Swirl Number Calculator

S = G_θ / (G_x × R) — characterises the degree of swirl in pipes, burners, and combustors. S > 0.6 indicates a central recirculation zone.

Fluid Mechanics II · Specialized

Inputs

Calculation method:

Pipe / duct outer radius R (mm)

Mean axial velocity Vx (m/s)

Tangential velocity at R Vθ (m/s)

Tangential velocity profile (determines shape factor k):

Solid-body core (forced vortex) — k = 1/2Free-vortex profile — k = 1Uniform tangential profile — k = 2/3

S = k × V_θ(R) / V_x

Definition:

S = G_θ / (G_x × R)

G_θ = ∫ ρ u_x u_θ r dA [N·m]

G_x = ∫ ρ u_x² dA [N]

Simplified forms (uniform axial velocity V_x):

Beer-Chigier swirl vane formula:

S = (2/3) × tan(φ) × (1 − (r_i/R)³) / (1 − (r_i/R)²)

Valid for axial swirlers with straight flat vanes. φ is the vane angle from the duct axis. r_i = inner hub radius, R = outer radius.

Swirl classification and CRZ:

S range	Class	Behaviour
S < 0.4	Weak	No recirculation zone, low mixing
0.4 ≤ S ≤ 0.6	Moderate	CRZ possible; geometry-dependent
S > 0.6	Strong	Central recirculation zone (CRZ) forms

Where: