Axial Compressor Velocity Triangles

What is modelled

One mean-line rotor row of an axial compressor. Air arrives with an axial velocity and some swirl, the moving blades turn it, and the change in swirl is the work done on each kilogram of air. The same triangles tell how hard the blades are asked to decelerate the flow, which sets how close they are to stalling.

Equations

• Triangles: C = W + U, tanβ1 = (U − Cθ1)/Ca, Cθ2 = U − Ca tanβ2.
• Euler work w = U (Cθ2 − Cθ1) = U Ca (tanβ1 − tanβ2); ΔT0 = w / cp.
• Stage pressure ratio (1 + η ΔT0 / T01)γ/(γ−1).
• Diffusion factor (Lieblein) DF = 1 − W2/W1 + ΔWθ / (2 σ W1); de Haller number W2/W1 ≥ 0.72; reaction (W1² − W2²) / (2w).

Checks run in the page

• Euler work against the kinetic-energy form built from the four vectors.
• Pressure ratio by numerical integration against the closed form.
• The de Haller exit angle by bisection against arccos.
• The work coefficient 1 - phi tan(b2) and its scaling with speed.

Honest simplifications

One mean-line radius (0.32 m), constant axial velocity, the exit relative angle given directly (deviation already included), and a simple illustrative loss law rather than a fitted correlation. There is no tip clearance, bleed, radial variation, surge dynamics or multi-stage matching.

• Press Throttled (low flow) and watch the diffusion factor rise towards the stall line.
• Press Heavily loaded, then Pre-whirl helps: swirl before the rotor lowers the inlet relative angle and the loading.
• Press Cold day to see the same work give a bigger pressure ratio in cold air.