A novel symmetry analysis methodology for general energy conversion systems

Abstract Symmetry has attracted extensive attention in the field of mathematics and physics. However, the previous studies of symmetry paid less attention to macroscopic system analysis. In this paper, the symmetry of macroscopic energy conversion systems/cycles is explored, and the symmetry analysis method is established for the first time. We found that general energy conversion systems/cycles show a certain symmetry after parameter transformations. Brayton cycle is analyzed as an example, and the potential-displacement-energy (PDE) diagram for system symmetry analysis is proposed. By establishing the specific C-P diagram (a kind of PDE diagram) to analyze the Brayton cycle, it is found that the ideal Brayton cycle has a regular symmetrical structure. When the rotational symmetry is the strongest, the maximum work is generated; and when the reflection symmetry is the strongest, the system is most efficient with constant specific heat capacity (cp). When the integral of varied cp to temperature can be decomposed into the symmetric structure of temperature along with the constraints met, cp has no effect on the intermediate maximum-work temperature, and this condition for cp is greatly broaden compared with previous literatures. Meanwhile, a more symmetrical cycle with circular-shaped structure is established with π/2 times greater of work output compared to conventional Brayton cycle, and the system efficiency is also improved due to its symmetry. By constructing the symmetrical structure, general energy conversion systems including P-V-T cycles can also be analyzed with the proposed symmetry analysis method.