A compressor's pressure-flow curve rises from right to left and reaches a peak. Left of that peak is not an operating region but an instability region.
Two distinct phenomena
Rotating stall. Some of the blade passages separate, and that separated region travels around the rotor at a speed different from the rotor's. The mean flow may stay constant, but the blades are loaded and unloaded in turn — dangerous for fatigue and costly for efficiency.
Surge. An instability of the whole system: the flow reverses abruptly, the downstream volume empties, the pressure falls, and the flow goes forward again. It is a low-frequency, high-amplitude cycle. It is audible, the axial bearing loads spike, and damage follows quickly.
The distinction matters: rotating stall is local to the compressor, while surge concerns the whole system and depends on the downstream volume. The same compressor shows different surge behaviour with different pipework volumes.
Modelling consequences
Surge cannot be studied with a compressor model alone. The system volume and resistance belong in the model; an isolated blade passage analysis cannot give the surge limit.
Steady state will not converge at the left end of the curve, and that is usually a signal from the physics. See the convergence note.
A single-passage periodic model is inadequate. Rotating stall breaks circumferential symmetry by definition; a single-passage model forbids it. See the symmetry note and the rotating machinery note.
Compressibility is required. If the pressure ratio is meaningful, the density change cannot be neglected. See the compressible flow note.
The practical output
What is usually wanted from the analysis is not to reproduce the surge cycle exactly but to give the surge margin: how far the operating point sits from the instability limit. Seeing where separation begins at part load also shows how to widen that margin geometrically.
References
- Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. DOI: 10.2514/3.12149
- Launder, B. E., Reece, G. J. & Rodi, W. (1975). Progress in the development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics, 68(3), 537–566.