Abstract
This work describes an inviscid solution for a cyclonic flowfield evolving in a hemispherical chamber configuration. In this context, a vigorously swirling motion is triggered by a gaseous stream that is introduced tangentially to the inner circumference of the chamber's equatorial plane. The resulting updraft spirals around while sweeping the chamber wall, reverses direction while approaching the headend, and then tunnels itself out through the inner core portion of the chamber. Our analysis proceeds from the Bragg–Hawthorne formulation, which proves effective in the treatment of steady, incompressible, and axisymmetric motions. Then using appropriate boundary conditions, we are able to obtain a closed-form expression for the Stokes streamfunction in both spherical and cylindrical coordinates. Other properties of interest are subsequently deduced, and these include the principal velocities and pressure distributions, vorticity, swirl intensity, helicity density, crossflow velocity, and the location of the axial mantle; the latter separates the outer annular updraft from the inner, centralized downdraft. Due in large part to the overarching spherical curvature, the cyclonic motion also exhibits a polar mantle across which the flow becomes entirely radial inward. Along this lower and shorter spherical interface, the polar velocity vanishes while switching angular direction. Interestingly, both polar and axial mantles coincide in the exit plane where the ideal outlet size, prescribed by the mantle position, is found to be approximately 70.7% of the chamber radius. We thus recover the same mantle fraction of the cyclonic flow analog in a right-cylindrical chamber where an essentially complex-lamellar motion is established.
Highlights
The modeling of cyclonic flowfields continues to receive attention in the propulsion community due to its relevance to several swirlenhanced combustion devices. These include the vortex injection hybrid rocket engine (VIHRE) developed by Knuth et al.,[1,2] the vortex combustion combined cycle (VCCC) engine explored by Chiaverini et al.,[3] and the vortex combustion cold-wall chamber (VCCWC) conceived by Chiaverini et al.[4]
Most computational studies have concentrated on the use of Reynolds-averaged Navier–Stokes equations (RANS) solvers including those by Hsieh and Rajamani,[5] Ogawa,[6] Hoekstra et al.,[7,8] Derksen and van den Akker,[9] Fang et al.,[10] Hu et al.,[11] Cortes and Gil,[12] Concha,[13] Zhu et al.,[14] Molina et al.,[15] and Majdalani and Chiaverini.[16]
Since the mass transport across the axial and polar mantles is important for bookkeeping and design considerations, it may be determined from Eqs. (32) and (33)
Summary
The modeling of cyclonic flowfields continues to receive attention in the propulsion community due to its relevance to several swirlenhanced combustion devices All results are considered and discussed, including the quasi complex-lamellar character of the resulting Euler solution
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