Annular swirling liquid layer with a hollow core

Abstract

A thick turbulent annular liquid layer that swirls inside a fixed pipe is studied by means of surface observations and stereoscopic particle image velocimetry in an index-matched nozzle facility. This flow combines the complexities of swirling and free-surface turbulence. The free surface of the layer changes the boundary condition compared to filled swirling pipes and introduces the equivalent of a hollow core. The liquid layer shares similarities with turbulent open-channel flows, with the high centrifugal force across the layer having a similar effect to that of gravity in channel flows. At the surface, the restoring forces are surface tension and centrifugal acceleration. The particular nozzle under study has been envisioned for inertial confinement fusion, but the flow has relevance to systems such as compact separators or liquid rocket fuel injectors. Data are acquired at five downstream locations from the nozzle exit for four Reynolds numbers for subcritical flows. Injection flow rate and fluid kinematic viscosity are controlled independently, which allows adjusting independently the Reynolds and Taylor–Reynolds numbers. This also enables control of the centrifugal force at the free surface to test the effects of turbulence intensity on the free surface in regimes where air entrainment and droplet ejection occur. The swirl number is fixed by the design of the nozzle. From velocimetry data, mean velocity and turbulence statistics are extracted. For all the conditions tested, three flow regimes are identified: developing, developed, and transitional. The developed regime appears self-similar on the mean; the swirl creates a favourable pressure gradient that sustains the axial flow and confines the boundary layer near the wall. Large coherent vortex structures are identified in the layer. A simple model is proposed to describe the layer thickness and the velocity distribution in it. In the transitional regime, helical varicose waves generated by centrifugal instability are observed on the surface. Additionally, wall effects are visible in the bulk of the flow, and the main flow features are large overturning motions.