Abstract
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/e2 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.
Highlights
Besides the fundamental interest in predicting the evolution of helical flows in physical transport and geophysical phenomena, the adaptation of swirl into various industrial applications continues to receive significant attention
Our modeling efforts lead to an irrotational Euler solution for a cyclonic flowfield that is driven by tangential injection into a hemispherical enclosure that is open at one end
Our analysis begins with the Bragg–Hawthorne equation (BHE), a reduced form of Euler’s momentum expression that is well suited for the treatment of steady, inviscid, incompressible, axisymmetric, and swirl-driven flows
Summary
Besides the fundamental interest in predicting the evolution of helical flows in physical transport and geophysical phenomena, the adaptation of swirl into various industrial applications continues to receive significant attention. It is speculated that switching from a cylindrical to a hemispherical chamber configuration, as shown, could lead to further improvements in the vortex engine’s combustion efficiency, namely, by promoting better mixing in the reactive zone, reducing the potential for oxidizer leakage, enhancing the wall-cooling effectiveness of the incoming oxidizer stream, and lowering the overall engine weight by decreasing the surface-to-volume ratio. Several mathematical descriptions of a wall-bounded cyclonic motion have been made available for cylindrically shaped enclosures, leading to different classes of helical solutions.[52–56] They have been developed for conically shaped cavities by Bloor and Ingham,[31] Cortes and Gil,[32] Concha,[33] Shtern and Borissov,[34] and Barber and Majdalani.[35]. We close by considering the behavior of the solution both inside and outside a fully enclosed spherical domain where the same boundary conditions continue to apply
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