Numerical Investigations on the Leakage Flow and Rotordynamic Performance of the Labyrinth Seal at Different Inlet Gas Volume Fractions

Utilizing the proposed two-phase numerical prediction method, the effects of the inlet gas volume fraction (GVF), rotational speed, and pressure ratio on the leakage flow rate and rotordynamic force coefficients of a labyrinth seal were analyzed. The results show that the proportion of the gas phase in the two-phase leakage of the labyrinth seal is low, not exceeding 0.6% when the inlet GVF is in the range of 0.03–0.12. When the inlet GVF increases, the increasing cross-coupling stiffness and the decreasing cross-coupling virtual mass reduce the effective damping by 1.9%–26.7%, thereby worsening the rotordynamic stability. The expansion of the gas phase due to pressure reduction is the main factor leading to the change in GVF inside the seal cavity. High rotational speed and high pressure drop contribute to an increase in GVF. At the same inlet GVF and pressure ratio, the direct stiffness and cross-coupling virtual mass decrease, while the direct virtual mass and cross-coupling stiffness increase with increasing rotational speed. The increase in rotational speed can enhance the radial force and change the direction of the tangential force from opposite to the shaft whirling direction to the same direction. This flow behavior can weaken the stability of the shaft. An increase in pressure drop has a lesser impact on the radial stability of the shaft but can increase the cross-coupling virtual mass, leading to an increase in effective damping.