Ranque-Hilsch effect revisited - Temperature separation traced to orderly spinning waves or 'vortex whistle'

An acoustic streaming model of the total temperature separation mechanism present in the air flow in a Ranque-Hilsch tube is detailed. Previous explanations of the phenomenon of cold air encountered in the core flow and elevated temperatures of the radial wall flow in a tube where the inlet stream enters tangentially are reviewed. The emergence of a vortex whistle is shown to be a selective amplification of background noise, present in the swirling flow, and drawing energy from the flow itself. Taking the base flow to be a helix with a constant axial velocity and a swirl which is a Rankine vortex, the imposition of unsteady disturbances is demonstrated to result in the establishment of an unsteady boundary forming an annular viscous region around an inviscid core. A feedback occurs between the acoustic streaming in the outer layer and the inviscid core. Results are given for calculations of the frequency, the form of the second-order waves, and the tangential acoustic streaming at the outer edge of the unsteady viscous layer.