N 0 rpmφ 0ψ 0PR 0η 0State -FPS 0

Drag to orbit, wheel or pinch to zoom. Particle colour = stagnation temperature (blue cold, red after the rotors add work). Time is slowed down by the slow-motion factor. Stator vanes are removed inside the cut-away window.

Axial Compressor Stage

How does a row of spinning blades raise air pressure, and why does it stall or surge when the flow is throttled?

Operating mode

You choose the flow coefficient φ = Ca/U directly and read the stage response (steady mean-line model).

Operation

Blading

Plenum and display

Live readouts

Stage characteristic

Compressor map (pressure ratio vs corrected flow)

Flow and pressure in time (exit-valve mode)

Experiments

Each button runs the model headless over a range and lists the result. Use the current speed, inlet temperature and swirl.

Independent numerical checks

Controls and missions

Drag or one finger: orbit; wheel or pinch: zoom; four camera presets. Slow-motion factor 200 means the rotor really turns 200 times faster than shown.
Set the flow: slide φ to move along the stage characteristic. Closing the throttle (smaller φ) raises ψ until the blades stall.
Exit valve + plenum: the valve opening fixes the load line, the plenum volume sets the B parameter; a big plenum can store energy and make the whole system surge.
Missions: (1) find the highest efficiency with the setting angle; (2) get a pressure ratio above 1.4 without leaving the stable region; (3) make the compressor surge, then stop it with the smallest change; (4) find the largest plenum that only stalls.

The science

Velocity triangles. In the rotor frame the air arrives with relative velocity W1 at angle β1 and leaves at β2; adding the blade speed U turns W into the absolute velocity C. With constant axial velocity Ca: tanβ1 = (U − Cθ1)/Ca, Cθ2 = U − Ca tanβ2.

Euler work. w = U (Cθ2 − Cθ1) = U Ca (tanβ1 − tanβ2) (J/kg) and ΔT0 = w/cp. Equivalent energy form: w = ½(C2² − C1²) + ½(W1² − W2²), which the page uses as an independent check. Isentropic stage pressure ratio: (1 + η ΔT0/T01)^(γ/(γ−1)).

Deviation and loading. The exit angle is the metal angle plus Carter's deviation δ = m θ/√σ, m = 0.23 + β2'/500 (a/c = 0.5). Diffusion factor (Lieblein) DF = 1 − W2/W1 + ΔWθ/(2σW1); de Haller number W2/W1 ≥ 0.72 is the classic limit. Degree of reaction Λ = (W1² − W2²)/(2w).

Losses (illustrative). Loss coefficients are a simple bucket: a minimum value, a quadratic incidence term, a steep rise once DF exceeds 0.5 and a Mach term above M_rel = 0.95, saturating at 0.75. The shape is taken from textbook loss correlations, the constants are chosen for teaching and are not fitted to any real machine [verify against a source before quoting numbers]. Efficiency is η = 1 − (½ωR W1² + ½ωS C2²)/w.

Stall and surge. The pressure-rise characteristic ψc(φ) of the stage comes from the model above, so it falls steeply on the left of its peak because the blades stall. The exit valve and plenum use the Greitzer lumped model: dφ/dξ = B(ψc(φ) − ψ), dψ/dξ = (φ − γ√ψ)/B, with B = U/(2a) · √(Vp/(Ac Lc)), ξ = ω_H t. Linearised, the operating point is unstable when B ψc'(φ) > φ/(2Bψ); for large B the system then surges in a deep limit cycle (flow can reverse), for small B it settles into a steady stalled state. Rotating stall cells are drawn as a pattern, not solved.

Simplifications. One mean-line radius (r_m = 0.32 m); constant axial velocity; the stage repeats (stator restores the inlet swirl, its deviation is ignored); incompressible-style loss accounting with ideal-gas temperature rise; blade twist in the 3D model follows a free-vortex design at 7460 rpm; no tip clearance flow, no bleed, no radial equilibrium at off-design; real engines have many more stages. Gas data: cp = 1005 J/(kg K), γ = 1.4, R = 287 J/(kg K), speed of sound 340 m/s (plenum model).

Independent educational model. The 3D model was built in Blender (aerofoil sections, Cycles-baked textures); interaction in Three.js.