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2746 Z. Shengjun et al. / Applied Energy 88 (2011) 2740–2754 Fig. 4. Thermal efficiency varying with evaporating temperature for fluids in subcritical ORC cycle. Table 5 Performance comparison of fluids under the optimal operation parameters based on thermal efficiency. DP 1⁄4 fG2 ð1=qout þ 1=qin ÞL=dh þ G2 ð1=qout 1=qin Þ ð40Þ f 1⁄4f0:002275þ0:00933exp1⁄2h=ð0:003drÞgReB1⁄2ðxin xoutÞhLG=ðLgÞ0:211 Re 1⁄4 ðGdh =lL Þ B 1⁄4 ð4:16 532h=dr Þ1 4.2. Global model It is clear that, in order to calculate the ORC system perfor- mance, a relevant number of parameters are to be set. The inlet temperature of the heat source and sink, the pinch temperature difference and flow rate of the heat source were assumed in Table 4. The flow rate of the heat sink is calculated to fulfill the cooling needs. Saturated vapor was assumed at the turbine inlet in subcrit- ical ORC system. The basic assumptions for the plant components are also listed in Table 4. The ORC simulation is performed by using a simulation program written in Matlab. With all the modeling equations specified, a glo- bal methodology has been developed and was schematized in Fig. 3. The thermodynamics properties of the working fluid are cal- culated by REFPROP NIST7.0. The global model is built by interconnecting the models of the components described in Section 4.1 and the steady state perfor- mance is acquired by using the solution logic given in Fig. 3. The initial step is to specify the values of all the fixed parameters and the range of the variable ones. In transcritical power cycle, the vari- ables are the turbine inlet temperature (tmax), the turbine inlet pressure (Pin) and the turbine outlet pressure (Pout, i.e. condensing pressure or condensing temperature without considering the pres- sure drop in the pipes). As for CO2, the pinch point appears at either end of the vapor generator [24]. Although the internal cycle param- eters can be fixed by the three variables (tmax, Pin and Pout), the mass flow rate of the fluids varied with the net power output value. So, the net power output is an additional variable for CO2. In sub- critical ORC, the parameters for optimization are the turbine inlet pressure (Pin, i.e. evaporating pressure or evaporation temperature) and turbine outlet pressure (Pout, i.e. condensing pressure or con- densing temperature). Refrigerant R123(Sub) R245ca(Sub) R245fa(Sub) R600(Sub) R236ea(Sub) R600a(Sub) R236fa(Sub) R152a(Sub) R227ea(Sub) R134a(Sub) R143a(Tran) R218(Tran) R125(Tran) R41(Tran) R170(Tran) CO2(Tran) Pin Pout tmax VER (MPa) (MPa) (°C) 0.54 0.09 84 5.61 0.63 0.10 84 6.14 0.87 0.16 84 5.85 1.10 0.25 84 4.64 1.10 0.21 84 5.66 1.46 0.36 84 4.47 1.37 0.28 84 5.68 2.55 0.61 84 4.53 2.02 0.47 84 5.81 2.87 0.69 84 5.11 3.99 1.29 84 3.73 2.99 0.89 84 4.99 4.21 1.41 84 3.70 8.61 3.92 84 1.93 8.18 4.28 84 1.84 12.39 6.58 84 1.61 vin (m3/kg) 0.0310 0.0296 0.0207 0.0363 0.0136 0.0255 0.0100 0.0110 0.0050 0.0057 0.0045 0.0026 0.0031 0.0055 0.0071 0.0034 th,wo (oC) 88.6 88.5 88.5 88.5 88.3 88.4 88.2 88.4 87.8 88.1 64.7 60.5 56.4 45.8 44.2 41.1 / 1⁄4 1:1 þ 1:3nG0:35X0:35=1⁄2gd q ðq q Þ0:175o v ttMv1v Rel 1⁄4Gð1xÞdM=ll 1 x0:9 qv 0:5 ll 0:1 Xtt1⁄4 x q l lv NuB 1⁄4 0:725HðeÞ1⁄2GrPrl=ðPh1gAÞ0:25 G 1⁄4gq2d3=l2 ð39Þ r1M1 HðeÞ 1⁄4 e þ e0:51⁄210ð1 eÞ0:1 8ð1 e0:5Þ 11⁄41þ ð1xÞqv e x q l Phl 1⁄4cp;lðTs TwÞ hLG 8>< 0:4þ0:6 >: hx ql þ 0:4ð1 xÞi0:5 9>= qv 1⁄2 x þ 0 : 4 ð 1 x Þ 0 : 5 >; The Kedzierski-Goncalves’s [52] correlation is used to calculating the pressure drop of fluids in condenser:PDF Image | Performance comparison and parametric optimization of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation
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