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836 J. Sarkar et al. / International Journal of Refrigeration 27 (2004) 830–838 Maximum system COP contours are shown in Fig. 6, where the evaporator temperature varies between 210 and 10 8C, and the gas cooler exit temperature varies from 30 to 50 8C. The maximum COP varies between 3.8 and 13.4. Iso-COP lines are fairly parallel; COP values increase from maximum cooler exit temperature and minimum evaporator temperature to mini- mum cooler exit temperature and maximum evaporator temperature. So to increase COP, the system has to be designed for the lowest possible cooler exit temperature and the highest possible evaporator temperature. Optimum discharge pressure and corresponding cooler inlet temperature contours have been shown in Figs. 7 and 8, respectively, for the same range of evaporator and gas cooler exit temperatures. It may be noted that the optimum pressure varies from 73 to 123 bar and the corresponding cooler inlet temperature varies from 73 to 151 8C. Both the iso-optimum pressure lines and corresponding iso-cooler inlet temperature lines are nearly parallel and vary the least at maximum cooler exit temperature and minimum evaporator temperature as opposed to a maximum variation at minimum cooler exit temperature and maximum evaporator temperature. So to obtain useful heating at higher temperatures from the system, it has to be designed for high compressor discharge pressure, which is corre- sponding to maximum cooler exit temperature and mini- mum evaporator temperature, although the COP will be low. However, to restrict the system to lower optimum cycle pressures, it has to be designed for the minimum cooler exit temperature and the maximum evaporator temperature and gives very high COP. With increase in cooler exit temperature or decrease in evaporator temperature, the optimum discharge pressure increases. This implies that for high temperature heating or low temperature cooling the system is not profitable in term of system COP as well as cost due to high optimum discharge pressure. Keeping the smallest possible refrigerant temperature difference between evaporator and cooler outlet (yielding high COP), one can Fig. 7. Optimum discharge pressure contour (in bar). Fig. 8. Gas cooler inlet temperature (8C) at optimum discharge pressure contour. design the system for low optimum discharge pressures (yielding lower pressure ratio) to obtain heating output at high temperature only through high superheat. Performing a regression analysis on the data obtained from the system model explained above, the following relations have been established to predict estimates of the optimum design parameters: COPmax 1⁄4 48:2 þ 0:21tev þ 0:05t3 ðt3 2 50Þ 2 0:0004t3 ; popt 1⁄4 4:9 þ 2:256t3 2 0:17tev þ 0:002t32; t2 ðat; popt Þ 1⁄4 210:65 þ 3:78t3 2 1:44tev 2 0:0188t32 þ 0:009t2 ev These correlations are valid for evaporation temperatures ðtevÞ ranging between 210 and 108C and cooler exit temperatures ðt3Þ ranging between 30 and 50 8C. 5.2. Exergy analysis Second law efficiency and percentages of irreversibility for different components have been obtained for different operating conditions. For the gas cooler, mass flow rates for both refrigerant and the fluid being heated are assumed the same (1 kg/s). In the evaporator, the secondary fluid exit temperature is assumed to be 2 C above the evaporator temperature and its mass flow rate has been calculated based on unit refrigerant flow rate (1 kg/s). Inlet conditions for both secondary fluids have been taken as 10 8C lower than the cooler exit temperature. The average pressure drop in the gas cooler is taken to be 2 bar. The minimum temperature difference required at cooler outlet to avoid pinch problem in the gas cooler increases as compressor discharge pressure decreases. This behavior gets more complex in the neighborhood of the critical point and the pinch problem becomes quite significant due to the irregular constantPDF Image | Optimization of a transcritical CO2 heat pump cycle
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