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The isentropic efficiency of the compressor is given by: his;comp 1⁄4 h2s 2 h1 h2 2 h1 ð10Þ ev o6 5 evTevef The exergy output of the evaporator, J. Sarkar et al. / International Journal of Refrigeration 27 (2004) 830–838 833 where cp;gcef is the average specific heat of external fluid being heated and DTp;gcef is its temperature rise across the gas cooler. (vii) Energy balance in evaporator with respect to external fluid being cooled: m_evefcp;evefDTevef 1⁄4m_rqev ð7Þ where cp;evef is the average specific heat of external fluid being cooled in the evaporator and DTevef is its temperature drop across the evaporator. COPs for the heating and cooling modes are given by: COPheating 1⁄4 qgc and COPcooling 1⁄4 qev ð8Þ wcomp wcomp The effectiveness of the internal beat exchanger is given by: 11⁄4T12T6 ð9Þ T3 2 T6 state equation: Net exergy transfer from the component 1⁄4 Exergy transfer due to heat transfer þ Exergy transfer due to work transfer þ Change in flow exergy (i) Compressor irreversibility, icomp1⁄4Toðs22s1Þ ð12Þ (ii) Expansion process irreversibility, iexp 1⁄4 Toðs5 2 s4Þ ð13Þ (iii) Internal heat exchanger irreversibility, iihx 1⁄4 To1⁄2ðs1 2 s6Þ 2 ðs4 2 s3Þ ð14Þ (iv) Total specific exergy change of the refrigerant in the evaporator, eev 1⁄4 Toðs6 2 s5Þ 2 qev ð15Þ Neglecting irreversibility due to pressure drop, the evaporator irreversibility is given by: i1⁄4Tðs2sÞ2q To ð16Þ where his;comp has been calculated from the following expression [12], p2 his;comp 1⁄4 0:815 þ 0:022 p 1 p2 2 p2 3 2 0:0041 p þ0:0001 p ð11Þ 11 It may be noted that the above correlation for his;comp is for a particular type of compressor, even though the analysis would exactly be the same for other types of compressor. Although real systems can have compressor isentropic efficiency dependent on the degree of superheat, this correlation is independent of superheat. 3.1. Exergy analysis An exergy analysis has been performed for each component of the system employing the fundamental steady T evef where T evef is the external T epev1⁄4qev12 o ð17Þ fluid thermodynamic average temperature, Tevef1⁄4 T92T10 lnðT9 =T10 Þ (v) Total specific exergy change of the refrigerant in the gas cooler; egc 1⁄4 qgc 2 Toðs2 2 s3Þ ð18Þ Irreversibility due to heat transfer through a finite temperature difference, i 1⁄4q To 2Tðs2sÞ ð19Þ gc;DT gcT o2 3 gcef where, Tgcef is the heating fluid thermodynamic average temperature and is estimated the same way as that for the evaporator. Irreversibility due to pressure difference: igc;DP 1⁄4 2RTo ln 1 2 DPgc !! ð20Þ P2PDF Image | Optimization of a transcritical CO2 heat pump cycle
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