A theory of rotating stall of multistage axial compressors
A theoretical analysis was made of rotating stall in axial compressors of many stages, finding conditions for a permanent, straight-through traveling disturbance, with the steady compressor characteristic assumed known, and with simple lag processes ascribed to the flows in the inlet, blade passages, and exit regions. For weak disturbances, predicted stall propagation speeds agree well with experimental results. For a locally-parabolic compressor characteristic, an exact nonlinear solution is found and discussed. For deep stall, the stall-zone boundary is most abrupt at the trailing edge, as expected. When a complete characteristic having unstalling and reverse-flow features is adopted, limit cycles governed by a Lienard's equation are found. Analysis of these cycles yields predictions of recovery from rotating stall; a relaxation oscillation is found at some limiting flow coefficient, above which no solution exists. Recovery is apparently independent of lag processes in the blade passages, but instead depends on the lags originating in the inlet and exit flows, and also on the shape of the given characteristic diagram. Small external lags and tall diagrams favor early recovery. Implications for future research are discussed.