Ternary Diagram of Bithermal Systems

Year 2018, , 27 - 36, 01.03.2018

Julien Ramousse

https://doi.org/10.5541/ijot.339904

Cited By: 2

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

• [1] S. Carnot, Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance. Paris: Bachelier, 1824. (transl. Carnot NLS, Thurston RH, Reflections on the motive power of heat, and on machines fitted to develop that power. New York: John Wiley & Sons, 1897).
• [2] R. Clausius, “Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen”, Annalen der Physik, 79: 368–397, 500–524, 1850. (transl. “On the moving force of heat, and the laws regarding the nature of heat itself which are deducible therefrom”, Phil. Mag. 2, 102–119, 1851).
• [3] JP. Joule, “On the mechanical equivalent of heat”, Phil. Trans. R. Soc. 140, 61–82, 1850.
• [4] E. Clapeyron. “Mémoire sur la puissance motrice de la chaleur”, Journal de l’École Royale Polytechnique, 14: 23, 153–190, 1834. (transl. E. Clapeyron and R. Clausius, Memoir on the motive power of heat, in Reflections on the motive power of fire by S. Carnot and other papers on the second law of thermodynamics, Mineola: NY Dover Publications, 1960).
• [5] R. Mollier, Neue Diagramme zur Technischen Wärmelehre, Berlin, 1904. (transl. New Graphs for Technical Thermodynamics).
• [6] A. Bejan, Advanced Engineering Thermodynamics, 4th Ed. Hoboken: Wiley, 2016.
• [7] M. Moran, H. Shapiro. Fundamentals of engineering thermodynamics, 6th Ed. USA: John Wiley & Sons, Inc., 2008.
• [8] L. Borel, D. Favrat. Thermodynamics and Energy Systems Analysis: From Energy to Exergy, Vol. 1. Lausanne: EPFL Press, 2010.
• [9] J.-P. Pérez. Thermodynamique : Fondements et applications, Vol. 1, 3rd Ed. Paris: Dunod, 2001. [in French]
• [10] C. Lhuillier, J. Rous. Introduction à la thermodynamique. Paris: Dunod, 1992. [in French]
• [11] Wikipedia Diagramme de Raveau [Online]. Available: https://fr.wikipedia.org/wiki/Diagramme_de_Raveau (accessed Sep. 25, 2017) [in French].
• [12] G. Alefeld, R. Radermacher. Heat Conversion Systems. Boca Raton: CRC Press, 1993.
• [13] J. Ramousse. “Représentation graphique des modes opératoires des systèmes dithermes”. in SFT 2016, Proceedings of congrès annuel de la Société Française de Thermique, Toulouse, 31 May – 3 June 2016. [in French]
• [14] P. Chambadal. Les centrales nucléaires. Paris : Armand Colin, 1957. [in French]
• [15] I.I. Novikov. “The efficiency of atomic power stations (a review)”. J. Nucl. Energy II, 7, 125-128, 1958.
• [16] F. L. Curzon, B. Ahlborn. “Efficiency of a Carnot engine at maximum power output”. Am. J. Phys., 43, 22-24, 1975.