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316 Norman Holaind et al. / Energy Procedia 123 (2017) 313–320 4 Norman Holaind et al./ Energy Procedia 00 (2017) 000–000 2.2. Turbomachinery design based on similarity considerations The Balje’s charts summarize total to static efficiencies of turbines and compressors with respect to non- dimensional parameters, namely specific speed and specific diameter [6]. Their expressions, proposed in Eqns. 8 and 9 respectively, allow to estimate reasonable values for revolution speed and wheel diameter since adiabatic head and flow rate are known from the cycle analysis. N =NQ1/2 H3/4 (8) s ad D=DH1/4 Q1/2 (9) s ad For a given turbomachinery technology in Balje’s charts, it is possible to draw a line that, for a given specific speed, provides a value of specific diameter that ensures the maximum efficiency. These lines, called Cordier’s lines, were graphically retrieved from Balje’s charts for the specific speed ranges strictly related to radial machines and taken into account in the sCO2 model using Eqns. 10 and 11 for compressor and turbine respectively. D S ,comp D S ,turb = 2.719 N −1.092 (10) S ,comp = 2.056 N −0.812 (11) S ,turb The turbine being the most influencing component for the actual energy recovery process, for a given value of its specific speed the model calculates the revolution speed of the turbine from Eqn. 8 and its diameter using Eqns. 11 and 9. Since the CGT configuration is considered a single shaft one, knowing the revolution speed from the turbine calculations allows to compute the compressor specific speed, specific diameter and impeller diameter using Eqns. 8, 10 and 9 respectively. 2.3. Parametric analysis The effects of cycle pressure ratio and turbine inlet temperature are reported in Figure 2. Both sets of results were calculated neglecting thermal losses in pipes as well as pressure drops in heat exchangers and pipes. In Figure 2 the analysis was carried out with reference to a flue gas mass flow rate of 1 kg/s at 650 °C and assuming a constant temperature difference of 50 K between exhaust gas outlet and CO2 inlet at the heater. For a given cycle pressure ratio, a higher turbine inlet temperature leads to a lower amount of CO2 mass flow rate in the supercritical loop. On the other hand, for a given turbine inlet temperature, a higher cycle pressure ratio leads to a lower turbine outlet temperature and, in turn, to a lower potential for regeneration. Therefore, at the sCO2 heater, more thermal power is exchanged using a higher CO2 mass flow rate. For a given cycle configuration, the net power output depends on the specific net work and the amount of working fluid mass flow rate. This fact explains the net electrical power trend that is shown in the top left chart of Figure 2: even though cycle pressure ratio and turbine inlet temperature both enhance the cycle efficiency and its net specific work, because of a lower amount of working fluid that is needed to balance the heat loads at the heater, the net power output decreases at high values of turbine inlet temperature. For instance, with a pressure ratio of 2 and a turbine inlet temperature equal to 400 °C, theoretical electrical power output would be over 87.4 kW with a 1st law efficiency of 24%. At 500 °C the cycle efficiency would rise to 28% but the net power output would drop to 75.7 kWe. Mass flow rate resulting from the energy balance at the heater and cycle pressure ratio affect revolution speed and diameter of the turbomachinery according to Eqns. 8 and 9. In particular, for a given flow rate, the compressor and turbine will rotate faster and be smaller with increasing pressure ratio. On the other hand, for a given enthalpy rise/drop, smaller flow rates will reduce the size of the machine increasing its revolution speed. Furthermore, in small machines useful flow passages tend to have the same dimensions as leakage paths. Therefore, efficiency values largely accepted and achievable for MW-scale machines can be hardly assumed in kW-scale ones. In particular, for a given revolutionPDF Image | Design of Radial Turbomachinery for S CO2 CFD
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