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Table 2 (continued) Location TAC B net power (kW) System parameters Heater input (kW) Pre-cooler (kW) LT recuperator UA (kW/K) HT recuperator UA (kW/K) Mass loading (kg) Heat lossc 4a to 4b (kW) Heat lossc 5a to 5b (kW) Heat lossc 6a to 6b (kW) Net electricity (kW) Cycle efficiency (%) Measured (Fig. 4, 7600 s) 5.7 341.7 239.2 67.6 55.2 101.2 62.3 40.9 10.5 16.6 4.9 Calculated (a) benchmark 15.8 422.6 240.2 67.6 55.2 101.8 65.8 25.8 10.8 22.3 5.3 Calculated (b) design conditions 57.0 891.0 476.4 70.0 40.0 104.0 104.9 41.5 17.2 135.5 15.2 Calculated (c) insulated 60.6 700.9 481.3 70.0 40.0 103.3 0.0 0.0 0.1 140.6 20.0 Calculated (d) efficient compressor 80.6 716.5 464.8 70.0 40.0 104.2 0.0 0.0 0.1 172.6 24.1 B.D. Iverson et al. / Applied Energy 111 (2013) 957–970 963 a Obtained using data presented in Fig. 6. b Obtained following Section 3. c Obtained following the approach in Section 2.3.1. d Input parameter for model. e Not directly measured. The corresponding upstream and downstream temperature reduc- tions for the 100% power reductions are 40 °C and 10 °C for the first transient, and 50 °C and 15 °C for the second transient. The up- stream response is muted and delayed for several reasons. First, there is a finite period of time required for the fluid to transit the loop. The fluid that is immediately affected in the heater requires that transit period to return to the heater inlet. Second, the recu- perators inherent in the design of a recompression system act to mitigate the sharpness and magnitude of thermal changes in the cycle. Finally, the thermal capacity of all piping and components acts to delay the magnitude of a thermal transient. In general, the various responses in the pressure, temperature and power output to the reduction in thermal power input exhibit an exponential decay, indicative of what is expected from stored thermal energy in a thermal capacitor. System response after the heating power is restored exhibits a complementary logarithmic rise. These trends are best displayed in the temperature histories in plot (c). When solar transients do occur, short perturbations of this type can easily be managed by thermal capacitance in the sys- tem with the extent of the exponential decay in system variables dependent on the total thermal mass and heat losses inherent in the heating system. 2.3. Measurement uncertainty A particular test case and operating conditions was selected for consideration of system losses and measurement uncertainty. A data point 7600 s into the test was selected from Fig. 4 and ana- lyzed at a time of steady power generation (see also Table 2). 2.3.1. Thermal loss Thermal losses between two separate locations in the cycle can be assessed by examination of temperature change across lengths of piping that are not directly heated or cooled as part of a cycle process. This is most significant along the high-temperature legs of the system. These segments are larger in diameter and are of considerable length to accommodate thermal expansion. The loop structure continues to be developed and is largely not insulated. This is responsible for a significant amount of the poor system performance from the standpoint of total system efficiency, providing context to discrepancies between theoretical and exper- imentally observed cycle characteristics. Fig. 1 indicates the locations of significant heat loss. Heat losses are estimated in these regions by a product of mass flow, heat capacity, and temperature change. For the selected test condition at 7600 s (Table 2), 62.3 kW of heat is lost from the HT recuperator to the heater inlet, 40.9 kW is lost upstream of the turbines, and 10.5 kW is lost from the turbine outlet legs to the HT recuperator inlet. Losses at the turbine volute are also noted to be 8.8 kW and 7.5 kW for turbines A and B, respectively. Volute thermal losses are estimated from known conditions at the inlet and outlet of the turbine, and turbine performance maps for a given set of conditions [40]. The discrepancy between measured turbine outlet conditions, and outlet conditions predicted by the performance map is attributed to a cooling mechanism at the back of the turbine volute due to rapid expansion of high pressure CO2 across the rotating seal, into the low-pressure alternator housing. In total for this test case, 130 kW is lost to various thermal mechanisms for a heater input of 342 kW (38%). 2.3.2. Losses to rotating friction Rotating loss, or windage, is also a significant contributor to conversion inefficiencies for the current test assembly. The high- speed environment, along with high density and low viscosity, generate a highly turbulent environment at the shaft and within tight clearances of the gas foil thrust and journal bearings. The presence of turbulence causes a sharp increase in the dependency of frictional loss and load capacity to environmental conditions, namely a heightened sensitivity to lubricant gas pressure and run- ner speed. This phenomenon was first observed in testing of jour- nal bearings at NASA’s Glenn Research Center [41]. Intensive Fig. 6. Breakdown of alternator windage losses for CO2 at 27 °C and 1.4 MPa. Each data set was determined by using turbulent correlations and then summed to illustrate the relative contribution of the components. 24 18 12 6 Journal Bearing 1 Journal Bearing 2 Shaft Thrust Bearing Sum (turbulent correlations) 0 20 30 40 50 60 70 80 Speed [krpm] Power Loss [kW]PDF Image | Supercritical CO2 Brayton cycles for solar-thermal energy
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