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A Systematic and Comprehensive Review on 2-D and 3-D Numerical Modelling of Stirling Engine

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Abstract

The present study summarises a comprehensive review of the simulation modelling of the Stirling engine. A Stirling engine, characterized as an external combustion engine, is versatile enough to operate on various fuels, including solar energy and waste heat. Among the different analysis approaches for the Stirling Engine, fourth-order analysis, which is Computational Fluid Dynamics (CFD) analysis, stands out as the sole method that takes into account the actual geometry of the engine. It is capable of identifying intricate gas flow patterns, as well as non-uniform pressure and temperature distributions within the engine. This results in better understanding and optimisation of the design parameters of the engine. The primary goal of this study is to compile and summarize 2D and 3D CFD simulation investigations, categorizing them based on the software employed, including ANSYS Fluent, OpenFOAM, and COMSOL. The focus will be on delineating the study type, computational domain, and the eddy viscosity models utilized for the modeling of Stirling engines. Comparison of various models and their deviation from experimental results is also listed. It was found that considering the radiation model resulted in an improvement of accuracy by 11%. The impinging effect, noted by CFD analysis, is responsible for vortex formation that improved heat transfer, resulting in a discrepancy of over 80% between the prediction of power output by the second-order method and CFD. For accuracy, simulation in full domain 3D is preferred over partial domain 3D and 2D CFD studies. However, it will require more computational resources, accurate 3D model and boundary conditions.

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References

  1. Frankel JA (2010) The Natural Resource Curse: A Survey. https://doi.org/10.3386/W15836

  2. Höök M, Tang X (2013) Depletion of fossil fuels and anthropogenic climate change—A review. Energy Policy 52:797–809. https://doi.org/10.1016/J.ENPOL.2012.10.046

    Article  Google Scholar 

  3. Bhandari B, Lee KT, Lee CS et al (2014) A novel off-grid hybrid power system comprised of solar photovoltaic, wind, and hydro energy sources. Appl Energy 133:236–242. https://doi.org/10.1016/J.APENERGY.2014.07.033

    Article  ADS  Google Scholar 

  4. Singh UR, Kumar A (2018) Review on solar Stirling engine: development and performance. Therm Sci Eng Progress 8:244–256. https://doi.org/10.1016/j.tsep.2018.08.016

    Article  Google Scholar 

  5. Sandoval OR, Caetano BC, Borges MU et al (2019) Modelling, simulation and thermal analysis of a solar dish/Stirling system: a case study in Natal, Brazil. Energy Convers Manag 181:189–201. https://doi.org/10.1016/J.ENCONMAN.2018.12.005

    Article  Google Scholar 

  6. Zayed ME, Zhao J, Elsheikh AH et al (2020) Optimal design parameters and performance optimization of thermodynamically balanced dish/Stirling concentrated solar power system using multi-objective particle swarm optimization. Appl Therm Eng 178:115539. https://doi.org/10.1016/j.applthermaleng.2020.115539

    Article  Google Scholar 

  7. Zayed ME, Zhao J, Elsheikh AH et al (2021) A comprehensive review on Dish/Stirling concentrated solar power systems: design, optical and geometrical analyses, thermal performance assessment, and applications. J Clean Prod 283:124664. https://doi.org/10.1016/j.jclepro.2020.124664

    Article  Google Scholar 

  8. Bataineh K (2022) Performance evaluation of a stand-alone solar dish Stirling system for off–grid electrification. Energy Sour Part A Recover Utilization Environ Eff 44:1208–1226. https://doi.org/10.1080/15567036.2022.2053249

    Article  Google Scholar 

  9. Guarino S, Buscemi A, Messineo A, Lo Brano V (2022) Energy and Environmental Assessment of a Hybrid Dish-Stirling concentrating Solar Power Plant. Sustainability 14:6098. https://doi.org/10.3390/su14106098

    Article  CAS  Google Scholar 

  10. Shboul B, AL-Arfi I, Michailos S et al (2021) Design and techno-economic assessment of a new hybrid system of a solar dish Stirling engine instegrated with a horizontal axis wind turbine for microgrid power generation. Energy Convers Manag 245:114587. https://doi.org/10.1016/j.enconman.2021.114587

    Article  Google Scholar 

  11. Bekele EA, Ancha VR (2022) Transient performance prediction of solar dish concentrator integrated with stirling and TEG for small scale irrigation system: a case of Ethiopia. Heliyon 8:e10629. https://doi.org/10.1016/j.heliyon.2022.e10629

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Geng D, Cui J, Fan L (2021) Performance investigation of a reverse osmosis desalination system powered by solar dish-Stirling engine. Energy Rep 7:3844–3856. https://doi.org/10.1016/j.egyr.2021.06.072

    Article  Google Scholar 

  13. Walker G (1973) The Stirling Engine. Sci Am 229:80–87. https://doi.org/10.1038/scientificamerican0873-80

    Article  CAS  Google Scholar 

  14. Walker G, Senft JR (1985) Free-Piston Stirling Engines. 23–99. https://doi.org/10.1007/978-3-642-82526-2_2

  15. Walker G (1979) ELEMENTARY DESIGN GUIDELINES FOR STIRLING ENGINES. Proc 14th Intersoc Energy Convers Eng Conf 1:1066–1068

    Google Scholar 

  16. Ben-Mansour R, Abuelyamen A, Mokheimer EMA (2017) CFD analysis of radiation impact on Stirling engine performance. Energy Convers Manag 152:354–365. https://doi.org/10.1016/j.enconman.2017.09.056

    Article  CAS  Google Scholar 

  17. Beale WT (1969) Free Piston Stirling engines - some model tests and simulations. SAE Tech Papers. https://doi.org/10.4271/690230

    Article  ADS  Google Scholar 

  18. IWAMOTO S, HIRATA K, TODA F (2001) Performance of Stirling Engines. Arranging method of experimental results and performance prediction. JSME Int J Ser B 44:140–147. https://doi.org/10.1299/jsmeb.44.140

    Article  CAS  Google Scholar 

  19. Babaelahi M, Sayyaadi H (2015) A new thermal model based on polytropic numerical simulation of Stirling engines. Appl Energy 141:143–159. https://doi.org/10.1016/J.APENERGY.2014.12.033

    Article  ADS  Google Scholar 

  20. Bataineh KM, Maqableh MF (2022) A new numerical thermodynamic model for a beta-type Stirling engine with a rhombic drive. Therm Sci Eng Progress 28:101071. https://doi.org/10.1016/J.TSEP.2021.101071

    Article  Google Scholar 

  21. Yang C, Zhuang N, Du W et al (2022) Modified Stirling cycle thermodynamic model IPD-MSM and its application. Energy Convers Manag 260:115630. https://doi.org/10.1016/J.ENCONMAN.2022.115630

    Article  CAS  Google Scholar 

  22. Qiu H, Wang K, Yu P et al (2021) A third-order numerical model and transient characterization of a β-type Stirling engine. Energy 222:119973. https://doi.org/10.1016/J.ENERGY.2021.119973

    Article  CAS  Google Scholar 

  23. Urieli I, Rallis CJ, Berchowitz DM et al (1977) Computer simulation of Stirling cycle machines. In: 12th IECEC. p Paper No. 779252

  24. Aksoy F, Solmaz H, Karabulut H et al (2016) A thermodynamic approach to compare the performance of rhombic-drive and crank-drive mechanisms for a beta-type Stirling engine. Appl Therm Eng 93:359–367. https://doi.org/10.1016/J.APPLTHERMALENG.2015.09.105

    Article  Google Scholar 

  25. Ansys Fluent | Fluid Simulation Software. https://www.ansys.com/en-in/products/fluids/ansys-fluent. Accessed 27 Apr 2023

  26. COMSOL - Software for Multiphysics Simulation. https://www.comsol.com/. Accessed 6 Nov 2023

  27. OpenFOAM. https://www.openfoam.com/. Accessed 6 Nov 2023

  28. Mahkamov K (2006) An Axisymmetric Computational Fluid Dynamics Approach to the analysis of the Working process of a Solar Stirling Engine. J Sol Energy Eng 128:45–53. https://doi.org/10.1115/1.2148979

    Article  Google Scholar 

  29. Salazar JL, Chen W-L (2014) A computational fluid dynamics study on the heat transfer characteristics of the working cycle of a β -type Stirling engine. Energy Convers Manag 88:177–188. https://doi.org/10.1016/j.enconman.2014.08.040

    Article  Google Scholar 

  30. Alfarawi S, AL-Dadah R, Mahmoud S (2016) Influence of phase angle and dead volume on gamma-type Stirling engine power using CFD simulation. Energy Convers Manag 124:130–140. https://doi.org/10.1016/j.enconman.2016.07.016

    Article  Google Scholar 

  31. Della Torre A, Guzzetti A, Montenegro G et al (2014) CFD modelling of a beta-type stirling machine. In: 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014

  32. Mohammadi MA, Jafarian A (2018) CFD simulation to investigate hydrodynamics of oscillating flow in a beta-type Stirling engine. Energy 153:287–300. https://doi.org/10.1016/j.energy.2018.04.017

    Article  Google Scholar 

  33. Abuelyamen A, Ben-Mansour R (2018) Energy efficiency comparison of Stirling engine types (α, β, and γ) using detailed CFD modeling. Int J Therm Sci 132:411–423. https://doi.org/10.1016/j.ijthermalsci.2018.06.026

    Article  Google Scholar 

  34. Chen W-L, Wong K-L, Chang Y-F (2014) A computational fluid dynamics study on the heat transfer characteristics of the working cycle of a low-temperature-differential γ-type Stirling engine. Int J Heat Mass Transf 75:145–155. https://doi.org/10.1016/j.ijheatmasstransfer.2014.03.055

    Article  Google Scholar 

  35. Almajri AK, Mahmoud S, Al-Dadah R (2017) Modelling and parametric study of an efficient alpha type Stirling engine performance based on 3D CFD analysis. Energy Convers Manag 145:93–106. https://doi.org/10.1016/j.enconman.2017.04.073

    Article  Google Scholar 

  36. Mahkamov K (2006) Design improvements to a Biomass Stirling Engine using Mathematical Analysis and 3D CFD modeling. J Energy Resour Technol 128:203–215. https://doi.org/10.1115/1.2213273

    Article  Google Scholar 

  37. Li Z, Haramura Y, Kato Y, Tang D (2014) Analysis of a high performance model Stirling engine with compact porous-sheets heat exchangers. Energy 64:31–43. https://doi.org/10.1016/j.energy.2013.11.041

    Article  Google Scholar 

  38. Cheng C-H, Chen Y-F (2017) Numerical simulation of thermal and flow fields inside a 1-kW beta-type Stirling engine. Appl Therm Eng 121:554–561. https://doi.org/10.1016/j.applthermaleng.2017.04.105

    Article  Google Scholar 

  39. Xiao G, Sultan U, Ni M et al (2017) Design optimization with computational fluid dynamic analysis of β-type Stirling engine. Appl Therm Eng 113:87–102. https://doi.org/10.1016/j.applthermaleng.2016.10.063

    Article  Google Scholar 

  40. Kuban L, Stempka J, Tyliszczak A (2019) A 3D-CFD study of a γ-type Stirling engine. Energy 169:142–159. https://doi.org/10.1016/j.energy.2018.12.009

    Article  Google Scholar 

  41. Caetano BC, Lara IF, Borges MU et al (2019) A novel methodology on beta-type Stirling engine simulation using CFD. Energy Convers Manag 184:510–520. https://doi.org/10.1016/j.enconman.2019.01.075

    Article  Google Scholar 

  42. El-Ghafour SA, El-Ghandour M, Mikhael NN (2019) Three-dimensional computational fluid dynamics simulation of stirling engine. Energy Convers Manag 180:533–549. https://doi.org/10.1016/j.enconman.2018.10.103

    Article  Google Scholar 

  43. Rogdakis E, Bitsikas P, Dogkas G, Antonakos G (2019) Three-dimensional CFD study of a β-type Stirling Engine. Therm Sci Eng Progress 11:302–316. https://doi.org/10.1016/j.tsep.2019.04.012

    Article  Google Scholar 

  44. Cheng C, Phung D (2021) Numerical and experimental study of a compact < scp > 100-W‐class β‐type Stirling engine. Int J Energy Res 45:6784–6799. https://doi.org/10.1002/er.6271

    Article  CAS  Google Scholar 

  45. Zhao W, Li R, Li H et al (2021) Numerical analysis of fluid dynamics and thermodynamics in a stirling engine. Appl Therm Eng 189:116727. https://doi.org/10.1016/j.applthermaleng.2021.116727

    Article  Google Scholar 

  46. Cheng C, Phung D (2021) Exchanging data between computational fluid dynamic and thermodynamic models for improving numerical analysis of Stirling engines. Energy Sci Eng 9:2177–2190. https://doi.org/10.1002/ese3.965

    Article  Google Scholar 

  47. (2022) ANSYS FLUENT user’s guide, 2022 R1. ANSYS Inc.

  48. (2016) ANSYS FLUENT Theory Guide., Release 17. ANSYS Inc.

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AK: Conceptualization, and supervision, Writing—review & editing, and supervision. VS: Visualization methodology, Writing—original draft and investigation.

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Correspondence to Anil Kumar.

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Singh, V., Kumar, A. A Systematic and Comprehensive Review on 2-D and 3-D Numerical Modelling of Stirling Engine. Arch Computat Methods Eng (2024). https://doi.org/10.1007/s11831-024-10080-z

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