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losses. Each has associated uncertainty. For the compressor and turbine evaluations, calculations depend on measurements of mass flow and enthalpy change across the component of interest. Using an in-house data reduction and analysis code, enthalpy is evalu- ated by using the RefProp [45] property tables based on local tem- perature and pressure at the inlet and outlet of each component. An exception to this is that measured density is used for the en- thalpy calculation at the compressor inlet, which is near enough to the saturation region that temperature and pressure alone can- not be relied upon. Uncertainty (U) in compressor work, for example, can be calcu- lated based on partial derivative of work (W) with respect to each input into the calculation (xi), using the following relative instru- ment uncertainties: temperature ±1%, mass flow ±4%, pressure ±5%, and density ±1%. Propagation of uncertainty was carried out by evaluating each partial derivative and combining them as shown in the following equation: For the particular test in Fig. 4 (at 7600 s), each turbine work uncertainty was calculated with measured uncertainties to be 2%. The main compressor work, which operates nearest to the critical point, also exhibited an uncertainty of 2%, while the recompressor work is accurate to within 4%. 3. Cycle modeling A Fortran model of the Sandia split flow recompression Brayton cycle has been developed to investigate performance trade-offs and inform improvement decisions. The inputs to this model in- clude main compressor inlet pressure and temperature, speeds for both TACs, and heater discharge temperature. Digital versions of the turbomachinery performance curves are interrogated, which requires an iterative approach to resolving a balanced steady state condition. Pressure losses throughout the loop are based on curve fits of experimental component pressure losses as a function of mass flow. Using these five inputs, a balanced operating point is obtained that defines the state points around the system, and com- ponent and system performance. An assessment of the model fidelity relative to measured data was calculated. A significant challenge in applying this model to current test data is that the main compressor in TAC-A has been re- placed with a recompressor wheel, which is designed to operate at conditions that the TAC-B recompressor wheel experiences. The primary difference is the inlet temperature. The recompressor wheel is designed for inlet temperatures approximately 28 °C high- er than that entering the TAC-A compressor. The result of operating the recompressor at much lower temperatures than design is sig- nificantly reduced accuracy when interrogating the recompressor performance maps. Thus, predictions from the model in the vicin- ity of the TAC-A recompressor deviate from test data. Stated suc- cinctly, fairly significant deviations between data obtained to date and model predictions are to be expected. Additional efforts to improve this prediction are underway and will come largely from expanding the envelope of speed, temperature, pressure, and power production experience. In Table 2, the ‘Measured’ column presents the state points and resulting cycle performance at 7600 s into the test run from Fig. 4 on 9/11/2012 and serves to compare actual system performance with predictions from the model of the test assembly including turbomachinery performance calculations based on boundary con- ditions. Table 2, column ‘Calculated (a)’ presents model predictions using actual test data measurements as inputs for only the five in- put parameters above. Comparison of the state points throughout the loop as well as the cycle performance parameters show good agreement and are adequate to have confidence in extrapolating to different operating conditions. In particular, the predicted cycle efficiency is 6.2% at a measured efficiency of 5.3%. Table 2, column ‘Calculated (b)’ is the model prediction output for the original design conditions of Sandia’s recompression Bray- ton cycle. In this model run, the main compressor wheel has been installed and model input values have been set to the design con- ditions. Therefore, these predictions are expected to reliably pre- dict the performance of the current loop. The original expectation for design performance included approximately 250 kW of elec- tricity at an efficiency of about 32%. However, the model predicts 135 kW and a cycle efficiency of 15.2%. The deviation between ori- ginal design performance and the predictions listed under the col- umn labeled ‘design’ are directly attributed to heat loss, leakage and windage that were excluded from original design predictions. In addition, actual pressure losses throughout the system have been found to be greater than the original design pressure losses. Thermal losses occur in the turbine housing, driven by the tem- perature difference between the hot turbine inlet volute and the water-cooled alternator compartment immediately adjacent to the turbine volute. Temperatures in the alternator volume are typ- ically on the order of 100 °C or less. This is dramatically lower than the turbine inlet temperature, with a separation of only a few cen- timeters. This situation causes a large temperature gradient that drives thermal conduction losses from the turbine volute. The fluid temperature at the radial turbine wheel inlet is not currently mea- sured. However, an attempt is made to quantify this loss by reduc- ing the temperature used to interrogate the turbine performance curves until the predicted discharge temperature is sufficiently close to the measured discharge temperature. It is for this reason that the temperatures for points 5b-A and 5b-B in the ‘Measured’ column are about 4 °C less than the adjacent ‘Calculated (a)’ col- umn in Table 2. Columns 5 and 6 in Table 2 present model predictions for the same design system, but with accumulating improvements to the system. These include installation of insulation to eliminate ther- mal losses (‘Calculated (c)’), and an improvement in compressor de- sign to obtain efficiencies in the mid 80% range (‘Calculated (d)’). With both of these improvements simulated, the model predicts power production of 172.6 kW, and a gross efficiency of 24.1%. Con- tinued improvements can be predicted assuming reduction of other losses, such as leakage flows, windage, and pressure losses. Other potential improvements to the cycle including raising the design temperature and pressure are possible. Currently, the in- stalled system is limited by the maximum design temperature and pressure ratio of 538 °C and 1.8, respectively. A Brayton cycle designed to operate with a solar energy source can operate at tem- peratures in excess of 600 °C with pressure ratios on the order of 2.5. These changes greatly increase the thermal to electric conver- sion efficiency, and will likely yield efficiencies in the vicinity of 50% as is commonly cited [46]. 4. Advances for sCO2 Brayton adoption There are a number of technical challenges that require atten- tion for sCO2 Brayton adoption in solar-thermal power generation. They include a significant amount of work in development of turbines, bearings, seals, heat exchanger design (especially when considering salt to sCO2 heat exchange) and materials. The follow- ing outlines several of the needs associated with this technology adoption and are addressed here in an effort to provide a realistic view regarding the path to implementation as well as a projection of plant cost. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi utXn "@W2 2 # Uw1⁄4 i1⁄41 @xi Uxi ð2Þ B.D. Iverson et al. / Applied Energy 111 (2013) 957–970 965PDF Image | Supercritical CO2 Brayton cycles for solar-thermal energy
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