Unsteady Flow and Whirl-Inducing Forces in Axial-Flow Compressors: Part II—Analysis

An experimental and theoretical investigation was conducted to evaluate the effects seen in axial-flow compressors when the centerline of the rotor becomes displaced from the centerline of the static structure of the engine, thus creating circumferentially nonuniform rotor-tip clearances. This displacement produces unsteady flow and creates a system of destabilizing forces, which contribute significantly to rotor whirl instability in turbomachinery. These forces were first identified by Thomas (1958. Bull. AIM, 71, No. 11/12, pp. 1039-1063.) for turbines and by Alford (1965. J. Eng. Power, Oct., pp. 333-334) for jet engines. In Part I, the results from an experimental investigation of these phenomena were presented. In this Part II, three analytic models were used to predict both the magnitude and direction of the Thomas/Alford force in its normalized form, known as the β coefficient, and the unsteady effects for the compressors tested in Part I. In addition, the effects of a whirling shaft were simulated to evaluate differences between a rotor with static offset and an actual whirling eccentric rotor. The models were also used to assess the influence of the nonaxisymmetric static pressure distribution on the rotor spool, which was not measured in the experiment. The models evaluated were (I) the two-sector parallel compressor (2SPC) model, (2) the infinite-segment-parallel-compressor (ISPC) model, and (3) the two-coupled actuator disk (2CAD) model. The results of these analyses were found to be in agreement with the experimental data in both sign and trend. Thus, the validated models provide a general means to predict the aerodynamic destabilizing forces for axial flow compressors in turbine engines. These tools have the potential to improve the design of rotordynamically stable turbomachinery.