Combustion Swirl Number & CTRZ Calculator
Aerodynamic flame stabilization: Compute axial vane swirler geometry, kinematic swirl number ($S$), and determine the onset of vortex breakdown and Central Toroidal Recirculation ($CTRZ$).
Swirler Vane Geometry
Deflection angle relative to burner axis
Outer passage radius
Central nozzle hub radius
Typically 8 to 16 curved or flat vanes
Definition of Swirl Number (S)
The dimensionless swirl number $S$ is the ratio of axial flux of angular momentum to axial flux of linear momentum:
$$S = \frac{G_\theta}{R \cdot G_x} \approx \frac{2}{3} \left[ \frac{1 - (R_h / R)^3}{1 - (R_h / R)^2} \right] \tan(\theta)$$
Vortex breakdown and internal recirculation (CTRZ) occur when $S > S_{\text{crit}} \approx 0.6$.
Swirl Aerodynamics
Swirl Number (S)
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Vortex Breakdown Status
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Recirculation Zone Dimensions
Estimated CTRZ Width (D_ctrz)
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Bubble maximum diameter
Recirculation Mass Fraction
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Hot combustion gas re-entrained
Flow Classification
Hub-to-Tip Radius Ratio (Rh / R):
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Tangential-to-Axial Velocity Ratio:
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Combustion Aerodynamic Regime:
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