Modified Stirling cycle thermodynamic model IPD-MSM and its application

Space nuclear energy consists of radioisotope thermoelectric generators (RTGs) and space nuclear reactors (SNRs). Unlike conventional space energy sources like solar panels, space nuclear power exhibits high energy density, larger power range, longevity and absence of orientation to the sun requirements, making it a promising energy source for future space operations. Nearly all the RTGs and SNRs utilizing space satellites and probes use static thermoelectric energy conversions, including thermionic thermoelectric conversion and thermocouples. Unfortunately, these static thermoelectric conversions have relatively low efficiency, below 10%. Therefore, high-efficiency space thermoelectric energy conversion is highly desirable, especially for large-scale space activities.

Among the available dynamic thermoelectric energy conversion methods, the Stirling cycle is highly efficient, simple and reliable. It is suitable for small- and medium-level RTGs and SNRs owing to its compact structure and modular organization. Stirling cycle thermodynamic model is commonly used to describe and predict the Stirling cycle and associated performance. To this end, developing a high-precision Stirling cycle thermodynamic model is of great significance in advancing space nuclear energy.

An ideal Stirling cycle model consists of two constant volumes and two isothermal processes. However, real processes digress from isothermal processes to produce inaccurate isothermal second-order models. Following the introduction of classical simple model to improve the actual processes involved in the Stirling cycle, several modifications have been developed. These models are derived from irreversible factors in the actual Stirling cycle, and the modifications mostly involve physical processes, such as fluid flow, heat transfer and mechanical motions. However, existing modifications are still inadequate to fully describe the irreversible Stirling cycle processes, necessitating further modifications of thermodynamic model loss mechanisms.

On this account, PhD candidate Chenhao Yang, Dr. Nailiang Zhuang, Mr. Weian Du, Dr. Hangbin Zhao and Professor Xiaobin Tang from Nanjing University of Aeronautics and Astronautics proposed a second-order adiabatic modification model, namely, Incorporated Pressure drop-modified Simple Model (IPD-MSM). This model was based on modifying the simple classical model, assuming that the total pressure loss in the Stirling cycle incorporated the friction flow loss and local loss. The thermal properties of different working fluids (He, H2 and He-Xe mixture) were analyzed and discussed. The work is currently published in the journal, Energy Conversion and Management.

The authors showed that IPD-MSM exhibited improved prediction accuracy at high-frequency and high-pressure conditions than other adiabatic models. Theoretically, H2 achieved the highest output power and thermal efficiency, although it was characterized by a severe explosion and leakage problems. Despite having relatively lower output power and thermal efficiency than He under low working pressure, the He-Xe mixture exhibited a superior performance under high working pressure.

The prediction accuracy and overall performance of the IPD-MSM model were validated by comparing it with GPU-3 Stirling engine experimental data and numerical simulation of other models. The prediction capability of the presented IPD-MSM model agreed well with the changing tendency of the data derived from the GPU-3 Stirling engine experiments. The underlying mechanism was also detailed. The added Xe that reduced non-ideal heat transfer loss exceeded the corresponding increase in the pressure loss. Under the working conditions considered in this study, the optimal mixing ratio was 2% by mole ratio of Xe.

In summary, the study and modification of irreversible losses in Stirling cycles based on a new IPD-MSM thermodynamic model was presented. The presented study provided a theoretical improvement in the prediction of free-piston Stirling engines. The characteristics and applications of the working fluids were detailed. In a statement to Advances in Engineering, the authors said their study provided useful insights that would advance the understanding of the impact of space environment and space nuclear reactors on Stirling cycle.

Chenhao Yang is a graduate student in the Department of Nuclear Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA). He received his bachelor’s degree in Energy and Power Engineering in South China University of Technology in 2020.

His current research focus on the Stirling thermoelectric conversion system of space nuclear energy. In his research field, Chenhao Yang has published 3 papers and held a patent. He won the ICONE Best Poster in 2022.

Nailiang Zhuang earned his Ph.D. in Nuclear Science and Technology from Harbin Engineering University(HEU) in 2019. He participated in a joint doctoral program at the Department of Nuclear Engineering, University of Michigan, USA, under the supervision of Prof. Annalisa Manera from 2017 to 2018. Dr. Zhuang has served as an Assistant Professor in Department of Nuclear Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA) since December 2019.

Dr. Zhuang engages in the research of reactor thermal hydraulics and space nuclear power. He is supported by the National Natural Science Foundation of China Youth Fund, Jiangsu Province Postdoctoral Research Fund, and Nanjing Science and Technology Fund for Returned Overseas Chinese, etc. He has published more than 20 papers.

Dr. Zhuang won the first prize of Jiangsu Province University Microteaching Competition in 2021. He has won the first prize in the micro-course teaching competition in Jiangsu Province in 2021.

  • Professor, Department of Nuclear Science and Technology, Nanjing University of Aeronautics and Astronautics
  • Associate Dean, College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics
  • Director, Key Laboratory of Nuclear Technology Application and Radiation Protection in Astronautics (Ministry of Industry and Information Technology)
  • Head, Interdisciplinary InnoCentre for Nuclear Technology

Professor Xiaobin Tang received his Ph.D. in Instrument science and technology from Nanjing University of Aeronautics and Astronautics (NUAA) in 2009. His Ph.D. supervisor was Chen Da, the academician of the Chinese Academy of Sciences. He continued his research as an Assistant Professor after graduation from NUAA. He became a professor in Department of Nuclear Science and Technology in 2016. From 2017, he has been the Associate Dean of the College of Materials Science and Technology, NUAA. Prof. Xiaobin Tang has also served as the director of the Key Laboratory of Nuclear Technology Application and Radiation Protection in Astronautics (Ministry of Industry and Information Technology) since 2018.

Prof. Tang’s research interest includes (1) Space Nuclear Energy Development and Energy Conversion Technology, (2) Material Irradiation Effect and New Materials for Nuclear applications, (3) Advanced Radiation Source Technology and Space Application System, (4) Radiation Detection& Measurement Method and Instruments Development, (5) Techniques and Effects of Doses in Radiological Diagnosis and Treatment. He has published over 210 papers and held more than 40 patents.

Prof. Tang teaches multiple courses in Nuclear Science and Technology. He has been awarded the national first-class undergraduate course (virtual simulation experimental teaching first-class course), the national high-quality video public course, the national excellent science micro-video works award, etc.


Yang, C., Zhuang, N., Du, W., Zhao, H., & Tang, X. (2022). Modified Stirling cycle thermodynamic model IPD-MSM and its applicationEnergy Conversion and Management, 260, 115630.

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