Frequency-Dependent Rotordynamic Coefficients of Supercritical CO2 Labyrinth Seals Considering Real Gas Effects

The Brayton cycle based on supercritical carbon dioxide (S-CO2) is widely used in turbomachinery. In this paper, the rotordynamic coefficients are systematically investigated for the labyrinth seal working with S-CO2 based on NIST REFPROP database. A three-dimensional numerical model of the labyrinth seal was developed using computational fluid dynamics (CFD). The rotordynamic characteristics of the labyrinth seal for different boundary conditions and various geometries were studied over a wide frequency range of 20–260 Hz. Results show that the direct complex stiffness coefficient exhibits strong frequency dependence in the low-frequency region, while the cross-coupled complex stiffness coefficient and average direct damping coefficient exhibit relatively slight frequency dependency. The effective damping coefficient increases with the increasing inlet pressure, rotational speed, blade quantities, and decreasing inlet temperature. The effective damping coefficient has a strong frequency dependency at low whirling frequencies less than 80 Hz and increases slightly with the decreasing sealing clearance. At high whirling frequencies above 80 Hz, the effective damping coefficient increases with the increasing sealing clearance. The effective damping coefficient of the labyrinth seal with S-CO2 is about 167~202% of that with air modeled as an ideal gas, indicating a more favorable contribution of the seal to rotordynamic stability. The frequency-dependent trends of the rotordynamic coefficients under real gas conditions differ significantly from those under ideal gas conditions, highlighting the importance of real gas effects for accurately predicting the rotordynamic performance and stability of S-CO2 labyrinth seals.