Interrelated Rotordynamic Effects of Cylindrical and Conical Whirl of Annular Seal Rotors

Abstract

A comprehensive approach for computing the dynamic coefficients of an annular seal is presented. The coefficients are partly those associated with a uniform lateral eccentricity mode of the rotor (known as the cylindrical whirl mode) and with an angular eccentricity (which gives rise to a conical whirl type). The rotor excitation effects in both cases are treated as interrelated by recognizing the fluid-exerted moments resulting from the lateral eccentricity and the net fluid force resulting from the angular eccentricity. In all cases, the rotor is assumed to undergo a whirling motion around the housing centerline. The computational procedure is a finite-element perturbation model in which the zeroth-order undisplaced-rotor flow solution in the clearance gap is obtained through a Petrov-Galerkin approach. Next, the rotor translational and angular eccentricities, considered to be infinitesimally small, are perceived to cause virtual distortions of varied magnitudes in the finite element assembly which occupies the clearance gap. Perturbations in the flow variables including, in particular, the rotor surface pressure, are then obtained by expanding the finite-element equations in terms of the rotor eccentricity components. The fluid-exerted forces and moments are in this case computed by integration over the rotor surface, and the full matrix of rotordynamic coefficients, in the end, obtained. The computational model is verified against a bulk-flow model for a sample case involving a straight annular seal. Choice of this sample model for validation was made on the basis that no other existing model has yet been expanded to account for the mutual interaction between the cylindrical and conical rotor whirl, which is under focus in this study.