Prediction of turbulent trailing vortex structure from basic loading parameters
A novel analytical method has been developed to accurately predict the core structure of a fully developed trailing vortex. Properties in the trailing vortex are calculated from the load distribution on the generating wing, and satisfy a set of fundamental conservation laws. The present rollup model is based on the Betz method, with significant improvements which address both viscous effects in the vortex core region, and also the effects of viscous drag on the generating wing. Turbulent mixing in the core is handled implicitly through the appropriate choice of solution velocity profiles, which contain free constants. These constants are determined uniquely by conserving properties between an inviscid Betz-type vortex and a vortex with experimentally consistent velocity distribution. The method is developed for arbitrary wing loading and results are presented for several important cases. Comparison with experiment demonstrates the accuracy of the model.
