In the early 1980's the interaction of the rotor-wake with the airframe was cited as the biggest obstacle in rotor performance predictions(Sheridan and Smith). The wake from the main rotor, especially the tip-vortex, is a primary component in many aerodynamic interactions. Today, rotor-airframe interactions can be predicted relatively easily, once the vortex characteristics are known(Conlisk). Smaller rotor-airframe spacings imply that the tip-vortex interacts with the airframe while still very strong and thus the airframe is subject to severe vortex loads and vortex-induced separation. The ability to modify the rotor-wake in order to reduce interaction effects also depends on knowledge of the tip-vortex formation at the blade-tip and its evolutionary characteristics. The understanding of the near-wake is thus essential to remove many of the obstacles to first-principles-based prediction of rotorcraft aerodynamics.
In fixed wing aircraft, trailing aircraft separation is a major factor in determining the net flow of air traffic. Air traffic can be increased by substantial amounts by reducing the spacing between successive aircraft. This is restricted currently by the observed persistance of the tip-vortices from large aircraft, for several miles downstream of the aircraft(Rossow). The hazard on trailing aircraft in terms of imposed roll is dependent on the strength and spread of the tip-vortex. A comprehensive system is under development at NASA-Langley called the Aircraft Vortex Spacing System(AVOSS). Hinton presents a description of the system, which uses the available knowledge of aircraft wake generation, atmospheric modification of those wakes, wake-encounter dynamics, and operational factors to arrive at dynamical wake-vortex spacing criteria for use at airports by the air traffic control. A major component of the system, thus, is the knowledge about the wake generated by a lifting wing, particularly the concentrated tip-vortices, and their downstream development.
There is a wide body of research involving measurements of the tip-vortex core, for both fixed and rotary-wings. The structure of the tip-vortex in the near wake cannot be assumed to be the same in rotary wings and fixed wings. Issues that do not appear to be of importance in fixed wings might play a significant role in rotary wing predictions and vice-versa. Our attempts to tackle the problem are based on the premise that, if the origin and nature of the tip-vortices from fixed and rotary wings can be related, then it would be possible to devise means to alleviate vortex-interaction related problems in both fixed wing and rotary wing communities simultaneously.
A consistent feature of the tip vortex
measurements on a 2-bladed rotor in forward flight at Georgia Tech(Mahalingam
and Komerath) is the presence of a substantial velocity component directed
along the axes of the strong vortices in the rotor wake. This is seen in
Fig.
1.
Figure 1: Typical velocity distributions
across vortex core
Figure 2: Variation in load distribution between a fixed and rotary wing due to incoming velocity variation
This is an aspect which is missing from most vortex representations used in predictions, and is yet of first-order importance to interaction problems(Mahalingam et al.). The lack of a three-dimensional representation to the tip-vortex is largely attributable to the considerable debate regarding the magnitude and direction of the core-axial velocity. Theoretical work by Batchelor and Saffman postulated a jet-like or wake-like flow in the core of a wing tip vortex depending on a parameter which was a function of the tip loading. The load distribution on a fixed wing configuration is considerably different from that on a rotary wing configuration due to the incoming velocity variation. This is shown in Fig. 2.
Experiments on fixed wings have shown both jet-like and wake-like core axial velocities. There have been several hypothesi s for the reasons behind the observed effects. Some researchers have claimed that Re No. has an effect on the axial velocity, vis-a-vis, an increase in wake deficit with Re No. Others have noticed dependence on the tip-shape and airfoil section used. There have been studies where the core axial flow has reversed direction during its downstream development. There has, however, been no systematic study of all the parameters, that can effect the core axial flow in a tip-vortex.
Rotary wing data are much more sparse with very few published results on core axial velocity. Measurements by McAlister et al on a two-bladed rotor in hover, showed strong wake like axial velocity. Shivananda used a split-film anemometer to resolve all three components of velocity in the wake of a single-bladed, square-edged rotor in hover. He found a wake-like core: the axial velocity was directed back along the trajectory of the vortex towards the blade. Thompson studied the same rotor blade wake, and resolved all three components of velocity in the vortex using a laser velocimeter. He was able to achieve high data rates using an off-axis light receiving system, and incense smoke particles which were small enough to stay inside the core. He showed not only a wake-like vortex core, but also secondary features inside the core, indicating several layers of vortex sheet roll-up. There is some flow visualization evidence in the literature on propeller wakes which supports this finding (Adams and Gilmore). Leishman et al measured the 3-components of velocity in the tip-vortex core of a 1-bladed rotor in hover and found a wake-like axial velocity. The axial velocity profiles dissipated within the first 90° of wake age. The core diameter increased while the core peak tangential velocity decreased rapidly in the first 180° of wake age.
Recent measurements on oscillating
wings have shown wake-like core axial velocities. Measurements by Ramaprian
and Zheng indicate an core axial velocity deficit increasing with the
pitch angle. Similar measurements by Chang and Seung
show core axial velocity deficits approaching upto the freestream velocity.
Thus, there are large variations in the magnitude and direction of core
axial velocities, measured in different tests over a range of conditions.
One aim of this research is to identify the factors that result in such
a broad band of observed data for core axial velocity.
Figure 3: Circulation and trailed vorticity distribution on a two-bladed rotor in forward flight, advance ratio = 0.1
Another topic of heated debate concerning tip-vortices is how soon after being trailed the tip-vortices diffuse or dissipate. There is again a very large band of data from several tests and no clear evidence of any one major factor causing wake decay/dissipation. There are, however, several hypothesis and wake decay models proposed by several researchers and they will be addressed in the results section. While it has been noted in many cases that fixed wing vortices tend to persist for several hundred chord lengths downstream of the wing(Orloff), some researchers have reported early decay times. An interesting approach to the vortex diffusion problem was presented by Roberts, who demonstrated that the presence of axial velocity deficit in the tip-vortex inhibited turbulent diffusion of the core. Sarpkaya, presents an in-depth analysis of the decay characteristics of the tip-vortex from flight tests of large aircraft using Lidar. He suggests that the decay of trailing vortices is governed by the mutual straining of the tip-vortices. Core diffusion has been generally accepted as an inevitability in rotary wing vortices. Claims of viscous diffusion in rotary-wing vortex cores are refuted easily by a simple analysis shown by Jain et al., showing that in the absence of turbulence, vortex cores will persist for over 200 revolutions. Some researchers have reported measurements that seem to indicate turbulent diffusion of the vortex core. However, on close scrutiny, it becomes clear that much of the turbulence attributed to the core is, in fact, an artifact of ensemble averaging point measurements in aperiodic flow-fields. Rotary wing flowfields, especially in hover, are highly susceptible to facility recirculation effects and ensuing aperiodicity(Shinoda and Johnson, Piziali and Felker). The tip-vortex core location meanders considerably from cycle to cycle, resulting in a smoothing out of the data, when averaged over several cycles. This smoothing is easily construed as turbulent diffusion. The effects of the core-meandering can be filtered out from the averaged data by a technique first demonstrated by Devenport et al. on fixed wings and used by Leishman on rotary wings. Another technique to ascertain flowfield unsteadiness and determining the minimum number of data points for ensemble averaging has been demonstrated by Mahalingam and Komerath. Unsteadiness in rotary wing hover tests is responsible for poor performance measurement as well as insufficient vortex-representation for prediction techniques. However, unsteadiness need not be accepted as a intractable problem. Caradonna et al., recently demonstrated that it is possible to eliminate the effects of facility recirculation in axial tests and extrapolate to attain hover performance. They also observed a periodic, deterministic pairing phenomenon, that resulted in a merger between the two tip vortices. There was no evidence of core diffusion. If anything, the strength of the merged cores is expected to be higher than each of the individual vortices.
There is one other major difference between fixed wing and rotary wing wakes. In a fixed wing the wake convects downstream and away from the generating wing. Thus, the trailed tip vortex does not affect the bound circulation distribution on the wing. The tip-vortices trailed from a rotary wing, however, stay in the vicinity of the rotor blades for a few revolutions of the vortex, significantly affecting the bound circulation distribution on the rotor blade. This was demonstrated by Bhagwat and Leishman on a two-bladed rotor in hover and is seen in fig.3. from blade element calculations at Georgia Tech. This calculation used experimentally measured inflow variation and flapping angles by Liou. Note the dip in the circulation distribution at about 0.75R. This corresponds to the increased inflow caused by the vortex from the previous blade. This in turn affects the trailed vorticity distribution seen in fig. 3. Inboard of the tip vortex, there are several filaments of trailed vorticity, with circulation opposite to that of the tip vortex.
Thus the vorticity trailed in a rotary wing might be considerably different from that in a fixed wing. This would alter the downstream development of the primary tip-vortex. This has been observed by Kim on a model rotor and recently by Ghee on a small-scale rotor with a tip-loading representative of a full-scale rotor, and at higher tip speed. It is also seen that this region of opposite circulation has a wake-like axial velocity.
A quick mention needs to be made about the choice of technique used to obtain vortex velocity data. Every technique used is subject to limitations or data contamination from probe obstruction. Optical techniques like LDV are widely used, but do not provide very reliable data in the core, due to lack of seeding in the core. Hot-wire data is susceptible to directional ambiguity as well as vibration in rotor flow-fields. Probes such as multiple-hole pressure sensors are large intrusions in the flow-field and presumably affect even the mean location of the tip-vortex. These constraints need to be taken into account when attempting to address the large band of results obtained in tip-vortex measurements. The following sections address each of the factors that might play a role in the observed vortex characteristics.
FACTORS DETERMINING TIP-VORTEX CHARACTERISTICS
In this section we study in detail each of the parameters that may determine the tip-vortex characteristics. The aim is to be able to describe a dependence between the tip-vortex characteristics such as circulation, radius, Maximum circumferential velocity, axial velocity and wake decay, in terms of lift coefficient, Re No., chord length, Aspect ratio, tip shape etc.