Descending Flight and the Vortex Ring State

The problem of the vortex ring state (VRS) has already been discussed in Sec­tions 2.13.6 and 5.7. VRS is a problem. that is not amenable to solution (prediction) by methods such as momentum theory, and more advanced prediction methods must be sought. Developments of free-vortex and vorticity transport models (see Section 14.3) have recently allowed the problem of VRS to be examined in much more detail, and for the effects of flight condition and rotor geometry on the VRS problem to be better exposed – see Brown et al. (2002) and Newman et al. (2004). However, a primary difficulty in either approach is to faithfully model the tip vortices in the rotor wake to old ages, as well as the problem of modeling accurately the physics of vortex-vortex and blade-vortex interactions. Another difficulty is that the descending flight problem is inherently unsteady, so time-accurate methods of solution such as discussed in the previous section are a necessary prerequisite.

To illustrate the general behavior of the wake in descending flight, Fig. 10.49 shows views of a rotor wake that have been predicted using a FVM for a notional four-bladed rotor when transitioning from hover into axial descent. Six free-vortex turns were used to model the rotor wake; a fairly large number of wake turns must be used because the older vortex filaments can come close to the rotor disk plane as VRS is approached and accurate modeling is important here. All results show a “snapshot” of the wake at an arbitrary instant in time.

In hovering flight Fig. 10.49 shows that the wake consist of sets of nearly helical, closely interdigitated vortices, but with some evidence of wake disturbances and an aperiodic behavior in the far wake, as discussed previously in Section 10.5.1. See also Leishman et al. (2002a). For very low rates of descent there is more evidence of a wake instability and the subsequent formation of vortex perturbations. Because of the imposed descent velocity, the wake cannot be convected as far downstream below the rotor in a given time and the downstream wake filaments begin to “bundle” together. If the rate of descent is low enough then the developing bundles of vorticity are still confined to the far wake well downstream of the rotor and are convected away from the rotor as fast as they develop. For these low rates of descent the bulk of the wake is still in equilibrium and there is little or no effect on the blade airloads or rotor performance.

As the rate of descent is increased further, however, the net velocity through the rotor disk is decreased and more of the vorticity generated at the blade tips begins to accumulate near the rotor TPP. At some point, the descent velocity is high enough to cause the tip vortices to convect into the TPP after they are first formed, thereby creating a form of BVI. Notice that the developing perturbations in the wake also become more evident, and because of the higher rotor descent velocity in this case these perturbations now lie much closer to the rotor. While the wake cannot yet be considered to have “broken down” for these descending flight conditions, a characteristic feature is that parts of adjacent vortices pair together and eventually tightly clump or bundle, essentially forming toroids or vortex rings. These vortex rings themselves are not stable and naturally begin to develop a series of Kelvin waves

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