Calculation of Rotor Dynamic Coefficients for Labyrinth Seals

Abstract

A single control volume, Iwatsubo based bulk flow method for the calculation of these coefficients is developed and implemented. The method herein uses a unique iterative technique to first identify the mass flow rate based on pressure drops across the individual teeth, which is then used in the governing sets of continuity and momentum equations. The method is applicable to different teeth geometries and arrangements. A parametric analysis of the effect of mass flow rate on rotor dynamic coefficients is performed and suggests that a small variation in mass flow rate does not significantly detract from the accuracy of the predicted dynamic coefficients; the mass flow rate calculation implemented in this paper is sufficiently accurate. Furthermore, the inclusion of some tangential momentum parameters has been previously proposed to improve the accuracy of the Iwatsubo method. However, from the current analysis the inclusion of such parameters is also shown to have little effect on the rotor dynamic coefficients and does not lead to improved correlation with experimental data. Comparisons to experimental data suggest that the method herein is reasonable for use as a design tool to predict the trends and actual values of cross‐coupled stiffness, the most important seal parameter in rotor dynamic analyses. The method is also shown to be useful in predicting the order of magnitude of principal stiffness and damping coefficients.