Advancements in Theoretical Models of Confined Vortex Flowfields

摘要

In this article, we review some of the theoretical solutions used to describe swirl dominated flows in both unidirectional and bidirectional flow orientations. This short survey starts with the Rankine vortex and culminates in the presentation of a compressible solution of the bidirectional vortex. After classifying representative swirl motions as external or internal depending on physical boundary conditions, their commonalities are identified along with their relevance to either geophysical or industrial applications. We also identify the key similarity parameters that control the problem, including the inflow parameter, Kilo, and the vortex Reynolds number, V. The latter combines the mean flow Reynolds number and the product of the swirl number and chamber aspect ratio. In this study, the core and sidewall boundary layers are quantified as function of V. The compressible solution is also obtained assuming a Rayleigh-Janzen expansion in the inflow Mach number squared.