| | | |

## Ternary Diagram of Bithermal Systems

#### Julien Ramousse [1]

##### 83 105

This paper proposes an original and synthetic graphical representation of bithermal systems operation on a normed ternary diagram (qh, qc, 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 rM 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).

ternary diagram, polar coordinates, bithermal systems operating modes, energy conversion efficiency
• [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.
Birincil Dil en Mühendislik Regular Original Research Article Orcid: 0000-0001-7367-7440Yazar: Julien RamousseÜlke: France
 Bibtex @araştırma makalesi { ijot339904, journal = {International Journal of Thermodynamics}, issn = {1301-9724}, eissn = {2146-1511}, address = {Yaşar DEMİREL}, year = {2018}, volume = {21}, pages = {27 - 36}, doi = {10.5541/ijot.339904}, title = {Ternary Diagram of Bithermal Systems}, key = {cite}, author = {Ramousse, Julien} } APA Ramousse, J . (2018). Ternary Diagram of Bithermal Systems. International Journal of Thermodynamics, 21 (1), 27-36. DOI: 10.5541/ijot.339904 MLA Ramousse, J . "Ternary Diagram of Bithermal Systems". International Journal of Thermodynamics 21 (2018): 27-36 Chicago Ramousse, J . "Ternary Diagram of Bithermal Systems". International Journal of Thermodynamics 21 (2018): 27-36 RIS TY - JOUR T1 - Ternary Diagram of Bithermal Systems AU - Julien Ramousse Y1 - 2018 PY - 2018 N1 - doi: 10.5541/ijot.339904 DO - 10.5541/ijot.339904 T2 - International Journal of Thermodynamics JF - Journal JO - JOR SP - 27 EP - 36 VL - 21 IS - 1 SN - 1301-9724-2146-1511 M3 - doi: 10.5541/ijot.339904 UR - http://dx.doi.org/10.5541/ijot.339904 Y2 - 2018 ER - EndNote %0 International Journal of Thermodynamics Ternary Diagram of Bithermal Systems %A Julien Ramousse %T Ternary Diagram of Bithermal Systems %D 2018 %J International Journal of Thermodynamics %P 1301-9724-2146-1511 %V 21 %N 1 %R doi: 10.5541/ijot.339904 %U 10.5541/ijot.339904 ISNAD Ramousse, Julien . "Ternary Diagram of Bithermal Systems". International Journal of Thermodynamics 21 / 1 (Mart 2018): 27-36. http://dx.doi.org/10.5541/ijot.339904