Investigation of the effective thermal conductivity of materials based on triply periodic minimal surfaces of the Diamond, Gyroid, and Fisher–Koch S types

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The article investigates the thermal conductivity properties of lattices based on the topology of triply periodic minimal surfaces (TPMS) such as Gyroid, Diamond, and Fisher–Koch S. Using numerical and experimental methods, empirical relationships were established between the effective thermal conductivity of these structures and their geometric parameters as well as the properties of the base material. The derived relationship allows for the creation of materials with specified thermal conductivity characteristics. The advantages and disadvantages of TPMS structures for implementation as fins in heat exchange devices were identified. The Fisher–Koch S structure can be considered for use as heat exchanger fins, as it demonstrates the highest surface area, effective thermal conductivity, and minimal stagnant zones among the TPMS considered. With equal surface period and lattice thickness, the Fisher–Koch S structure shows 39% higher thermal conductivity compared to Diamond and 96% higher compared to Gyroid.

Full Text

Restricted Access

About the authors

D. M. Bragin

Samara State Technical University

Author for correspondence.
Email: dimabragin2204@yandex.ru
Russian Federation, Samara

A. V. Eremin

Samara State Technical University

Email: dimabragin2204@yandex.ru
Russian Federation, Samara

References

  1. Liu P. et al. Experimental study on the thermal-hydraulic performance of a tube-in-tube helical coil air–fuel heat exchanger for an aero-engine // Energy, 2023. V. 267. P. 126626.
  2. Ma Z. et al. Shading effect and energy-saving potential of rooftop photovoltaic on the top-floor room // Solar Energy. 2023. V. 265. P. 112099.
  3. Fan Z. et al. Investigation on heat transfer enhancement of phase change material for battery thermal energy storage system based on composite triply periodic minimal surface // Journal of Energy Storage. 2023. V. 57. P. 106222.
  4. Fan Z., Gao R., Liu S. Thermal conductivity enhancement and thermal saturation elimination designs of battery thermal management system for phase change materials based on triply periodic minimal surface // Energy. 2022. V. 259. P. 125091.
  5. Видин Ю.В., Злобин В.С. Нелинейная нестационарная теплопроводность плоского тела // Известия Российской академии наук. Энергетика. 2020. № 6. С. 76–80.
  6. Видин Ю.В., Казаков Р.В. Расчет температурного поля в плоском ламинарном потоке жидкости, обогреваемом с одной стороны // Известия Российской академии наук. Энергетика. 2022. № 6. С. 64–67.
  7. Зудин Ю.Б., Уртенов Д.С., Устинов В.С. Анализ сопряженной задачи “испарение-теплопроводность” // Изв. РАН. Энергетика. 2020. № 1. С. 138–158.
  8. Tsai Y.C., Liu F.B., Shen P.T. Investigations of the pressure drop and flow distribution in a chevron-type plate heat exchanger // International communications in heat and mass transfer. 2009. V. 36. № 6. P. 574–578.
  9. Gürel B. et al. Investigation on flow and heat transfer of compact brazed plate heat exchanger with lung pattern // Applied Thermal Engineering. 2020. V. 175. P. 115309.
  10. Attarzadeh R., Attarzadeh-Niaki S. H., Duwig C. Multi-objective optimization of TPMS-based heat exchangers for low-temperature waste heat recovery // Applied Thermal Engineering. 2022. V. 212. P. 118448.
  11. Kaur I., Singh P. Critical evaluation of additively manufactured metal lattices for viability in advanced heat exchangers // International Journal of Heat and Mass Transfer. 2021. V. 168. P. 120858.
  12. Lotfi B., Sunden B.A. A novel trussed fin-and-elliptical tube heat exchanger with periodic cellular lattice structures // International Journal of Numerical Methods for Heat & Fluid Flow. 2022. V. 33. № 3. P. 1076–1115.
  13. Yeranee K., Rao Y. A review of recent investigations on flow and heat transfer enhancement in cooling channels embedded with triply periodic minimal surfaces (TPMS) // Energies. 2022. V. 15. № 23. P. 8994.
  14. Qureshi Z. A. et al. Heat transfer performance of a finned metal foam-phase change material (FMF-PCM) system incorporating triply periodic minimal surfaces (TPMS) // International Journal of Heat and Mass Transfer. 2021. V. 170. P. 121001.
  15. Han L., Che S. An overview of materials with triply periodic minimal surfaces and related geometry: from biological structures to self‐assembled systems // Advanced Materials. 2018. V. 30. № 17. P. 1705708.
  16. Rathore S.S. et al. Flow characterization in triply periodic minimal surface (TPMS)-based porous geometries: Part 1 – Hydrodynamics // Transport in Porous Media. 2023. V. 146. № 3. P. 669–701.
  17. Брагин Д.М., Мустафин Р.М., Попов А.И., Зинина С.А., Еремин А.В. Исследование аэродинамических процессов в пористых материалах на основе трижды периодических минимальных поверхностей // Известия высших учебных заведений. Проблемы энергетики. 2024. Т. 26. № 5. С. 66–78.
  18. Attarzadeh R., Rovira M., Duwig C. Design analysis of the “Schwartz D” based heat exchanger: A numerical study // International Journal of Heat and Mass Transfer. 2021. V. 177. P. 121415.
  19. Kus K. et al. Numerical and experimental investigation of the gyroid heat exchanger // International Journal of Heat and Mass Transfer. 2024. V. 231. P. 125882.
  20. Wang J. et al. Investigation on flow and heat transfer in various channels based on triply periodic minimal surfaces (TPMS) // Energy Conversion and Management. 2023. V. 283. P. 116955.
  21. Bragin D.M., Popov A.I., Eremin A.V. The thermal conductivity properties of porous materials based on TPMS // International Journal of Heat and Mass Transfer. 2024. V. 231. P. 125863.
  22. Wohlgemuth M. et al. Triply periodic bicontinuous cubic microdomain morphologies by symmetries // Macromolecules. 2001. V. 34. № 17. P. 6083–6089.
  23. Blanquer S.B.G. et al. Surface curvature in triply-periodic minimal surface architectures as a distinct design parameter in preparing advanced tissue engineering scaffolds // Biofabrication. 2017. V. 9. № 2. P. 025001.
  24. Michielsen K., Kole J.S. Photonic band gaps in materials with triply periodic surfaces and related tubular structures // Physical Review B. 2003. V. 68. № 11. P. 115107.
  25. Rajagopalan S., Robb R.A. Schwarz meets Schwann: design and fabrication of biomorphic and durataxic tissue engineering scaffolds // Medical image analysis. 2006. V. 10. № 5. P. 693–712.
  26. Callens S.J.P. et al. Decoupling minimal surface metamaterial properties through multi‐material hyperbolic tilings // Advanced Functional Materials. 2021. V. 31. № 30. P. 2101373.
  27. Feng J. et al. Triply periodic minimal surface (TPMS) porous structures: from multi-scale design, precise additive manufacturing to multidisciplinary applications // International Journal of Extreme Manufacturing. 2022. V. 4. № 2. P. 022001.
  28. Yoo D. J. Porous scaffold design using the distance field and triply periodic minimal surface models // Biomaterials. 2011. V. 32. № 31. P. 7741–7754.
  29. Vijayavenkataraman S., Kuan L.Y., Lu W.F. 3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants // Materials & Design. 2020. V. 191. P. 108602.
  30. Hsieh M.T., Valdevit L. Minisurf – A minimal surface generator for finite element modeling and additive manufacturing // Software Impacts. 2020. V. 6. P. 100026.
  31. Jones A. et al. TPMS designer: A tool for generating and analyzing triply periodic minimal surfaces // Software Impacts. 2021. V. 10. P. 100167.
  32. Hsieh M. T., Valdevit L. Update (2.0) to Minisurf — A minimal surface generator for finite element modeling and additive manufacturing // Software Impacts. 2020. V.6. P. 100035.
  33. Zhang Y., Hsieh M.T., Valdevit L. Mechanical performance of 3D printed interpenetrating phase composites with spinodal topologies // Composite Structures. 2021. V. 263. P. 113693.
  34. Zhang Y. Mechanical Properties of Architected Materials with Spinodal Topologies: An Experimental Investigation. University of California, Irvine, 2021.
  35. Hsieh M.T., Begley M.R., Valdevit L. Architected implant designs for long bones: Advantages of minimal surface-based topologies // Materials & Design. 2021. V. 207. P. 109838.
  36. Brakke K.A. The surface evolver // Experimental mathematics. 1992. V. 1. № 2. P. 141–165.
  37. Brakke K.A. Surface evolver manual // Mathematics Department, Susquehanna Univerisity, Selinsgrove, PA. 1994. V. 17870. № 2.24. P. 20.
  38. Lee D.W., Khan K.A., Al-Rub R.K.A. Stiffness and yield strength of architectured foams based on the Schwarz Primitive triply periodic minimal surface // International Journal of Plasticity. 2017. V. 95. P. 1–20.
  39. Ma Q. et al. Elastically-isotropic open-cell minimal surface shell lattices with superior stiffness via variable thickness design // Additive Manufacturing. 2021. V. 47. P. 102293.
  40. Dalaq A.S., Abueidda D.W., Al-Rub R.K.A. Mechanical properties of 3D printed interpenetrating phase composites with novel architectured 3D solid-sheet reinforcements // Composites Part A: Applied Science and Manufacturing. 2016. V. 84. P. 266–280.
  41. Catchpole-Smith S. et al. Thermal conductivity of TPMS lattice structures manufactured via laser powder bed fusion // Additive Manufacturing. 2019. V. 30. P. 100846.
  42. Zhou Z. et al. Effective Thermal Conductivity and Heat Transfer Characteristics of a Series of Ceramic Triply Periodic Minimal Surface Lattice Structure // Advanced Engineering Materials. 2023. V. 25. № 17. P. 2300359.
  43. Карташов Э.М., Крылов С.С. Новые аналитические решения математических моделей теплового удара локально-неравновесного теплообмена // Изв. РАН. Энергетика. 2023. № 6. С. 44–60.
  44. Карташов Э.М., Кудинов И.В., Кудинов В.А. Новые модельные представления нестационарного теплообмена // Изв. РАН. Энергетика. 2019. № 4. С. 67–74.
  45. Видин Ю.В., Злобин В.С. К расчету нестационарного температурного поля цилиндрического тела // Изв. РАН. Энергетика. 2023. № 1. С. 51–56.
  46. Кротов Г.С. Аналитическое решение и функция Грина первой краевой задачи нестационарной теплопроводности в ограниченной области с границей, движущейся по корневой зависимости // Изв. РАН. Энергетика. 2021. № 1. С. 149–160.
  47. Chen F. et al. Heat transfer efficiency enhancement of gyroid heat exchanger based on multidimensional gradient structure design // International Communications in Heat and Mass Transfer. 2023. V. 149. P. 107127.
  48. Tang W. et al. Analysis on the convective heat transfer process and performance evaluation of Triply Periodic Minimal Surface (TPMS) based on Diamond, Gyroid and Iwp // International Journal of Heat and Mass Transfer. 2023. V. 201. P. 123642.
  49. Yan G. et al. Simulation and experimental study on flow and heat transfer performance of sheet-network and solid-network disturbance structures based on triply periodic minimal surface // International Journal of Heat and Mass Transfer. 2024. V. 219. P. 124905.
  50. Qian C. et al. Experimental investigation on heat transfer characteristics of copper heat exchangers based on triply periodic minimal surfaces (TPMS) // International Communications in Heat and Mass Transfer. 2024. V. 152. P. 107292.
  51. Liang D. et al. Design, flow characteristics and performance evaluation of bioinspired heat exchangers based on triply periodic minimal surfaces // International Journal of Heat and Mass Transfer. 2023. V. 201. P. 123620.
  52. Bragin D.M., Popov A.I., Eremin A.V. Effective Thermal Conductivity of Porous Material Based on TPMS // 2023 5th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA). IEEE, 2023. P. 965–968.
  53. Baobaid N. et al. Fluid flow and heat transfer of porous TPMS architected heat sinks in free convection environment // Case Studies in Thermal Engineering. 2022. V. 33. P. 101944.
  54. Yan G. et al. Experimental study on flow and heat transfer performance of triply periodic minimal surface structures and their hybrid form as disturbance structure // International Communications in Heat and Mass Transfer. 2023. V. 147. P. 106942.
  55. Popov A.I., Eremin A.V., Kechin N.N. Study of heat and mass transfer in a channel with fins based on a triply periodic minimal surface // Urban construction and architecture. 2023. V. 13. № 4. P. 49–56.
  56. Bragin D., Karpilov I., Pashchenko D. Flow dynamics through cellular material based on a structure with triply periodic minimal surface // Chemical Engineering Science. 2024. С. 120291.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Surface area of ​​one unit cell based on the Fisher–Koch S (FKS), Diamond (D), Gyroid (G), Primitive(P), Neovius(N) and Schoen’s I-WP (IWP) surfaces with geometric parameters “𝑎” = 5 mm, “δ” = 0.3 mm.

Download (178KB)
Indexing metadata
3. Table 1.1

Download (68KB)
Indexing metadata
4. Table 1.2

Download (83KB)
Indexing metadata
5. Table 1.3

Download (72KB)
Indexing metadata
6. Fig. 2. CAE modeling: (a) mesh sensitivity analysis; (b) FKS model with given boundary conditions.

Download (206KB)
Indexing metadata
7. Fig. 3. Full-scale experiment: (a) Schematic diagram of the laboratory setup ITP-MG “100”; (b) Experimental samples based on TPMS types Diamond (1–3), Fisher–Koch S (4–6), Gyroid (7–9).

Download (250KB)
Indexing metadata
8. Table 2.1

Download (41KB)
Indexing metadata
9. Table 2.2

Download (49KB)
Indexing metadata
10. Table 2.3

Download (37KB)
Indexing metadata
11. Fig. 4. Heat flow distribution: (a) Diamond-based design; (b) Gyroid-based design; (c) Fisher–Koch S-based design.

Download (225KB)
Indexing metadata
12. Fig. 5. Distribution of effective thermal conductivity of Diamond, Gyroid, Fisher–Koch S structures made of PHP material.

Download (155KB)
Indexing metadata
13. Fig. 6. Effective thermal conductivity of TPMS-based structures made of PHP, Hastelloy-X [41], Ti6Al4V [41], 3YSZ [42] materials, obtained during CFD modeling and a full-scale experiment.

Download (437KB)
Indexing metadata

Copyright (c) 2025 Российская академия наук