Ternary Diagram of Bithermal Systems

Abstract

This paper proposes an original and synthetic graphical representation of bithermal systems operation on a normed ternary diagram (q_h, q_c, w). Thanks to the normed axes, an intuitive graphical interpretation of the operating conditions is derived by using polar coordinates. The energy flow intensity involved in the system is directly linked to its distance r_M to the origin and its efficiency is only related to the angle \alpha defined in this work. Thus, the potential operating modes depending on the energy flow directions, are distributed into sectors of angle \pi/3. In addition to the potentially reversible operating modes (heat engine and heat pump modes), the two dissipative operating modes (forced heat transfer and thermal dissipation modes) are also described. Moreover, the characterization of the operating mode interfaces validates the physical continuity of the proposed description. According to the second law of thermodynamics, the operation of bithermal systems is restricted to the top half-plane bounded by the Carnot boundary (function of the reservoirs temperature ratio). Furthermore, the introduction of an unconventional definition of the energy efficiency when the hot reservoir is used as a heat sink leads to positive and below unity efficiencies in both reversible modes and negative efficiencies in both dissipative modes. In order to illustrate the use of the proposed representation, two examples are introduced: (i) operation of the classical thermodynamics cycles of Carnot, Stirling and Erricson is plotted for graphical interpretation, (ii) endoreversible (exo-irreversible) system representation helps to rediscover graphically the Chambadal/Novikov/Curzon-Ahlborn efficiency (constant energy efficiency at maximum work in heat engine mode).

Keywords

• ternary diagram,polar coordinates,bithermal systems operating modes,energy conversion efficiency

References

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