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964 B.D. Iverson et al. / Applied Energy 111 (2013) 957–970 frictional losses not only serve as a parasitic load, but also can cause extreme local heating of bearings and other turbomachinery internals, causing turbine malfunction. Modeling TAC windage has revealed that the major loss is due to the shaft itself and the thrust bearing assembly; these combine for upwards of 85% of frictional loss [38]. The two radial journal bearings account for the remainder. These estimates are based on consideration of the turbomachinery assembly as a simplified ser- ies of tightly-housed concentric cylinders and disks and applying friction relations for turbulent boundary layers by Schlichting and Gersten [43] and Vrancik [44]. Fig. 6 illustrates the relative contribution of windage loss (based on these turbulent correla- tions) for the journal bearings, thrust bearing and rotating shaft. The sum of these power losses is also provided in the figure. Ongo- ing work seeks to optimize the thrust bearing assembly for reduced friction and resistance at higher temperatures without compromis- ing load capacity. This is the primary challenge in attaining high speeds approaching 75 krpm for the current test assembly. To isolate and quantify empirical rotating losses for the present test assembly, a series of tests was conducted to identify the net contribution of the windage losses (illustrated in Fig. 6) plus that due to seals. This total rotating loss was measured by removing the turbine and compressor wheels from the shaft, and recording the resultant power consumption required to spin the bare shaft alone at high speeds within prototypic CO2 environments. Sensitiv- ity to CO2 properties, shaft speed, and thrust loads were evaluated directly [42]. CFD modeling of the sCO2 lubrication layer was also undertaken to confirm that observed losses were consistent with turbulent theory. The resulting correlation for power loss that scales with angular velocity (x) and fluid properties (density q and viscosity l) is as follows: mass flow, temperature and pressure of this flow is measured and considered in the data reduction process as follows. During the compression stage, leakage flow in the seals is included in the compressor work calculation, since it is judged that the flow cannot reach the seals without first passing the through the cen- trifugal wheel. During expansion, leakage flow is not included in the turbine work calculation, since the leakage flow largely by- passes the turbine wheel. The current approach for seals limits leakage flow to less than 5%. Consequently, the impact to compressor and turbine work cal- culations is minimal, but can still represent up to 5% of unrecover- able loss. Given the nature of abradable seals and the small-scale geometry of the present rotating hardware, this flow rate may change somewhat over time for a fixed set of CO2 conditions up- stream of the seal, as the labyrinth seal experiences wear. For this test on 9/11/2012 near 7600 s, the total mass flow topped 3.5 kg/s while leakage flow was 0.1 kg/s in total, or 2.8%. 2.3.4. Uncertainty analysis Analysis of net power generation requires knowledge of com- pressor and turbine work (as measured by enthalpy change across each active component), and estimated thermal and frictional Fig. 7. (a) First law efficiency as a function of heat exchanger (HX) effectiveness and (b) exergetic efficiency as a function of heat exchanger DT for direct (e.g. sCO2 in receiver) and indirect (e.g. salt or secondary media in receiver) approaches for several storage capacities at 700 °C, assuming a 98% storage efficiency and 8 h of daylight operation. (a) 1 0.95 0.9 0.85 0.8 0.75 0.75 Direct Receiver, 16 hrs Direct Receiver, 8 hrs Direct Receiver, 6 hrs Direct Receiver, 4 hrs Indirect Receiver 0.8 0.85 0.9 0.95 1 Heat Exchanger Effectiveness [-] (b) 1 0.995 0.99 0.985 0.98 0.975 0.97 Direct Receiver, 16 hrs Direct Receiver, 8 hrs Direct Receiver, 6 hrs Direct Receiver, 4 hrs Indirect Receiver 0 10 20 30 40 50 Heat Exchanger Temperature Difference [°C] 2:8 q 0:8 l 0:2 Pturb 1⁄4 0:155x 21:1 1⁄2kg=m3 14:9 1⁄2lPa s ð1Þ Eq. (1) can be used for estimating windage losses in test data within ±5% for speeds less than 50 krpm. This correlation runs approximately 20% higher than that predicted by turbulent theory (as in Fig. 6) for rotating disks and cylinders alone [42]. This can be attributed to the simplified modeling approach and neglect of shaft seals. Empirical testing results yielding Eq. (1) indicates an esti- mated 4.9 kW loss for turbine A, and 10.1 kW loss for turbine B. The difference between A and B in this case is due to their speed differential at 7600 s and fluid properties in the rotor housing. Here, CO2 properties of density and viscosity are taken within the turbine housing, where the shaft and gas bearings operate. Typical temperatures and pressures in the rotor housing are 150 °C and 1.4 MPa. 2.3.3. Leakage flows At each turbine and compressor wheel, leakage flow bypasses the rotating element in the housing through abradable labyrinth shaft seals and into the turbine housing where the gas bearings and alternator spin in a reduced pressure environment (Fig. 3). The leakage flow critically provides bearings with a hydrodynamic film for load support and transfers frictional heating. A gas scaveng- ing system pulls CO2 from the housing to prevent buildup of pres- sure, driving a cooling flow through the turbine, and pumps it back into the high pressure loop to complete the closed cycle. A sup- plementary bypass line connects from the compressor inlet at each TAC unit and penetrates into the turbine housing in the vicinity of the high temperature turbine-end radial bearing. This additional cooling is metered by a manual needle valve along the flow path. The combination of leakage flow in the seals and bypass flow for cooling bearings is considered the total system leakage flow. The Exergetic Efficiency [-] Efficiency [-]PDF Image | Supercritical CO2 Brayton cycles for solar-thermal energy
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