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The leak rate through the labyrinth seals are estimated by using a correlation by Egli (Egli, 1937), or by a simpler but related correlation by Martin, (Martin, 1908). The Egli correlation was provided to SNL by Barber Nichols Inc. In addition, SNL has checked these estimates by using simple choked flow and compressible flow through orifice calculations based on formulas provided in Bird Stewart and Lightfoot (Bird, 1969) and by Martin. A discharge coefficient of 0.61 for all models. In general, the flow through the labyrinth seal is proportional to the flow area, and the upstream pressure, and density. Unfortunately due to the complexity of the turbomachinery the actual values for the seal upstream density and pressure are uncertain. Figure 5-17 shows a detail of the compressor wheel and the location of the labyrinth seals. At operating conditions, the compressor inlet pressure is ~1120 psi (~7690 kPa), but the exit pressure can be as high as ~2007 psia (~14,000 kPa). The pressure on the back face of the wheel is uncertain, but for the purposes of bounding the leakage flow estimates, we have assumed that it equals the compressor exit pressure and temperature which are typically 324-325 K and 2007 psia. In actuality, the upstream pressure could be significantly smaller than this because the pump-out vanes on the back face of the compressor wheel are provided to approximately reproduce the pressure profile that exists along the front face of the wheel (this is done to balance the thrust load). Thus, the actual pressure will likely be much lower than the full 2007 psia. An analysis by Vernon (unpublished) indicates that the pressure at the entrance to the labyrinth seal is actually closer to the compressor inlet pressure than to the outlet pressure. As will be shown in the figures below, this lower upstream pressure greatly reduces both the leakage flow rate and the subsequent pumping power. Table 5.3 reproduces the originally estimated leakage flow rate that was provided to SNL by Barber Nichols Inc. This calculation is based on a 1937 correlation by Egli (see, Egli, 1937) where the leakage rate of steam was measured through multiple stepped labyrinth seals. Based on this correlation, the labyrinth leakage is estimated to be 0.154 lb/s or ~0.068 kg/s. This flow rate is only 2% of the total mass flow rate of 3.53 kg/s. The SNL estimates are shown in the bottom portion of Table 5.3 for these same operating conditions. Note that the leakage flow rates estimates of 0.088 and 0.077 kg/s agree fairly well with the Egli correlation leakage flow rate of 0.068 kg/s. For comparison purposes, the last two columns show what the leakage flow would be for an upstream seal pressure of 7700 kPa (~1120 psi) rather than 13,842 kPa. The mass flow rate for these two cases is 0.032 kg/s assuming choked flow which is about two to three times less flow rate than for the higher upstream cavity pressure. Overall, it appears that the leakage flow rate through the labyrinth seals is on the order of 1-2% (per seal) of the total mass flow rate, and is most strongly dependent on the upstream pressure at the seal. 64PDF Image | Operation and Analysis of a Supercritical CO2 Brayton Cycle
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