Critical swirl number for the onset of vortex breakdown in isothermal confined swirling flows: Roles of swirl-generation strategy and reference location

Swirl number characterizes swirl-strength and is widely used to correlate vortex-breakdown (VB) onset, yet reported critical values vary, likely because studies differ in swirl-number formulation, its axial evaluation location, Reynolds number ( R e ), expansion ratio ( 𝐸 𝑅 ), and swirl-generation-strategy. This work investigates the most appropriate swirl-number formulation and suitable evaluation location, its critical value for stable-VB onset in non-reacting flows, and how swirl-generation strategy affects these aspects. A baseline isothermal-flow in a single-stream model dump-combustor with 𝐸 𝑅 = 2 . 0 , R e ≈ 2 . 0 × 1 0 ⁢ ⁴ , and a 45° axial-vaned swirler is first simulated using an LES-based solver and validated against available experimental mean-flow and coherent-dynamics measurements. Then the validated solver setup is applied to other combustor cases differing from the base-case only in vane-angle or swirler-configuration: four axial-vaned swirler cases with 17°, 25°, 40°, and 45° vane-angles, and four tangential-vaned swirler cases with 45°, 55°, 68°, and 75° vane-angles. Stable-VB is absent in the 17° axial and 45° tangential cases, and appears from 25° and 55° onwards, respectively. The generic swirl-number, 𝑆 ⁢ 𝑁 𝑔 , including mean-velocity, velocity-fluctuation, and pressure contributions in a radius-normalized ratio of axial angular-momentum to axial-momentum fluxes, emerges as the most appropriate swirl-strength measure. However, meaningful comparison across different swirl-combustor cases using 𝑆 ⁢ 𝑁 𝑔 also requires its evaluation upstream of the expansion-plane, sufficiently close to the swirler. Using this criterion, critical 𝑆 ⁢ 𝑁 𝑔 lies between 0.22 and 0.35 for axial-swirler cases and between 0.25 and 0.37 for tangential-swirler cases, suggesting near-independence from swirl-generation strategy under the investigated isothermal conditions at fixed values of R e , 𝐸 𝑅 and downstream geometry.