Reynolds Number Based Blade Tip Vortex Model

A mathematical model has been developed to estimate the temporal growth properties of helicopter blade tip vortices at any vortex Reynolds number. One unique feature of the model is that it takes into account rotational stratification (Richardson's number) effects on the distribution of turbulent viscosity inside the tip vortices. This model is combined with another model for the effects of filament stretching for predicting the net temporal evolution of the vortex. A turbulent growth model solves exactly for the tangential (swirl) velocity starting from the Navier– Stokes equations using an assumed variation in eddy viscosity across the vortex core. This variation is a function of the local Richardson's number, and the final solution becomes dependent on vortex Reynolds number. A more parsimonious functional approximation is given to represent the induced velocity distribution in the tip vortices for practical applications. It is shown that the temporal core growth rate predicted by the new model increases with an increase in vortex Reynolds number, which is consistent with experimental observations. The predictions from the model were validated, wherever possible, with tip vortex measurements from both model- and full-scale rotors.