Inviscid models of cyclonically driven internal flows

In this article, we review several inviscid, helical solutions that are developed in the context of cyclonic, swirl-driven combustors. Specifically, the survey focuses on three solutions: an exact inviscid solution, a heuristic model for swirl velocities, and a compressible vortex model derived from a modified form of the Bragg–Hawthorne equation. As part of this endeavor, an overview of the derivations and assumptions is provided. The structures of the resulting solutions are then contrasted by comparing their velocity fields. In all cases the outer region of the helical motion is characterized by the presence of a free, irrotational vortex. The key difference between the three models presented here originates from the manner by which their core regions are treated. In the exact inviscid solution, the swirl velocity remains singular as it approaches the centerline. Conversely, in the constant shear stress and compressible Bragg–Hawthorne models, the core singularity is suppressed. The resulting formulations provide the basis for ongoing efforts to increase the available toolsets for modeling-confined helical motions.