Influence of tooth geometrical shape on the leakage and rotordynamic characteristics of labyrinth seals in a cryogenic liquid turbine expander

Cryogenic liquid turbine expanders have been used in many refrigeration systems to save energy, and rotor stability is a top concern in their development. The present study focuses on the influence of tooth geometrical shape on the leakage and rotordynamic characteristics of labyrinth seals in a cryogenic liquid expander, whose rotordynamic characteristics are typically special because of the thermodynamic effect of cryogenic liquid and a large pressure drop. Computational fluid dynamics (CFD) simulations are conducted in thirteen-teeth labyrinth seals with isosceles trapezoid shaped teeth and two types of right-angle trapezoid shaped teeth for a given geometric parameter through the whirling rotor method and total energy model. The flow behavior in the three labyrinth seals with different tooth geometrical shapes is explored, and their influence on the leakage and rotordynamic characteristics of the labyrinth seal is obtained. The results show that the leakage flow rate of the labyrinth seal with front right angle trapezoid shaped teeth is 1.1% and 0.6% less than that with rear right angle trapezoid shaped teeth and isosceles trapezoid shaped teeth, respectively, because of a larger divergence angle and more leakage flow involved in dissipation, while the labyrinth seal with isosceles trapezoid shaped teeth produces a larger fluid-induced tangential force opposite to the direction of whirling velocity and is more favorable for rotor stability. In addition, a parametric study is conducted to analyze the influence of clearance, tooth height, tooth thickness and inclination angle on the leakage and rotordynamic characteristics of the three labyrinth seals.