The notion of exergy, also called availability, was introduced at the end 19th century by Georges Gouy. This concept merge both the first and second law of thermodynamics and then allow to take into account the amount of energy transfer during a process but also the quality of this energy transfer. The exergy could be physically defined as the maximum mechanical work that a system could provide during a transformation between a thermodynamic state and a reference state. This means if a system is in thermodynamic non-equilibrium compared to the ambiance, the maximum work it could provide to reach back ambient conditions is the exergy; the difference between the achieved work and the exergy between the two states being the losses or irreversibilities. In this case, the exergy is positive; a negative exergy meaning that work should be provided to the system to reach back the reference state. Exergy is a state function and is defined as

e = (h — h°)-T0 (s — s0) (9

de = dh — T0ds

the indexes "0" referring to the reference state. For driving cycles, the reference state is conventionally the standard conditions, T0 = 15°C, P0 = 1bar. In addition, in the case of vapor evolving in a closed system, the only equilibrium condition compared to the ambient is the temperature condition. Indeed at equilibrium the system will reach the same temperature than the

ambient. However the equilibrium pressure will be the saturation pressure. For such system the reference state is T0 = 15°C, P0 = Psat (T0 ) . For driving cycle this definition is convenient since

this reference temperature is closed to the cold source temperature of the cycle, providing a very small or almost zero exergy loss at the condenser. Indeed, even though a large amount of energy is lost to the ambient, the quality of this energy is quite poor.

In our trithermal air-conditioning cycle, the hot source is the hot water previously heated up by solar collectors. The useful effect occurs at the cold source e. g. the water to cool down (for room air-conditioning) while the sum of those two previous heat quantity is discharged to the ambient through the condenser which is the medium temperature source of the cycle. Similarly to what happens at the condenser for a driving cycle, this significant amount of energy has a poor quality in regards to the targeted effect (cool down compared to ambient). Consequently, an almost zero exergy loss should be requested at this component. In addition the useful effect at evaporator occurs close to 15°C (tow — tiw «12 -18) providing an almost zero exergy variation for cooled

water and almost 100% of losses at the evaporator. All these conditions show that the usual reference state for driving cycles is not suited to air-conditioning cycles. Consequently in this study the reference temperature will be the ambient temperature Tciw at the condenser side. For the refrigeration cycle, the reference pressure will be the saturation pressure at T0 for propane and for secondary cycles (generator, condenser, evaporator) it is the atmospheric pressure (P0 = 1bar).

From an energy point of view the quality of a compression air-conditioning cycle is determined by the global COP as

COP = Qe (10)

comp, global p

1 comp, a

For an ejector based air-conditioning cycle this global COP would then be:

COP, c„b,, = P &+ Q (II)

pump, a sol

With subscript “a” for “absorbed” and Qsol the useful thermal power received by collectors.

However it could be convenient to define cycle based COP in order to eliminate mechanical efficiencies of components which may change significantly according the technology, power, etc…, and also to eliminate the source of heat supply. Indeed, in the proposed cycle solar collector are used to heat up the water but other low grade energy sources could be used to provide this energy; and in this case the way of calculating the energy transfer between the water and a source would be different or it would use very different efficiencies. Consequently to be more general, the concept of cycle based COP is used in this analysis:

COPcomp = PQ^ (12)

comp

Qe
COP = e P	(13)
-Qw. g + Qw

These purely energy criteria are not satisfactory to make a relevant comparison between both systems. Indeed for the compression system the energy input is purely mechanical and then this energy is actually a pure exergy, while the ejector system uses primarily thermal energy which does not have the same exergetic value than a mechanical energy. Therefore, in order to compare

both systems on the same objective basis, these COP should be turned into exergetic COP. For the compression system it is obvious because the compression power is purely exergy while for the ejector system Qw should be replaced by its exergy equivalent. An easy way of calculating this exergetic value would be to consider the secondary water as a perfect source delivering a thermal power Qwg at a certain temperature T and using the Carnot factor:

This method may also be used for condenser or evaporator and was used in literature [3]. However this provides not accurate results since the water temperature varies and then it is not a perfect source. In this way the real exergy flux through the generator is used since all secondary cycles (generator, evaporator, condenser) are fully computed in this work:

ew, g = mgw (ew,0 — ew,, )g +amgw (ew,0 — ew,, LP (15)

In addition as proposed in literature an exergetic value of Qe should be used in exergetic COP.

This definition is not used in the current analysis because the useful effect is not mechanical such as in driving cycles/machines but thermal. Such definitions are not relevant since the exergetic value of Qe is very low giving even lower COP and not relevant to compare with classical COP. Consequently it is proposed to compare COP for a same thermal effect at evaporator:

Results are presented in the table 2. It is seen that in an energetic point of view, the ratio between the COP obtained for a conventional compression system and the EACS is very high (18.42 to 29.9). But the ratio of exergetic COP is noticeably lower, with values of around 3.4 to 5.7. It is thus important to highlight that both kind of systems are more comparable in an exergetic point of view, and this definition points out the valorization of the low grade energy. For Tciw=28.4°C, COPej and

COPe undergo the same increase of 6.6 % when the subcooler is used. For Tciw=29°C, COPej

and COPe decrease both of 29%. Note that a comparison between two cases at different Tciw is not

possible in an exergetic point of view, because the chosen reference T0 used for the exergetic analysis is equal to Tciw and thus varies with the considered case.

Table 2: COP and COPex comparison of the EACS and vapor compression cycle, for a=0.13, with and without the use of the subcooler. * denotes a working with regenerator using (P>0) T (°C) cm COP comp COPjj COPex comp COPex e COP COP. comp ej COPex COPex comp ej with subcooler 28,4 8,65 0,4327 7,59 2,2466 19,98 3,38 29* 8,59 0,2878 8,59 1,5068 29,9 5,7 without subcooler 28,4 7,64 0,4057 7,64 2,1066 18,83 3,63 29 7,47 0,4056 7,47 2,123 18,42 3,52

3. Conclusion

A detailed rating modeling of the EACS was presented. It was seen that the subcooler can have either beneficial or harmful effect on performances. The advantage of using of a regulator is clearly demonstrated. Moreover, reducing the system performances to an optimization of the ejector entrainment ratio is not judicious. The whole cycle must be taken into account. Finally, a first step of the exergy analysis of the EACS emphasized the more relevant comparison with a conventional vapor compression system. A more detailed exergetic study is in progress to determine the distribution of irreversibilities in the cycle and its variation with different parameters.

References

[1] W. Pridasawas and P. Lundqvist, A year-round dynamic simulation of a solar-driven ejector refrigeration system with iso-butane as a refrigerant, International Journal of Refrigeration, Vol. 30, 2007, 840-850.

[2] G. K. Alexis, E. K. Karayiannis, A solar ejector cooling system using refrigerant r134a in the Athens area, Renewable Energy, Vol. 30, 2005,1457-1469.

[3] W. Pridasawas and P. Lundqvist, An exergy analysis of a solar-driven ejector refrigeration system, Solar Energy, Vol. 76, 2003, 369-379.

[4] A. Hemidi, Y. Bartosiewicz, J. M. Seynhaeve, Ejector air-conditioning system: cycle modeling, and two — phase aspects, Heat 2008 conference, Vol. 2, 421-428.

[5] A. Hemidi, Y. Bartosiewicz, J. M. Seynhaeve, Modeling of an ejector air-conditioning system: sizing and rating tools, IIR conference, 2008.