An exact irrotational solution for a hemispherically bounded cyclonic flowfield

This study focuses on the development of an internal potential flow solution in the context of a hemispherically bounded cyclonic chamber. The analysis proceeds from the Bragg-Hawthorne equation, which is quite effective in the treatment of steady, inviscid, and axisymmetric flows when expressed in terms of the streamfunction. Once the streamfunction is obtained, other flow properties are readily deduced; these include the principal velocity and pressure distributions, swirl intensity, crossflow velocity, and mantle location. Furthermore, given the overarching spherical geometry, two different types of mantles are identified and related to the coexistence of axially bidirectional and circularly bipolar regions. The first, axial mantle, which is traditionally used in the analysis of cylindrical and conical cyclone separators, consists of a rotating, non-translating interfacial layer along which the axial velocity vanishes. It thus separates the outer, vertical updraft, from the inner, swirling downdraft. The second, polar mantle, which arises in the context of a hemispherical flow configuration, coincides with the spherical interface along which the polar velocity vanishes. It hence partitions the flow domain into a much larger outer region, where the flow direction remains strictly counterclockwise, and a proportionally smaller inner region, where the outflow becomes clockwise. Despite their dissimilar structures, both axial and polar mantles meet in the exit plane at a fractional radius of 1 / e 2 or 13.53%. In this study, the unique characteristics of the resulting irrotational motion, which reduces to a continuously looping, hemispherically cyclonic potential vortex, are evaluated and discussed.

Automated summary

This study focuses on the development of an internal potential flow solution in a hemispherically bounded cyclonic chamber using the Bragg-Hawthorne equation. The analysis results in deductions of various flow properties and identification of two different types of mantles based on the overarching spherical geometry.