A preliminary study on graphical method of thermodynamic process parameters under dynamic boundary conditions
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PUBLIC SUMMARY
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Novel representation of thermodynamic laws through radius rotation in a circle.
Geometric parameters effectively describe system performance at all scales.
Coupled analysis method applicable across various energy conversion devices.
New dimension enables insights into multi-energy conversion processes.
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ABSTRACT
Thermodynamic graphical methods are useful tools for visualizing thermodynamic state equations and are widely applied in the design and optimization of thermodynamic systems. However, the integration of renewable energy and thermal storage systems introduces finite heat capacity characteristics, resulting in continuous dynamic variations in system performance, which poses challenges to existing graphical methods. To accurately describe system performance under dynamic boundary conditions, this study investigates the continuous analysis characteristics of the Energy-Energy (E-E) diagram. Based on the ideal gas model, mathematical expressions for thermal and mechanical energy are derived, and systematic comparisons between E-E and Temperature (T)-Entropy (s) diagrams under finite heat capacity conditions are conducted, elucidating the intrinsic relationships among geometric parameters, initial boundary conditions, and system performance. Through parametric analysis, we reveal that increasing the initial heat reservoir temperature from 500 K to1500 K enhances the energy conversion potential, with the rotation angle increasing from 20.77° to 37.15°. Additionally, increasing the heat reservoir to cold reservoir capacity ratio results in a decreased rotation angle, indicating lower efficiency. The E-E diagram achieves visualization by analogizing energy conversion processes to the rotational motion of a radius in a circle. Compared to the T-s diagram, it employs lines and slopes instead of areas and area ratios, exhibiting advantages in analyzing varying boundary conditions. This complementary coupling provides a new perspective for describing dynamic energy conversion processes in thermodynamic systems. -
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Huang K., Huang Z., Chen R., et al. (2025). A preliminary study on graphical method of thermodynamic process parameters under dynamic boundary conditions. The Innovation Energy 2:100084. https://doi.org/10.59717/j.xinn-energy.2025.100084
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Huang K., Huang Z., Chen R., et al. (2025). A preliminary study on graphical method of thermodynamic process parameters under dynamic boundary conditions. The Innovation Energy 2:100084. https://doi.org/10.59717/j.xinn-energy.2025.100084
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Figure 1.
Principles of E-E diagram
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Figure 2.
Schematic and graphical representation of heat-work conversion process
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Figure 3.
Graphical comparison between T-s diagram and E-E diagram. Ideal working conditions
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Figure 4.
Graphical representation under different working conditions
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Figure 5.
Potential application of E-E diagram
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Figure 6.
Extension of E-E diagram
