Investigation of the working mechanism and unsteady effects inside a single-outlet vortex tube by implementing unsteady computational fluid dynamics and spectral proper orthogonal decomposition

Abstract

Although various steady and unsteady working mechanisms underlying energy separation in Ranque–Hilsch vortex tubes have been investigated since the 1930s, a clear consensus has yet to be established. In the present research, unsteady energy separation mechanisms in a single-outlet vortex tube are investigated. The single vortex tube is modelled using both steady and unsteady Computational Fluid Dynamics (CFD) approaches. The unsteady CFD simulations are conducted using a Detached Eddy Simulation, and the steady simulations are performed with the Reynolds Stress Model. The experimental energy separation performance of a single-outlet vortex tube reported in the literature, with and without damping of the unsteady disturbances, is reproduced numerically. The explanation given in the original work, which describes energy separation as a result of changes in the time-averaged tangential velocity profile due to acoustic streaming, is not supported by the current numerical results. Therefore, a further investigation is made to determine other unsteady mechanisms occurring within the device. The inherent complexity of the transient three-dimensional flow field complicates the interpretation of fundamental flow structures and their associated unsteady dynamics. This is overcome by applying Spectral Proper Orthogonal Decomposition (SPOD) to the CFD dataset. Analysis of the dominant SPOD modes reveals two unsteady mechanisms within the flow field, including the radial transport and dissipation of vortical structures as well as the rotation of semi-coherent “blades” formed by Rossby vortices. An important finding of this study is that the combined effect of these mechanisms accounts for the energy separation observed in the single-outlet vortex tube.