It is now widely recognized that destabilizing forces, tending to generate forward rotor whirl, are generated in axial flow turbines as a result of the non-uniform torque induced by the non-uniform tip-clearance in a deflected rotor — the so called Thomas/Alford force (Thomas, 1958 and Alford, 1965). It is also recognized that there will be a similar effect in axial flow compressors, but qualitative considerations cannot definitively establish the magnitude or even the direction of the induced whirling forces — that is, if they will tend to forward or backward whirl.
Applying a “parallel compressor” model to simulate the operation of a compressor rotor deflected radially in its clearance, it is possible to derive a quantitative estimate of the proportionality factor β which relates the Thomas/Alford force in axial flow compressors (i.e., the tangential force generated by a radial deflection of the rotor) to the torque level in the compressor. The analysis makes use of experimental data from the GE Aircraft Engines Low Speed Research Compressor facility comparing the performance of three different axial flow compressors, each with four stages (typical of a mid-block of an aircraft gas turbine compressor) at two different clearances (expressed as a percent of blade length) — CL/L = 1.4% and CL/L = 2.8%.
It is found that the value of β is in the range of +0.27 to −0.71 in the vicinity of the stages’ nominal operating line and +0.08 to −1.25 in the vicinity of the stages’ operation at peak efficiency. The value of β reaches a level of between −1.16 and −3.36 as the compressor is operated near its stalled condition. The final result bears a very strong resemblance to the correlation obtained by improvising a normalization of the experimental data of Vance and Laudadio (1984) and a generic relationship to the analytic results of Colding-Jorgensen (1990).