 Fisher-Koch C(S) cos(2𝑥)+cos(2𝑦)+cos(2𝑧)+2[sin(3𝑥)sin(2𝑦)cos(𝑧)+cos(𝑥)sin(3𝑦)sin(2𝑧)+ sin(2𝑥)cos(𝑦)sin(3𝑧)]= 0 Fisher-Koch Y cos(𝑥)cos(𝑦)cos(𝑧)−sin(𝑥)sin(𝑦)sin(𝑧)+sin(2𝑥)sin(𝑦)+sin(𝑥)sin(2𝑦)+ sin(𝑥)sin(2𝑧)+cos(𝑥)sin(2𝑦)cos(𝑧)+cos(𝑦)sin(2𝑧)= 0 Figure 2: Lidinoid structure and MATLAB TPMS Designer UI 231 2.2 Additive manufacturing The process of creating an element through additive manufacturing involves several sequential stages. Initially, a digital three-dimensional representation of the element is crafted. This is accomplished by employing computer-aided design (CAD) software to construct the 3D geometry. Various CAD programs, both commercial and freely accessible, cater to this purpose. Once the 3D model is created, it must be translated into a format suitable for additive manufacturing. This typically involves converting the digital model into a standard tessellation language (STL) file, which describes the surface geometry of the object as a mesh of triangles. This step is crucial, especially for TPMS designs, because the quality of the mesh can significantly affect the precision and quality of the final product. The mesh needs to accurately represent the intricate curves and surfaces of the TPMS without significantly increasing the file size, which could lead to longer processing times and potential errors during printing. 2.3 Software tools for designing TPMS A wide range of commercial and freeware software tools for the design of TPMS are currently available, offering various features that cater to both industrial and academic needs. These tools provide capabilities ranging from basic visualization of TPMS geometries to advanced customization options that allow for intricate modifications based on specific design requirements or FEA. A list of investigated software tools is available in Table 2. Minisurf Minisurf is a software tool designed to operate on MATLAB Runtime, a freely available MATLAB compiler, enabling the visualization and generation of CAD files for TPMS. These files typically bear the .inp extension (filename.inp) for finite element method (FEM) analysis using Simulia Abaqus, as well as the .stl extension for AM purposes (Hsieh and Valdevit, 2020). The software includes a total of 19 different minimal surfaces, utilizing MATLAB's built-in isosurface function. This function facilitates the discretization of surfaces into sets of triangular elements, providing essential details about the connections between facets and vertices. TPMS Studio TPMS Studio is a CAD application developed by research team from Biomolecular Interaction Centre at University of Canterbury, designed for the real-time interactive creation of intricate lattice structures for 3D printing (Leung et al., 2023). The software natively supports the generation of over 30 types of TPMS and other custom unit cells, allowing for a wide range of structural optimization and biomimicry applications in various engineering fields. It facilitates the seamless conversion of these models into STL files, the standard format in the 3D printing industry (Dutkowski et al., 2022), enabling straightforward integration with various printing technologies. Moreover, TPMS Studio enhances workflow efficiency by offering direct import and export capabilities to many common MSLA (Mask Stereolithography) resin printer formats. This compatibility feature allows users to directly handle files that are specific to their printing hardware, streamlining the design to production process. nTopology nTopology, a commercial software, can define geometry by mathematical expressions (Mahmoud et al., 2023). Scripting nTopology automates the production of many geometry variations quickly and easily. It could be utilized to create HX designs featuring integrated gyroid channels. It contains a validated library of several TPMS structures, including gyroids. The software allows customization of the gyroid type, either sheet or skeletal, and offers optimization of various parameters that could influence the efficiency of gyroid-based HXs. For instance, the unit cell size of the gyroid, which likely impacts channel size, can be adjusted. The software also enables control over the gyroid's aspect ratio to achieve a stretching effect. Autodesk Netfabb Autodesk's Netfabb software provides a range of latticing modules that allow for basic control over cell parameters (Netfabb, 2024). These modules include functionalities for simple lattice infill and lattice simulation under quasistatic loads. Autodesk's Meshmixer software offers limited lattice design options, complemented by basic tools that aid in preparing and constructing AM projects. This includes STL file repair and optimization of part orientation. Materialise software Materialise 3-matic (Materialise 3-matic, 2024) and Materialise Magics (Materialise Magics, 2024) provide basic and rather limited capabilities for using lattices as infills, with users unable to adjust cell parameters like porosity or to modify the topology. 232 Freeware solutions Several free and open-source lattice generation software tools are available, offering greater flexibility for research applications compared to commercial alternatives. These include MATLAB-based standalone tools like Minisurf (Hsieh and Valdevit, 2020), TPMS Designer (Jones et al., 2021), Lattice_Karak (Raju and Onkar, 2022), Flatt Pack (Maskery et al., 2022), and MSLattice (Alketan and Abu Al-Rub, 2020), which are particularly advantageous for research due to their adaptability (Gado et al., 2024). Figure 2 illustrates the lidinoid structure alongside the user interface of the TPMS Designer software tool. Table 2: Available software tools for modelling implicit geometries Software Type Number of TPMS Licencing FEA tools Minisurf MATLAB 19 Freeware No TPSM Designer MATLAB 11* Freeware No Lattice_Karak MATLAB 12 Freeware No FLatt Pack MATLAB 8 Freeware No MSLattice MATLAB 8* Freeware No TPMS Studio In-house 30 Unspecified No nTopology In-house 6* Commercial Yes Autodesk netfabb In-house Unspecified Commercial Yes Materialise 3-matic In-house Unspecified Commercial Yes *Software allows for building customized TPMS. 3. Conclusions Based on the literature review, following conclusions about the software solutions dealing with triply periodic minimal surfaces (TPMS) were made: • A wide array of software options is available for designing graded lattices, including many free and academically licensed programs. However, advanced design and optimization software typically requires a purchase and comes with a steep learning curve, necessitating skills in areas such as FEA, programming, or data science. • The investigated software platforms offer different degree of the integration of computational methods for structural analysis and optimization, enhancing the utility of TPMS in practical applications such as biomedical implants, aerospace components, and architectural designs. • All software platforms, investigated in this paper, allow for the generation of STL file, which is considered a standard in AM and computational fluid dynamics. In case of AM, any of the presented software could be utilised. However, careful consideration is advised when using the STL for FEA purposes, as finer and more precise mesh grid is required. • Numerous tools, including commercial, free, and open-source options, have been developed for designing TPMS-based structures. In particular, FLatt Pack, Minisurf and nTopology were highlighted as being particularly versatile, adaptable, and suitable for research-oriented applications. • Devices utilizing TPMS architecture show immense potential across numerous scientific fields, primarily because of their high specific surface density, compactness, and ultralight characteristics. These properties facilitate a range of innovative research opportunities in energy conversion and efficient energy utilization, promoting advances in sectors such as renewable energy, thermal management systems, and sustainable technology development. • Further work of the authors of this paper will aim at the utilization of TPMS in high-efficiency, low pressure drop, heat exchangers. The impact of various manufacturing processes on the resulting lattice structures will be examined and analysed. Nomenclature 𝑎 – scaling factor 𝑐 – parameter governing the relative density of the gyroid 𝑥,𝑦,𝑧 – cartesian coordinates Acknowledgments This publication was supported by the project "Mechanical Engineering of Biological and Bio-inspired Systems", funded as project No. CZ.02.01.01/00/22_008/0004634 by Programme Johannes Amos Commenius, call 233 Excellent Research, and by the internal research project of Brno University of Technology, reg. no. FSI-S-238192. References Alketan O., Abu Al-Rub R., 2020, MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces. Material Design & Processing Communications, 3(6):e205. Dutkowski K., Kruzel M., Rokosz K., 2022, Review of the State-of-the-Art Uses of Minimal Surfaces in Heat Transfer. Energies, 15, 7994. Gado M.G, Al-Ketan O., Aziz M., Al-Rub R.A, Ookawara S., 2024, Triply Periodic Minimal Surface Structures: Design, Fabrication, 3D Printing Techniques, State-of-the-Art Studies, and Prospective Thermal Applications for Efficient Energy Utilization. Energy Technology, 2301287. Hsieh M.T., Valdevit L., 2020, Minisurf – A minimal surface generator for finite element modeling and additive manufacturing. Software Impacts, 6, 100026. Jones A., Leary M., Bateman S., Easton M., 2021, TPMS Designer: A tool for generating and analyzing triply periodic minimal surfaces. Software Impacts, 10, 100167. Leung J., Verwilligen V., Clarke D., Adebileje S., Latifi S., Liu H., McCane B., Reynolds B., Yun G., 2023, TMS studio. University of Canterbury, Biomolecular Interaction Centre. Li Wen., Li Wei., Yu Z., 2022, Heat transfer enhancement of water-cooled triply periodic minimal surface heat exchangers. Applied Thermal Engineering, 217, 119198. Mahmoud D., Rammohan S., Tandel S., Yakout M., Elbestawi M., Mattiello F., Paradiso S., Ching C., Zaher M., Abdelnabi M., 2023, Enhancement of heat exchanger performance using additive manufacturing of gyroid lattice structures. The International Journal of Advanced Manufacturing Technology, 126, 4021-4036. Maskery I., Parry L.A., Padrão D., Hague R.J.M., Ashcroft I.A., 2022, FLatt Pack: A research-focussed lattice design program. Additive Manufacturing, 49, 2022, 102510. Materialise 3-matic, 2024, 3D Modeling Software, <materialise.com/en/software/3-matic>, accessed: 10.6.2024. Materialise Magics, 2024, STL Editor, <materialise.com/en/software/magics>, accessed: 10.6.2024. Nazir A., Abate K. M., Kumar A., Jeng J.-Y., 2019, A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures. The International Journal of Advanced Manufacturing Technology, 104, 3489–3510. Netfabb, 2024, Additive Manufacturing and Design Software, Autodesk, <autodesk.com/products/netfabb/overview?term=1-YEAR>, accessed: 10.6.2024. Parittothok, P., Poolwech, C., Tanteng, T., Wongwiwat, J., 2022, Performance Improvement of Glass Microfiber Based Thermal Transpiration Pump Using TPMS. Micromachines, 13, 1632. Picón-Núñez M., García-Castillo J.L., Crespo-Quintanilla J.A., Minchaca-Mojica J.I., 2023, Increasing Heat Recovery in Heat Exchanger Design Using a Combined Twisted Tape and Twisted Tube Technology. Chemical Engineering Transactions, 103, 403-408. Raju S.K.K., Onkar P.S., 2022, Lattice_Karak: Lattice structure generator for tissue engineering, lightweighting and heat exchanger applications. Software Impacts, 14, 100425. Reynolds B. W., Fee C.J., Morison K. R., Holland D.J., 2023, Characterisation of Heat Transfer within 3D Printed TPMS Heat Exchangers. International Journal of Heat and Mass Transfer, 212, 124264. Veloso F., Gomes-Fonseca J., Morais P., Correia-Pinto J., Pinho A.C.M, Vilaça J.L., 2022, Overview of Methods and Software for the Design of Functionally Graded Lattice Structures. Advanced Engineering Materials, 24, 2200483. Zheng X., Duan F., Song Z., Mo H., Li Z., Song Y., Su Y., and Wang X., 2022, A TMPS-designed personalized mandibular scaffolds with optimized SLA parameters and mechanical properties. Frontiers in Materials, 9, 966031. 234