Detailed Structure of the Tip Vortices

The roll-up of the tip vortex in terms of its strength, velocity distribution, and location defines the initial conditions for the subsequent behavior of the rotor wake. Tip vortex formation is a complex problem involving high velocities with shear, flow separation, pressure equalization, and turbulence production. On most helicopters, which will have rectangular or mildly tapered blade tips, experimental evidence shows that a single vortex is fully formed at the trailing edge of the blade tip, as in Fig. 10.17, which is a shadowgraph of the flow near the tip of the blade. The tip region is enveloped with a region of high vorticity, which rolls up quickly into a dominant vortex. Because rotor blades have very large pressure differences over their tip region, the resulting tip vortices have high circulation, high swirl velocities, and relatively small viscous cores.

Most vortex wake models used for rotor loads, performance, and acoustics will have some kind of semi-empirical representation of the tip vortex characteristics. Because tip vortex properties are not as well documented as they should be for helicopter rotors, the required parameters to formulate a suitable model of the vortex are often interpreted or extrapolated from those measured in fixed-wing studies – see Rorke et al. (1972) and Rorke & Moffitt (1977). However, because of the sustained proximity of the blades to the tip vortices, the mutual interactions between the vortices, and the stretching of the filaments as they are convected in the nonuniform flow, there is questionable validity in simply extrapolating fixed-wing results to the rotor case. Another complication is that the blade tip shape is known to affect the strength and location of the blade tip vortex as it is trailed off into the wake, and these effects are even less poorly understood. For some tip shapes, multiple vortices may be produced, although one of these is usually stronger and tends to dominate the flow.

Even for rectangular tips, the overall roll-up of the tip vortex in terms of its strength and initial location behind the blade is found to be difficult to predict. Based on classical centroid of vorticity approaches, which are used in some forms of rotor analysis, the computed vortex

release locations generally tend to be predicted radially much further inward toward the hub than are observed from flow visualization experiments. Using fundamental vortex dynamics, Rule & Bliss (1998) have highlighted the complexity of modeling the problem. Modem first-principles finite-difference methods, such as those discussed by McCroskey (1995) and Tang & Baeder (1999), have achieved better success in predicting the exact point of origination of the tip vortex. However, for many methods, numerical diffusion and dispersion tends to produce significant errors in the subsequent vortex behavior, overpredicting the growth of the viscous core to the point that these methods cannot yet be used to confidently model the rotor wake and its induced velocity field – see Section 14.10.2.