A semi-empirical model for streamwise vortex intensification

Abstract

Vortex intensification plays an important role in a wide range of flows of engineering interest. One scenario of interest is when a streamwise vortex passes through the contracting streamtube of an aircraft intake. There is, however, limited experimental data of flows of this type to reveal the dominant flow physics and to guide the development of vortex models. To this end, the evolution of wing-tip vortices inside a range of streamtube contractions has been measured using stereoscopic particle image velocimetry. A semi-empirical model has been applied to provide new insight on the role of vorticity diffusion during the intensification process. The analysis demonstrates that for mild flow contractions, vorticity diffusion has a negligible influence due to the low rates of diffusion in the vortex flow prior to intensification and the short convective times associated with the streamtube contraction. As the contraction levels increase, there is a substantial increase in the rates of diffusion which is driven by the greater levels of vorticity in the vortex core. A new semi-empirical relationship, as a function of the local streamtube contraction levels and vortex Reynolds number, has been developed. The model comprises a simple correction to vortex filament theory and provides a significant improvement in the estimation of vortex characteristics in contracting flows. For the range of contractions investigated, errors in the estimation of vortex core radius, peak tangential velocity and vorticity are reduced by an order of magnitude. The model can be applied to estimate the change in vortex characteristics for a range of flows with intense axial strain, such as contracting intake streamtubes and swirling flows in turbomachinery.