Axisymmetrical Turbulent Swirling Natural-Convection Plume: Part 1—Theoretical Investigation

A theoretical investigation is made of the behavior of an axisymmetrical turbulent swirling natural-convection plume in an otherwise motionless ambient fluid. With the introduction of the assumption of similar axial and swirling velocity profiles and similar buoyancy profile, and the assumption of lateral entrainment of ambient fluid, the order of the governing differential equations is reduced by one after the initial integration following the von Karman integral method. The behavior of the swirling plume is found to depend solely on two physical parameters associated with the source characteristics, the source Fronde number, and the source swirling velocity parameter. A series solution developed in the vicinity of the source of the swirling plume is obtained for any values of these two physical parameters. Numerical solutions for extended range of axial distance from the source of the swirling plume and for wide ranges of selected representative values of these two physical parameters are obtained with the use of a digital electronic computer. The behavior of the swirling plume is found to approach that of a nonswirling jet, a swirling jet, or a nonswirling plume when these two physical parameters are assigned values approaching those designating each of the aforementioned simpler, boundary situations.