Design and Thermodynamic Analysis of a Gamma Type Stirling Engine with Rhombic Drive Mechanism

Abstract

In this study, design, kinematic and thermodynamic analysis of a novel gamma type Stirling engine with rhombic drive mechanism having an output power of approximately 100 W were conducted. In the kinematic analyses, the displacement and volume changes of the piston and the displacer were calculated as a function of the rhombic gear rotation angle. A 3D model of the engine was created in Solidworks software. Pressure-volume changes of the engine were obtained at 1, 3 and 5 bar charge pressures using the isothermal approximation and nodal analysis method for 800 K hot and 300 K cold source temperatures. 14.52 J net work was obtained from the engine at a charge pressure of 5 bar using the isothermal approach. Using the nodal analysis method, 11.71 J net work, 45.05% thermal efficiency and 97.58 W output power were obtained at an engine speed of 500 rpm. In this study, the rhombic drive mechanism, commonly used in beta-type engines in the literature, has been adapted to a novel gamma-type Stirling engine. The externally heated Stirling engine designed and analyzed in this study, could be used for electricity generation using solar energy or waste heat, and small-scale irrigation.

Keywords

• Gamma type Stirling engine
• Rhombic mechanism
• Engine design
• Kinematic analysis
• Thermodynamic analysis

Ethical Statement

I declare that all processes of this study comply with research and publication ethics, and that I have adhered to ethical rules and principles of scientific citation.

Gama Tipi Rombik Mekanizmalı Bir Stirling Motorunun Tasarımı ve Termodinamik Analizi

Abstract

Bu çalışmada yaklaşık 100 W çıkış gücüne sahip, gama tipi rombik hareket mekanizmalı özgün bir Stirling motorunun tasarımı, kinematik ve termodinamik analizleri yapılmıştır. Kinematik analizlerde rombik dişli dönüş açısına bağlı olarak piston ve yer değiştirme pistonunun, yer değiştirme ve hacim değişimleri hesaplanmıştır. Solidworks programında motorun 3 boyutlu modeli oluşturulmuştur. 800 K sıcak ve 300 K soğuk kaynak sıcaklıkları için izotermal yaklaşımı ve nodal analiz yöntemi ile 1, 3 ve 5 bar şarj basınçlarında motorun basınç-hacim değişimleri elde edilmiştir. Motordan 5 bar şarj basıncında izotermal yaklaşımı ile 14,52 J net iş elde edilmiştir. Nodal analiz metodu ile 11,71 J net iş ve 500 rpm motor hızı için 97,58 W çıkış gücü ve %45,05 termik verim elde edilmiştir. Literatürde beta tipi motorlarda yaygın olarak kullanılan rombik hareket mekanizması bu çalışmada özgün bir gama tipi Stirling motoruna uyarlanmıştır. Bu çalışmada tasarımı ve analizleri yapılan dıştan ısı vermeli Stirling motorunun güneş enerjisinden veya atık ısıdan faydalanarak elektrik üretimi ve küçük ölçekli sulama gibi amaçlarla kullanılması hedeflenmektedir.

Keywords

• Gama tipi Stirling motoru
• Rombik mekanizma
• Motor tasarımı
• Kinematik Analiz
• Termodinamik analiz

Ethical Statement

Çalışmanın tüm süreçlerinin araştırma ve yayın etiğine uygun olduğunu, etik kurallara ve bilimsel atıf gösterme ilkelerine uyduğumu beyan ederim.

References

1. [1] Al-Nimr M, Khashan SA, Al-Oqla H. Novel techniques to enhance the performance of Stirling engines integrated with solar systems. Renewable Energy. 2023; 202: 894-906.
2. [2] Wang K, Sanders SR, Dubey S, Choo FH, Duan F. Stirling cycle engines for recovering low and moderate heat: A review. Renewable and Sustainable Energy Reviews. 2016; 62: 89-108.
3. [3] Schneider T, Müller D, Karl J. A review of thermochemical biomass conversion combined with Stirling engines for the small-scale cogeneration of heat and power. Renewable and Sustainable Energy Reviews. 2020; 134: 110288.
4. [4] Yang HS, Ali MA, Teja KVR, Yen YF. Parametric study and design optimization of a kW-class beta type Stirling engine. Applied Thermal Engineering. 2022; 215: 119010.
5. [5] Wang H, Chen Y, Luo J, Zhang L, Kang H, Luo E, Zhu S. A novel high-power free-piston Stirling engine generator with integrated heat pipes for thermal-to-electric conversion of clean energy. Energy. 2025; 314: 134218.
6. [6] Kongtragool B, Wongwises S. A review of solar-powered Stirling engines and low temperature differential Stirling engines. Renewable and Sustainable Energy Reviews. 2003; 7: 131-154.
7. [7] Phan TQ. Investigation on solar-powered low-temperature Stirling motor. International Journal of Innovative Research in Science, Engineering and Technology. 2017; 6: 21008-21013.
8. [8] Yang HS, Cheng CH. Development of a beta-type Stirling engine with rhombic-drive mechanism using a modified non-ideal adiabatic model. Applied Energy. 2017; 200; 62-72.

9. [9] Electricity and heat production from biogas CHP: discover technologies, https://biogasworld.com/news/biogas-chp-discover-technologies/, Erişim tarihi: 30.12.2025.
10. [10]Wazed SM, Hughes BR, O’Connor D, Calautit JK. Solar driven irrigation systems for remote rural farms. Energy Procedia. 2017; 142: 184-191.
11. [11]Wazed SM, Hughes BR, O’Connor D, Calautit JK. A review of sustainable solar irrigation systems for Sub-Saharan Africa. Renewable and Sustainable Energy Reviews. 2018; 81: 1206-1225.
12. [12]Chen WL, Wong KL, Po LW. A numerical analysis on the performance of a pressurized twin power piston gamma-type Stirling engine. Energy Conversion and Management. 2012; 62: 84-92.
13. [13]NASA Tests New Heat Source Fuel for Deep Space Exploration, https://www.nasa.gov/humans-in-space/nasa-tests-new-heat-source-fuel-for-deep-space-exploration/, Erişim tarihi: 30.12.2025.
14. [14]De Moura EF, Henriques IB, Ribeiro GB. Thermodynamic-dynamic coupling of a Stirling engine for space exploration. Thermal Science and Engineering Progress. 2022; 32: 101320.
15. [15]Yang HS, Zhu HQ, Xiao XZ. Comparison of the dynamic characteristics and performance of beta-type Stirling engines operating with different driving mechanisms. Energy. 2023; 275: 127535.
16. [16]Li R, Grosu L, Li W. New polytropic model to predict the performance of beta and gamma type Stirling engine. Energy. 2017; 128: 62-76.
17. [17]Alfarawi S, Al-Dadah R, Mahmoud S. Enhanced thermodynamic modelling of gamma-type Stirling engine. Applied Thermal Engineering. 2016; 106: 1380-1390.
18. [18]Ntegmi GJB, Ninkam GM, Lanzetta F, Sapnken FE, Fateh MO, Pomou BFK, Tchinda R. Energy optimization of a dish/Stirling solar system for electricity generation. Results in Engineering. 2026; 29: 108501.
19. [19]Ergin T. Experimental optimization of displacer working gap in a gamma-type Stirling engine. Engineering Science and Technology, an International Journal. 2024; 52: 101677.
20. [20]Cheng CH, Yang HS, Keong L. Theoretical and experimental study of a 300-W beta-type Stirling engine. Energy. 2013; 59: 590-599.
21. [21]Topgül T, Okur M, Şahin F, Çınar C. Experimental investigation of the effects of hot-end and cold-end connection on the performance of a gamma type Stirling engine. Engineering Science and Technology, an International Journal. 2022; 36: 101152.
22. [22]Karabulut H, Yücesu HS, Çınar C, Aksoy F. An experimental study on the development of a β-type Stirling engine for low and moderate temperature heat sources. Applied Energy. 2009; 86: 68-73.
23. [23]Topgül T. Design, manufacturing, and thermodynamic analysis of a gamma-type Stirling engine powered by solar energy. Strojniški Vestnik - Journal of Mechanical Engineering. 2022; 68: 757-770.
24. [24]Cinar C, Solmaz H, Ipci D, Yılmaz E, Aksoy F. Performance enhancement of a beta type rhombic drive Stirling engine. International Journal of Green Energy. 2020; 17: 884–893.
25. [25]Aksoy F, Solmaz H, Karabulut H, Cinar C, Ozgoren YO, Polat S. A thermodynamic approach to compare the performance of rhombic-drive and crank-drive mechanisms for a beta-type Stirling engine. Applied Thermal Engineering. 2026; 93: 359-367.
26. [26]Aksoy F, Cinar C. Thermodynamic analysis of a beta-type Stirling engine with rhombic drive mechanism. Energy Conversion and Management. 2013; 75: 319-324.
27. [27]Salih SA, Aljashaami BA, Alwan NT, Quasim MA, Shcheklein SE, Velkin VI. Isothermal thermodynamic analysis investigation of the Stirling engine types (alpha, beta, gamma): A theatrical study. Materials Today: Proceedings. Article in Press, 2023.
28. [28]Kwasi-Effah CC, Obanor AI, Aisien FA, Ogbeide O. Review of existing models for Stirling engine performance prediction and the paradox phenomenon of the classical Schmidt isothermal model. International Journal of Energy and Sustainable Development. 2016; 1: 6-12.
29. [29]Chmielewski A, Gumiński R, Maczak J. Analysis of isothermal thermodynamic processes in the Stirling engine. Proceedings of the Institute of Vehicles, Zeszyty Naukowe Instytutu Pojazdów. 2016; 106: 21-29.
30. [30]Karabulut H, Düzgün M, Topgül T. Üç silindirli gama tipi bir Stirling motorunun ve geleneksel gama tipi bir Stirling motorunun nodal termodinamik analizleri ve performans kıyaslaması. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi. 2023; 38: 45-56.
31. [31]Garcia MT, Trujillo EC, Godino JAV, Martinez DS. Thermodynamic model for performance analysis of a Stirling engine prototype. Energies. 2018; 11: 1-25.
32. [32]Solmaz H, Karabulut H. Performance comparison of a novel configuration of beta-type Stirling engines with rhombic drive engine. Energy Conversion and Management. 2014; 78: 627-633.
33. [33]Karabulut H, Aksoy F, Öztürk E. Thermodynamic analysis of a β type Stirling engine with displacer driving mechanism by means of a lever. Renewable Energy. 2009; 34: 202-208.
34. [34]Aksoy F, Solmaz H, Çinar C, Karabulut H. 1.2 kW beta type Stirling engine with rhombic drive mechanism. International Journal of Energy Research. 2017; 41: 1310-1321.