An exact irrotational solution for a hemispherically bounded cyclonic flowfield
An exact irrotational solution for a hemispherically bounded cyclonic flowfield
复制标题
DOI：
10.1063/5.0051111
复制
发表时间：
2021-06
影响因子：
4.6
通讯作者：
Langston L. Williams;J. Majdalani
中科院分区：
文献类型：
--
作者：
Langston L. Williams;J. Majdalani
本研究的重点是发展的内部势流解决方案的上下文中的半球有界的气旋室。分析从布拉格-霍桑方程出发，当用流函数表示时，该方程在处理定常、无粘和轴对称流时是相当有效的。一旦获得流函数，其他的流动性质很容易推导出来，这些包括主要的速度和压力分布，旋流强度，横流速度，和地幔位置。此外，由于总体球形几何形状，两种不同类型的地幔被确定和轴向双向和圆形双极区的共存。第一种是传统上用于分析圆柱形和圆锥形旋风分离器的轴向罩，它由一个旋转的、非平移的界面层组成，轴向速度沿该界面层沿着消失。因此，它将外部的垂直上升气流与内部的旋转下降气流分开。第二，极地地幔，这是在一个半球形的流动配置的上下文中出现的，与球形界面沿着极地速度消失。因此，它将流动域划分为一个大得多的外部区域和一个成比例较小的内部区域，在外部区域中，流动方向保持严格的逆时针方向，在内部区域中，流出变为顺时针方向。尽管它们的结构不同，轴向和极性地幔满足在出口平面的分数半径为1 / e 2或13.53%。在这项研究中，所产生的无旋运动，这减少到一个连续的循环，半球气旋性的潜在涡的独特特征，进行了评估和讨论。
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.