Compressor Surge & Stall Cycle

Engine Operating Point

Greitzer B parameter 1.00

Throttle opening γ 0.85

Live State

Stable operating point

Flow coeff. φ

0.000

Pressure coeff. ψ

0.000

Mass flow (kg/s)

0.0

Pressure ratio

1.00

Compressor Map

How it works

This is the Moore–Greitzer lumped-parameter model of a single-spool axial compression system: rotor + stator, a downstream plenum volume, and a throttle valve. Two nondimensional states track the whole system — flow coefficient φ (mass flow through the rotor) and pressure-rise coefficient ψ (plenum pressure above inlet):

dφ/dξ = B·(ψc(φ) − ψ)
dψ/dξ = (1/B)·(φ − φT(ψ))

ψc(φ) = ψ0 + H·[1 + 1.5(φ/W − 1) − 0.5(φ/W − 1)³]   (compressor characteristic)
φT(ψ) = γ·√max(ψ, 0)                                  (throttle valve law)

B (Greitzer parameter) — ratio of plenum-to-duct inertia (∝ wheel speed·√(Vp/(AcLc))). Low B lets flow recover through mild rotating stall; high B locks the system into a large deep-surge limit cycle with flow reversal.
Throttle opening γ — closing the throttle (lower γ) pushes the equilibrium left, past the peak of ψc(φ) where dψc/dφ > 0 — the classic surge-line instability criterion.
Inlet Distortion Pulse — knocks φ down suddenly, the way inlet flow distortion or a gust does on a real engine, to test whether the current (B, γ) point recovers or falls into surge.
The rotor blades flash and the exhaust plume reverses colour when φ crosses zero — a real deep-surge event briefly reverses flow back out the inlet.

Real-world relevance: this instability is why jet engines have surge margins, bleed valves and variable stator vanes — an axial compressor pushed too close to its stall line at low corrected speed (rapid throttle chops, distorted inlet flow, foreign-object ingestion) can surge audibly and, if sustained, cause flameout or mechanical damage from the pressure pulses.

Rotor / stator Forward flow Reversed flow (surge)

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