Labyrinth Seal Rotordynamic Characteristics Part II: Geometrical Parameter Effects

Abstract

The objective of this work was to determine the effects of the operational conditions [as shown in Part 1 (LiZ.LiJ.FengZ., “Labyrinth Seal Rotordynamic Characteristics Part I: Operational Conditions Effects,” Journal of Propulsion and Power, Vol. XXX, No. XXX, 2016, pp. XXX–XXX)] and geometrical parameters (as shown in this paper) on the leakage and rotordynamic characteristics of labyrinth seals. In this paper, the effects of the geometrical parameters, such as the sealing clearance, tooth number, and cavity depth, were numerically investigated using a proposed three-dimensional transient computational-fluid-dynamics perturbation method based on the multifrequency elliptical whirling orbit model. Transient leakage flow rates and frequency-dependent rotordynamic coefficients of labyrinth seals were presented and compared for three sealing clearances, three tooth numbers, and four cavity depths. All these labyrinth seal designs have identical tooth profile, rotor diameter, and axial length. For all labyrinth seal designs, transient computational-fluid-dynamics solutions were carried out at the same operating condition: inlet pressure of 6.9 bar, pressure ratio of 0.45, rotational speed of 15 krpm, and medium inlet preswirl ratio of 0.5. The numerical results show that the cavity depth is the most important factor that significantly influences the seal rotordynamic coefficients, followed by sealing clearance and tooth number in descending order. Too small sealing clearance may result in a risk of high rotor vibrations during a critical-speed transition or even instability if the natural frequency drops below the crossover frequency due to the negative effective stiffness. Increasing tooth number or increasing cavity depth of the labyrinth seal can improve the rotor stability and extend the useful operating frequency range of the machine, due to the increased positive effective damping and decreased crossover frequency.