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In the Sandia compression loop separate gas booster pumps lower the pressure and density in the rotor cavity by pumping the CO2 out of the rotor cavity and back into the low pressure leg of the loop. This is illustrated by the red lines in Figure 2-6 and in Figure 2-7. In addition the compressor wheel uses pump- out vanes to balance the forces across the compressor and thus reduce the thrust load on the shaft. The rotor cavity pressure also affects the thrust load. The turbo-alternator-compressor has two types of rotor shafts. One shaft uses ball bearings and the other shaft uses gas foil bearings. The ball bearing rotor has a limited life, but it is configured with a load cell to measure the axial thrust load (see Figure 5-13). The load cell is used to measure the actual thrust and to validate the thrust models. Because the thrust load capability of gas foil bearing is limited, it also allows the manufacturer (Barber Nichols) to trim the pump- out vanes. A flow meter was also installed to measure the leakage flow rate through the rotor cavity. The final configuration of the compression loop will operate with gas-foil bearings. Separate tests of gas- foil bearings (DellaCorte, 2006) reveal that the power losses in the gas foil bearing increases with gas pressure, just as the windage increases with pressure. Thus, to avoid overheating the bearings, it is desirable to operate the gas-foil bearings at low pressures as well. In the Sandia/Barber-Nichols turbo- alternator-compressor design, our design goal is to operate the rotor cavity a pressures below approximately 300 psia. The leakage flow through the labyrinth seals also provides the necessary cooling because the gas cools substantially upon adiabatic expansion through the labyrinth seal. To estimate windage losses we use the model developed by NASA (Vrancik, 1968). In the Vrancik model, the frictional losses are calculated from the geometry of the rotor and the properties of the fluid, given the Reynolds number of the fluid in the gap between the rotor and the stator. The equation for the windage losses is: Pwr C(Re)r 43L d rotor r Where Cd is a discharge coefficient that is a function of the Reynolds number, is the fluid density, r is the radius of the rotor, is the angular frequency of the rotor, and Lr is the length of the rotor. Note that the power is directly proportional to the fluid density, the shaft speed to the third power, and to the radius of the rotor to the 4th power. This makes the actual power losses very sensitive to the shaft speed and size. Early evaluations indicate that the fractional power losses due to windage decrease as the size of the machine increases. The Reynolds number and the discharge coefficient are defined by the equations Re r tgap and r Cd 2.041.768ln(Re Cd ) 1 . Cd The rotor radius is defined as rr, tgap is the gap between the rotor and the stator, and is the viscosity of the fluid. It is found that the discharge coefficient is not a strong function of Reynolds number, but varies from 0.01 to 0.06 (a factor of six) for Reynolds numbers that vary from 108 to 104 (four orders of magnitude), though important this term does not strongly affect the power loss. Note also that the discharge coefficient term is the only term in the equation that is sensitive to the gap width. Another 59PDF Image | Operation and Analysis of a Supercritical CO2 Brayton Cycle
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