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834 (vi) J. Sarkar et al. / International Journal of Refrigeration 27 (2004) 830–838 Hence total irreversibility in the gas cooler is given by: igc 1⁄4 igc;DT þ igc;DP ð21Þ Thus exergy output of the gas cooler, are quite steep. As pressure increases, the quantity Dh3 is large compared to Dh2; as is evident from Fig. 3, and this causes an increase in the modified COP value as can be observed from Eq. (26). At a particular pressure, the COP attains a maximum value and the corresponding pressure is termed the optimum pressure for the cycle. With further increase in pressure, Dh3 does not produce the required gain over Dh2 and thus the COP begins to fall. The pressure range where the isotherms are fairly flat and where this beneficial gain in COP occurs varies considerably with cooler outlet temperature. Hence the gas cooler outlet temperature plays an influential role in determining the optimum operating conditions for the cycle. 5. Results and discussion Important design and performance parameters for the carbon dioxide based heating and cooling systems are coefficient of performance, the exergetic efficiency, the various temperatures and pressures of the working fluid at hot and cold ends, and individual component irreversibility fractions. These parameters are suitably plotted to illustrate the various performance trends and optimum operating points. The performance of the carbon dioxide system being studied for simultaneous heating and cooling applications is evaluated on the basis of heating and cooling COPs, which have been estimated for various operating conditions with a 0.5 bar step increase in compressor discharge pressure. Results are presented in terms of combined system COP, which is simply the sum of the heating and cooling mode COPs. The variation of maximum system COP with corre- sponding optimum discharge pressure for various evapor- ator temperatures for a cooler outlet temperature of 35 8C and internal heat exchanger effectiveness of 60% is shown in Fig. 4. With an increase in evaporator temperature from 210 to 10 8C, the system COP increases sharply recording an increase of over 75%. However, optimum pressure variation with evaporator temperature is much less signifi- cant. Although experimental results show that with increase in evaporator temperature the optimum pressure increases due to increase in cooler outlet temperature, here optimum discharge pressure exhibits a different nature due to the constraint on cooler outlet temperature. As mentioned earlier, due to divergent nature of the isotherms in the supercritical region, the COP reaches a maximum at higher values of discharge pressure for lower evaporator tempera- tures as shown in Fig. 4. In the present study, it is observed that the influence of internal heat exchanger effectiveness on system COP and optimum pressure is marginal. With changes in effectiveness for a cooler outlet temperature of 35 8C and an evaporator temperature of 0 8C, negligible variations occur in maximum COP and optimum compressor epgc 1⁄4 egc 2 ðigc;DT þ igc;DPÞ Finally combined exergy output of the system is, ð22Þ epo 1⁄4 epev þ epgc ð23Þ Second law (exergy) efficiency for the system is given by the ratio of net exergy output and the work input to the compressor: hII 1⁄4 epo ð24Þ w The percentage irreversibility has also been estimated to represent the contribution of each component to the total irreversibility in the system and is given by the ratio of the irreversibility of the component to the total irreversibility of the system. Based on the thermodynamic analysis presented above, a simulation code was developed. This code was integrated with the thermodynamic properties code CO2PROP to compute relevant thermodynamic parameters. 4. Optimum discharge pressure Studies [8,9,12] show that the COP of transcritical CO2 systems is significantly influenced by the gas cooler pressure, and interestingly non-monotonically. Hence there exists an optimum pressure where the system yields the best COP and the knowledge of the optimum operating conditions corresponding to the maximum COP is a very important factor in the design of a transcritical CO2 cycle. The gas cooler exit temperature is dependent on external fluid inlet temperature; hence, at any discharge pressure, cooler exit temperature will be fixed for a certain fluid inlet condition. The existence of an optimum pressure for fixed cooler exit temperatures can be supported by the following argument. For cycle 1–2–3–4–5–6–1 (Fig. 3), COP for the heating mode is given by: h2h COPheating 1⁄4 2 3 With increase in discharge pressure from p2 to p02 for a constant cooler exit temperature of t3 ; the heating coefficient of performance expression gets modified as: ð26Þ Due to the unique behavioral pattern of carbon dioxide properties around the critical point and beyond, the slope of the isotherms is quite modest for a specific pressure range; at other pressures above and below this range, the isotherms h2 2 h1 ð25Þ ðh 2hÞþDh þDh COP0heating1⁄4 2 3 2 3 ðh2 2h1ÞþDh2PDF Image | Optimization of a transcritical CO2 heat pump cycle
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