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Table 5.4: Estimated leakage flow rate through the labyrinth seal and pumping power. Third to last Column compares BNI/Egli at 13842 kPa with SNL choked flow results (near bottom of column). For comparison, the SNL choked flow leakage flow is shown at an upstream pressure of 7700 kPa, with pumping powers for Haskel pump inlet temperatures of 320 and 295 K. Leakage Flow Rate Estimates through Labyrinth Seals Egli (BNI) SNL @ 7700 kPa SNL @ 7700 kPa Leakage Flow Rate (Egli) mdot.leakage kg/s 0.068181818 Rotor Cavity Temperature Rotor Cavity Pressure Enthalpy of rotor Cavity Efficiency of Haskel Pump Exit Pressure of HP Temp of HP exit Enthalpy of HP exit T.rc K p.rc kPa H.rc kJ/kg eff.HP (Haskel Pump) - P.exit kPa T.out.HP K H.out.HP kJ/kg 320 1379 514.0282014 0.85 7700 483.8526998 652.8451996 320 1379 514.0282014 0.85 7700 483.8526998 652.8451996 295 1379 490.213375 0.85 7700 451.382254 616.0237866 Pumping Power of HP (single stage) Pwr.HP kW 12.24486371 4.527406818 4.103207261 shaft radius r.s m gap t.gap m 0.006985 0.0000381 0.006985 0.0000381 0.006985 0.0000381 Orifice Area S.o m^2 1.67213E-06 1.67213E-06 1.67213E-06 T.gas Upstream of Orifice P.gas Upstream of Orifice 325 13842 325 7700 325 7700 den.o2 Cp.rv Cv.rv Gamma.rv Gamma Upstream 647.3292932 0.949689484 0.703613305 1.34973213 3.686802832 198.3421303 0.949689484 0.703613305 1.34973213 2.449371612 198.3421303 0.958212819 0.690452759 1.387803592 2.449371612 Leakage Choked Flow mdot.CF kg/s 0.088208677 0.032614211 0.032614211 Leakage (Comp flow Nozzel) mdot.orifice kg/s Barber-Nichols Egli Correlation mdot.Egli kg/s 0.077188917 0.029017862 0.029017862 0.068181818 Pumping Power and Mass Flow rate through the Labyrinth Seals 0.1 0.09 0.08 0.07 0.06 0.05 0.04 14 12 10 8 6 4 2 320 330 Upstream Seal Temperature Pump Pwr at 320 K Pump Pwr at 295 K 7700 kPa Upstream Pressure Flow Rate (320 K) 340 350 360 370 Figure 5-18: Estimated ranges of pumping powers and mass flow rates for various conditions. The dark blue and magenta curves show the estimated pumping power required to pump the fluid as a function of upstream temperature. The magenta curve illustrates the effect that pre-cooling the gas down to 295 k has on the pumping power. The mass flow rate is shown as the green curve for both the magenta and dark blue curves. However, an even larger power reduction benefit can be achieved if the pump-out vanes reduce the upstream labyrinth seal pressure to the comp inlet pressure of 1115 psi versus the exit pressure of 2007 psia. In this case the pumping power could be as low as 3-4 kW. 67 Pumping Power (kW) Mass Flow Rate (kg/s)PDF Image | Operation and Analysis of a Supercritical CO2 Brayton Cycle
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