Whirl Frequency Dependent Alford Forces in Axial Compressors

Explicit closed form expressions are derived for the whirl frequency dependence of the Alford force in an axial compressor operating in steady-state away from the onset of rotating stall. The analysis includes the compressor flow dynamics using the Moore-Greitzer approximation. By asymptotic expansion in terms of the whirl orbit amplitude, expressions for the direct and cross-coupling impedance are obtained analytically. Several components in the cross-coupling impedance are shown to change phase as the whirl frequency transits the rotating stall frequency. This implies that for a given compressor design the Alford force can be stabilizing or destabilizing depending on flow rate and whirl frequency. Further, the analysis shows that the coupling between mean flow quantities and rotor whirl is of second order. Thereby, the present asymptotic expansion results in a fluid-structure coupling model, which is consistent in accuracy with usual linearized rotordynamic analysis.