Free-Vortex Wake Calculations of Helicopter Rotors and Tilt-Rotors Operating-In and Transitioning Through the Vortex Ring State

June 2001 (Updated: May 2002 and July 2002)
 

Introduction
Approach
Documented Case Studies
Publication References
 
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Introduction

An improved understanding of the vortical wake structure generated by lifting rotors is a key factor in accurately predicting the aerodynamic behavior of all modern rotorcraft. While the accurate prediction of rotor flow fields is difficult under most flight conditions, prediction of the wake dynamics during descending flight has proven to be particularly challenging. This is because of the close proximity of the blades to their tip vortices, as well as the inherent unsteadiness (aperiodicity) of the rotor wake when the rotor is in descending flight conditions.

Under conditions when the upward component of velocity normal to the rotor disk plane is a more substantial fraction of the average induced velocity downward through the rotor disk, such as when descending at higher rates, the rotor can begin to operate in an adverse condition known as the "vortex ring state" (VRS). Under VRS conditions the wake vorticity produced by the blades cannot convect away from the rotor, and accumulates near the rotor plane, clumping or bundling together forming a flow condition that is analogous to flight in a vortex ring.

The VRS flight condition is manifest by unsteady blade airloads, fluctuating rotor thrust, significant vibrations, and high induced rotor power requirements. The significance of this flow state was first recognized by Georges de Bothezat in 1922. These adverse conditions mostly occur within a boundary confined to a part of the flight envelope at low forward airspeeds and at steep angles of descent or high rates of descent. However, it is also known that symptoms of the VRS may occur under other flight conditions that may produce significant upward components of flow velocity normal to the rotor disk plane, such as during certain types of maneuvering flight.

A representative example of the complex flow topology surrounding a descending helicopter rotor operating deeply in the VRS, is shown in the adjacent (left) figure. This is a smoke flow visualization image taken by illuminating a cross-section through the rotor wake (photo from the classic work of Drees and Hendal in 1950). Deeply into VRS, the flow near the rotor is found to resemble that of a three-dimensional bluff body operating at low Reynolds numbers, with unsteady recirculation of the flow near and in the rotor plane. Another example documenting the complexity of the flow when a rotor operates in the VRS is shown in the right figure, which is a shadowgraph flow visualization for similar axial descending flight conditions. (Photo from the University of Maryland collection). In this case, the individual blade tip vortices comprising the recirculating wake are now visible, which are seen to bundle together near the rotor plane. For rotor operations in the VRS, an inherent unsteadiness (aperiodicity) is a characteristic of the flow state, which is reflected by the waves and knots produced on the tip vortex filaments.

Operationally, entry into the VRS manifests as rotor thrust fluctuations and also an increase in the average rotor shaft torque (power required), the latter which is necessary to overcome the higher induced aerodynamic losses associated with rotor operations inside its own wake. Most helicopters do not have a lot of excess power available at low airspeeds, so the extra power required to overcome these additional induced losses can be of sufficient magnitude to negate the decreased rotor power requirements associated with giving up altitude (potential energy). Therefore, when in the VRS, the application of high rotor torque (power) may be required to maintain equilibrium flight, even though the aircraft is rapidly descending. This scenario is often referred to by pilots as "power settling" or `"settling with power," and can be a safety of flight issue. These terms, however, are not accurate descriptors of VRS conditions because "settling" issues can also occur under operational flight conditions when VRS is not present.

The unsteady flow conditions obtained during flight in or near VRS, may also result in highly unsteady blade airloads, significant rotor vibrations, and unpredictable, aperiodic blade flapping. The blade flapping can lead to substantial loss of control effectiveness and high piloting workload. The rotor thrust fluctuations usually lead to low-frequency vertical vibrations and a characteristic "bounce" of a helicopter. While operation in the VRS is obviously undesirable, it can be entered inadvertently through poor piloting technique. Recovery is usually attained quickly, however, by the application of cyclic control inputs to cause some increase in forward or sideward airspeed so as to sweep the recirculating wake away from the rotor disk.

Recently, there has been renewed interest in understanding and predicting the flow mechanisms that lead to the onset of the VRS, both for helicopters and other rotating-wing aircraft such as tilt rotors. Modern military rotorcraft are required to fly over a wide range of operational conditions, including evasive combat maneuvers at low airspeed, rapid pull-ups, and descending wind-up turns. These flight conditions may cause the main rotor(s) to operate inside their own wake, and possibly near to or inside the VRS boundary, if such a boundary exists. The trend toward helicopter designs with higher main rotor disk loadings means that the VRS boundary may be pushed to higher rates of descent but also to higher forward airspeeds. Therefore, the symptoms of VRS may begin to intrude more into their operational envelope.

The behavior of tilt rotors at high rates of descent have recently come under particular scrutiny because of a hypothesized susceptibility to an asymmetric form of VRS between the two rotors. Flow field predictions have suggested that there are significant asymmetric, interacting wake dynamics associated with closely spaced rotors when operating at higher rates of descent. near the VRS. This can manifest as asymmetric airloads between the two rotors before the more characteristic, classical VRS conditions are reached.

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Approach

Time-accurate free-vortex wake calculations have been conducted where rotors transition through the "vortex ring state" or VRS. Several different case studies have been examined, including transition flight through the VRS from hovering flight, which in many of the calculations shown in the results here provides the initial condition for the problem. The solutions are all fully time-accurate, with the vortex filaments in the rotor wake(s) being tracked in a Lagrangian sense using the free-vortex method of Bhagwat & Leishman. The integration method uses a second-order accurate predictor corrector method. Click here or see below to download a copy of the papers documenting the methodology.

The method uses a Lagrangian description of the flow. Discrete line vortices are used to represent the structure of the rotor wake. Markers are placed at equal intervals of time along vortex filaments trailed from the rotor blades, and are linked together using a piecewise-linear reconstruction. The numerical solution proceeds by time-marching after the partial derivatives in the governing equations have been approximated using finite differences. Because most standard numerical integration schemes exhibit some type of non-physical instability if used to advance the free-vortex equations, special integration schemes must be developed to preserve both the temporal accuracy and the stability of the method. The present approach uses Bhagwat & Leishman's PC2B scheme, which has a five-point central difference approximation to the spatial derivatives, and a three-point second-order backward difference approximation to the temporal derivatives. The PC2B scheme is specially designed to introduce truncation terms that are dissipative, so balancing and stabilizing the governing equations for the wake while retaining its overall second order accuracy. The velocity field is evaluated by applying the Biot-Savart law to all the vorticity being shed and trailed from the blades, and for straight-line segmentation this approach is spatially second-order accurate. The free-vortex method for the rotor wake is fully coupled to a rotor blade model, and the blade air loads and rotor flapping response are calculated simultaneously in a time-accurate fashion.

The helicopter results use a generic 3-bladed, fully articulated rotor. The tandem is also a three-bladed articulated rotor. The tilt-rotor results use a gimbaled hub, which is a bit like a 3-bladed teetering rotor. In most cases, only the dominant tip vortex filaments are shown in the wake movies to preserve clarity. The results show that VRS can be viewed as a form of wake instability. In normal operational flight, including shallow descents, any instabilities in the wake are usually convected away from the rotor as quickly as they are formed. These instabilities originate from different types of instability "modes" that are associated with helicoidal wake filaments (see papers below). However, in descending flight the instabilities move closer to the rotor. Eventually, at a rate of descent that varies from configuration to configuration, the instabilities in the wake begin to reach the rotors and so begin to affect the air loads there. For the side-by-side (or tilt-rotor) configuration, this corresponds to the onset of significant asymmetric aerodynamics between the two rotors.

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Documented Case Studies.

Click on case number to jump to page. All images © J. Gordon Leishman , Shreyas Ananthan & The University of Maryland. All rights reserved.

Single Rotor Helicopter:

Tandem Rotor Helicopter:

Single Rotor From a Tilt-Rotor:

Tilt-Rotor:

Other Cases of Interest:

Tilt-Rotor Maneuvers:

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Selected Publications on Wake Model, Wake Stability, and VRS Calculations

  1.   Bhagwat, M. & Leishman, J. G. "Time-Accurate Free-Vortex Wake Model for Dynamic Rotor Response." (Click on the image below to download a pdf version of this paper - file size 0.8MB ).
  2. Bhagwat, M. & Leishman, J. G. "Transient Rotor Inflow Using a Time-Accurate Free-Vortex Wake Model " (Click on the image below to download a pdf version of this paper - file size 0.8MB ). Also published in the Journal of the American Helicopter Society, January 2001.
  3. Bhagwat, M. & Leishman, J. G., "On the Aerodynamic Stability of Helicopter Rotor Wakes." (Click on the image below to download a pdf version of this paper - file size 400KB). Also published in the Journal of the American Helicopter Society, October 2000.
  4. Leishman, J. G., Bhagwat, M. J. and Ananthan, S., "The Vortex Ring State As a Spatially and Temporally Developing Wake Instability." (Click on image below download a pdf version of this paper - file size 7MB - please be patient !).
  5. J. Gordon Leishman, Mahendra J. Bhagwat and Shreyas Ananthan. "Free-Vortex Wake Predictions of the Vortex Ring State for Single-Rotor and Multi-Rotor Configurations" Click here or on the image below to download a pdf version of this paper.
  6. R. Brown, J. G. Leishman, F. J. Perry & S. J. Newman. "Blade Twist Effects on Rotor Behavior in the Vortex Ring State" Click here to download a pdf version of this paper.

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Case 1h - Helicopter Rotor in Axial Descent Transitioning into Autorotation Through VRS:

At time zero, the rotor operating state is changed from the hover state by a simultaneous reduction in collective pitch and an increase in vertical descent velocity into a high rate of descent that takes the rotor into the autorotational flight condition. Note the onset of wake instabilities, which cause the filaments to exhibit smooth sinuous deformations. The filaments also tend to band together, forming "rings". These rings are analogous to the starting vortex system trailed from a fixed-wing when set into rectilinear motion. The rings themselves are also unstable, and may deform and break away from the rotor and/or the wake. The rotor then transitions through the vortex ring state where there is a large recirculation of flow in the plane of the rotor, into autorotational flight and into the windmill brake state where the wake flow returns to a well-behaved periodic solution. During the transition process from hover into the windmill brake state, the rotor thrust and power show large fluctuations. Note also from the movies, the large amount of rotor flapping that occurs as the rotor enters into the vortex ring state or VRS. This blade flapping tends to produce side forces on the rotor, which helps a freely flying helicopter to gain airspeed to exit the VRS.

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Case 2h - Helicopter Rotor in Low Speed Axial Descent (Incipient VRS), Followed by Transition into Low-Speed Forward Flight:

At time zero, the rotor is operating in hover and the operating state is changed by a simultaneous reduction in collective pitch and an increase in vertical descent velocity into a low speed vertical descent. The rotor then enters an incipient VRS, where there is periodic recirculation of the rotor wake in the plane of the rotor. There are mild but significant fluctuations in rotor thrust in these conditions. After a few seconds of operation in the VRS, the rotor is given a mild increase into forward flight speed (while still maintaining the same rate of descent) and the rotor begins to transition out of the VRS. However, in this case the rotor never gets completely out of the VRS because there are clearly always concurrent upward and downward regions of flow over the rotor disk.

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Case 3h - Helicopter Rotor in Low Speed Axial Descent (Incipient VRS), Followed by Transition into High-Speed Forward Flight:

At time zero, the rotor is operating in hover and the operating state is changed by a simultaneous reduction in collective pitch and an increase in vertical descent velocity into a low speed vertical descent. The rotor then enters an incipient VRS, where there is periodic recirculation of the rotor wake in the plane of the rotor. There are mild but significant fluctuations in rotor thrust in these conditions. After a few seconds, the rotor is given a rapid acceleration into forward flight speed (while still maintaining the same rate of descent) and the rotor begins to exit the VRS. After a few seconds (7-8 rotor revolutions) the descending rotor is well out of the VRS.

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Case 4h - Helicopter Rotor in Low Speed Axial Descent Undergoing a Pitch-Up Type of Maneuver:

This is an example where the application of a maneuver causes the rotor to enter into a VRS condition. For these calculations, the rotor was first trimmed to obtain equilibrium conditions at low forward speed and moderately high rate of descent. This flight condition is outside, but close to, the envelope where VRS conditions would normally be expected to exist for this rotor. The solution was then time-marched for a further 20 rotor revolutions to allow any remaining transients to convect out of the solution. The flow conditions subsequently obtained were nominally periodic, but the descent velocity was still sufficient high to cause some instabilities to develop in the far downstream wake below and behind the rotor. Note that for these conditions, the blade tip vortices lie in, above, or close to the plane of the rotor. This flight condition formed the initial condition for the maneuver.

The maneuver simulated in this case was a rapid pull-up type of maneuver, which was represented by an increase in collective pitch and longitudinal cyclic inputs to give a disk angle of attack of 15 degrees and a non-dimensional pitch rate of q=0.04. These input conditions were then held, and the wake solution was time-marched from the initial condition for a further 8 rotor revolutions (just under 2 seconds in real-time), at which time the pitch rate was removed, the collective pitch reduced to the starting value, and the disk angle of attack was then maintained at 10 degrees The rotor was not trimmed during this process, but the blade flapping was calculated in a time-accurate manner consistent with the wake solution.

The results show that the wake developments that take place are relatively rapid, with clear evidence that the imposition of the maneuver state first causes wake vorticity to clump and bundle below the rotor. What is interesting is that this bundling of vorticity quickly forms into a "vortex ring" in a manner analogous to that shown previously for the steady vertical rates of descent. The vortex ring in this case, however, is much more of a transient nature, and can be considered the rotating wing analog of the starting vortex formed behind a fixed (non-rotating) wing placed into rectilinear motion. Notice that this ring of vorticity is then convected up toward the rotor, and passes through the rear of the rotor disk. As the blades interact with the powerful induced velocity field surrounding this vortex ring, large unsteady airloads are produced on the rotor.

The pitch rate was removed at the end of 8 rotor revolutions, and the disk angle of attack was reduced by five degrees. At this point the vortex ring that was formed has become unstable, and has begun to fold over on itself forming into a twisted "figure-of-eight" form. The upstream loop of the folded ring is then entrained back through the rotor, while the downstream part of the loop passes into the downstream wake. At about t+16 rotor revolutions, the downstream loop undergoes a further deformation, which induces a velocity field on the upstream loop that causes it to be convected back up toward the rotor again. This is followed by a twisting of the vortex loops so that the loops now lie more in a lateral plane. Finally, the flow adjustments cause the wake to reestablish a nominally helicoidal structure, and by about t+30 revolutions the wake structure returns to a form closely resembling the initial condition.

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Case 1ht - Tandem Helicopter Rotor Operating in Low Speed Vertical Descent

In this case, the rate of descent is about 1/3 of the hover- induced velocity. The initial condition is the time accurate hover wake result. Note that in the rotor overlap region, there is a much higher induced velocity, so the vortex filaments in the wake are convected more quickly in this region. There is some evidence of the development of wake instabilities, but these are convected away from the rotor as fast as they are formed. Note that the higher induced velocity in the overlap region helps convect any developing instabilities away from the rotor.

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Case 2ht - Tandem Helicopter Rotor Operating in Vertical Descent Approaching VRS:

In this case, the rate of descent is about 0.6 of the hover-induced velocity. The initial condition is the final solution from Case 1ht. Note that in the rotor overlap region, there is a much higher induced velocity, so the vortex filaments in the wake are convected more quickly in this region. There is considerable evidence of the development of wake instabilities, but note that the higher induced velocity in the overlap region helps convect any developing instabilities away from the rotor. It has been found from other calculations at higher rates of descent that it is very difficult to get a tandem rotor configuration into the VRS, and there is little of any fore-aft asymmetries in the airloads between the two rotors.

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Case 1st - Single Isolated Rotor of A Tilt-Rotor Operating in Hover:

Initial condition is a prescribed wake. These results show that for an isolated rotor operating in hover, the wake structure takes on a nominally helical structure.

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Case 2st - Single Isolated Rotor of a Tilt-Rotor Operating in Low Speed Vertical Descent:

These results show that for an isolated rotor operating in hover, the nominally helical structure of the wake begins to break down in the far wake and form instabilities. This has no effect on the rotor performance.

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Case 1t - Tilt-Rotor Operating in Hovering Flight:

These results show how the wakes generated by a multiple rotor configuration may interact. In this case, the rotors are perfectly synchronized so as to impose symmetry in the solution. Such a solution is purely artificial, because in reality there must always be some loss of symmetry to the problem because of differential pilot control inputs, turbulence, gusts etc. However, it serves to illustrate the well-behaved numerics of the solver for the wake equations. The solution starts from a "prescribed" wake geometry, which is only an approximate solution, and the time-marching allows the rotor wake solution to "relax" to the correct force-free vortex positions over several rotor revolutions. Notice that as the solution proceeds there is an initial formation of "vortex rings" in the wake, which are essentially groups of vortex filaments that are drawn into a concentrated bundle. These rings are unstable, and the instability of the ring starts through a series of sinusoidal waves on the filament. At longer times, all the rings and other transients are convected out of the solution, and the wakes become essentially periodic at the rotor frequency. Any other types of disturbances tend to be quickly convected out of the wake solution, which remains stable. Note that because of the symmetry of the problem imposed in this in this case, the rotor wake solutions are always exact mirror images.

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Case 2t - Tilt-Rotor Operating in Low-Speed Vertical Descent:

These results show two side-by-side, perfectly synchronized rotors operating at a low rate of vertical descent. The rate of descent is roughly 0.3 of the hover induced velocity, or about 1,200 ft/min in this case for a tilt-rotor of the weight class of the V22. While this is an idealized flight condition, it serves to illustrate the basic physics of the descending wake dynamics problem on side-by-side rotors. In the initial stages of the solution, the wakes are perfect mirror images of the other, but one of the of the rotors is given a small series of disturbances so that the symmetry of the problem is destroyed, as would be typical of actual flight conditions. Under these descending flight conditions, the helical pitch of the vortex filaments is smaller (filaments are closer together) and the wake is very much more prone to the onset of flow instabilities that may be caused by small disturbances at the rotor or elsewhere in the wake. Note the onset of instabilities in the wake, in this case, after several rotor revolutions. However, the rate of descent is low enough that the instabilities are always convected away from the rotors. The wake and induced inflow near the rotor is unaffected by the instabilities in the far wake, and so the rotor air loads are nominally constant and the thrusts on the two rotors are almost exactly in phase.

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Case 3t - Tilt-Rotor Operating in Higher-Speed Vertical Descent and in Incipient VRS:

These results show two side-by-side, perfectly synchronized rotors operating at a moderate/high rate of vertical descent and approaching the VRS. The rate of descent is roughly 0.6 of the hover induced velocity, or about 2,400 ft/min in this case. In the initial stages of the solution, the wakes are perfect mirror images of the other, but one of the of the rotors is given a small initial disturbance so that the symmetry of the problem is destroyed, as would be typical of actual flight conditions. While this is also an idealized flight condition, it serves to illustrate the basic physics of the VRS onset problem on side-by-side rotors. Under these descending flight conditions, the wake is very much more prone to the onset of flow instabilities that may be caused by small disturbances at the rotor or elsewhere in the wake. Near the rotors, note that in this case the tip vortices are convected slightly above the tip-path-planes, and in this case it is the resulting interactions of blades and tip vortices that is the source of the disturbances that initiate the wake dynamics. It is clear that the downstream wakes from the two rotors begin interact, slowly at first, but these interactions become larger with time, and quickly producing an asymmetric aerodynamic condition. Notice the significant low frequency, alternating, interacting structure of the rotor wakes. Bundles of concentrated vorticity convect up, and partly through the rotors, alternatively on the left rotor and then on the right rotor, and at low frequency. The effect on the rotor air loads and performance under these conditions is relatively large, and leads to significant out-of-phase 3/rev and sub-harmonic air loads between the two rotors. The gimbaled rotor allows for little blade flapping under these conditions compared to he helicopter case.

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Case 4t - Tilt-Rotor Operating in High-Speed Vertical Descent and in VRS:

These results show the two side-by-side, synchronized rotors operating at a high rate of descent, well into the VRS.  The rate of descent is roughly 0.9 of the hover-induced velocity, or about 3,600 ft/min in this case. In the initial stages of the solution, one of the of the rotors is given a small initial disturbance so that the symmetry of the problem is destroyed. While this pure vertical descent is an idealized flight condition, it serves to illustrate the basic physics of the VRS problem on side-by-side rotors. Note that the solution proceeds for a relatively long time (about 15 rotor revolutions) before the initial small disturbance leads to a larger instability of the wake. It is clear that the downstream wakes from the two rotors interact producing a powerful asymmetric aerodynamic condition. Notice the powerful, low frequency, interacting structures of the rotor wakes. Bundles of concentrated vorticity in the form of "rings" convect up and partly through the rotors, alternatively on the left rotor and then on the right rotor. The effect on the rotor air loads and performance under these conditions is very significant.

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Case 5t - Tilt-Rotor Operating in High-Speed Vertical Descent and in Severe VRS:

These results show the two side-by-side, synchronized rotors operating well into the most severe form of the VRS.  The rate of descent is roughly equal to the hover induced velocity, or about 4,000 ft/min in this case. In the initial stages of the solution, one of the rotors is given a small initial disturbance so that the symmetry of the problem is destroyed. Note that the solution proceeds for a relatively long time (about 15 rotor revolutions) before the initial small disturbance leads to a larger instability of the wake. It is clear that the downstream wakes from the two rotors interact producing an extremely powerful asymmetric aerodynamic condition. Notice the low frequency, alternating, interacting structure of the rotor wakes. Bundles of concentrated vorticity in the form of "rings" are continuously formed, and convect up and remain in the planes of the rotors, alternatively on the left rotor and then on the right rotor, and at a fairly low frequency.

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Case 6t - Tilt-Rotor in Low-Speed Descending Forward Flight Near VRS Boundary:

In this case, the rotors are tilted forward by 20 degrees, which simulates the transition from helicopter mode to airplane mode. These results show that some of the asymmetric VRS conditions found in axial flight are carried forth into forward flight. Because the induced velocity at the rotors decreases with increasing forward flight speed, the initial effect is that the rotors go more deeply into the VRS. This is reflected in the general shape of a VRS boundary for a helicopter, which generally shows that a lower rate of descent is required to reach VRS at low forward-speeds. The asymmetric aerodynamic effects associated with the side-by-side rotor configurations on rotor air loads and performance is still very large, and leads to significant out-of-phase air loads between the two rotors. Note again the instabilities in the wake, which result in the formation of vortex "rings" in the wakes of both rotors. The rings are unstable and tend to deform and may merge with each other. There is also a distinct low frequency periodicity associated with the wake behavior under these conditions, as for the axial flight case.

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Case 7t - Tilt-Rotor in Low-Speed Descending Forward Flight Exiting VRS:

In this case, the rotors are tilted forward by 20 degrees, which simulates the transition from helicopter mode to airplane mode. These results show that with a high enough forward flight speed, the rotors will exit out of the VRS conditions. Note that there are still instabilities that form in the far wake, but now the forward speed is sufficiently high that these instabilities are convected away from the rotors as fast as they are formed. In this case, the rotors behave very much as isolated rotors, although there are still clearly some interactions between the wakes and this has a mild effect on the rotor loads and performance.

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Case 8t - Tilt-Rotor in Low-Speed Descending Flight Undergoing Simulated Roll Rate Maneuver:

This example shows how the initiation of a maneuver (in this case a roll rate to starboard) can initiate asymmetries in the wake solution. The rotors are in low speed vertical descent, with a progressively increasing rate of descent up to about 0.6 of the hover induced velocity. Toward the end of the sequence, the rotor system is given a roll rate about the longitudinal axis running between the rotors. Initially, when the roll rate is applied, the rotors are operating near VRS and the onset of the roll rate is high enough in this case to cause a large asymmetry in the development of the VRS between the two rotors. In fact, notice that the wake from left rotor (the one out of the roll) is convected into the right rotor (the one into the roll). The behavior of the airloads under these conditions is complicated, but the rotor thrust variations indicate very severe asymmetries.

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Case 9t - Tilt-Rotor with Unsynchronized Blades Operating in Hovering Flight:

These results show how the vortical wakes generated by a multiple rotor configuration may interact. The solution starts from a "prescribed" wake geometry and the time-marching allows the solution to "relax" to the correct force-free vortex positions over several rotor revolutions. In this case, the blades are not synchronized, so the wakes are not mirror images of each other. Because of the lack of symmetry, there are interactions between the filaments that start out as "pairing" between loops of vortex filaments. These interactions can be seen in the far wake can be a source of disturbances, which tend to cause larger scale interactions between the evolving rotor wakes. These interactions occur at a relatively low frequency, and are a sub-harmonic of the rotor frequency. This behavior has been verified experimentally. In this case, the disturbances convect out of the solution. The effects of these transients on the rotor air loads and performance is small. Notice again the formation of "vortex rings" in the wake as the initial transients are convected out of the solution.

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Case 10t - Tilt-Rotor Operating in Hovering Flight, with Momentary Control Inputs:

This case shows how small pilot control inputs and some small blade flapping can induce a local wake disturbance, which may subsequently lead to a larger-scale wake disturbance. In the absence of further inputs, the initial disturbance in this hovering case is eventually propagated out of the flow field and the wake returns to a mostly periodic solution free of any kind of instabilities. This would not always be the case, especially in descending flight. The disturbance at the right rotor is a form of blade vortex interaction or BVI, which occurs as the blades flap up and down and intersect the tip vortex filaments. The resulting disturbance then is propagated into the wake, which causes the filaments to form vortex ring. Note that a "starting" vortex ring forms under both rotors, but in this case there is no symmetry imposed so the rings are not mirror images of each other. The rings then become unstable through the development of a series of sinusoidal waves, and then the two rings interact with each other. After about 15 rotor revolutions, the wake returns to its regular, almost periodic form, as per the last few rotor revolutions. These results show how the wakes generated by a multiple rotor configuration may strongly interact during any phase of flight given control input disturbance or an aerodynamic disturbance. The local disturbances can be a source of larger and more powerful wake distortions, which tend to cause powerful transient interactions between the two evolving rotor wakes. Note that these interactions occur at a relatively low frequency. The effect on rotor the air loads and performance is often small because the dynamic interactions between the wakes occur well below (downstream) of the rotor. However, in some case, the effects are more significant, and in this particular case, the result leads to mild out-of-phase air loads (e.g., thrust) between the two rotors.

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Case 11t - Tilt-Rotor Descending Along a 60-degree Flight Path Angle:

This shows the rotor wake dynamics for a side-by-side (tilt-rotor) configuration for an idealized case when moving from hover into the autorotational and windmill brake state. The rotors fly along a 60-degree descending flight path angle. These results again show how the vortical wakes generated by a multiple rotor configuration may interact. The time-marching solution starts from hover and, the rotors slowly enter into an incipient VRS condition. Because of the forward flight velocity, there is good mirror symmetry between the rotors in this case. As the rotor goes more into the VRS, there is a greater asymmetry that develops. Eventually, the rotors pass through the VRS and into the autorotational flight state, and finally into the windmill brake state, where the wake returns to a regular periodic structure. The wake expands above the rotors in the windmill brake state because the rotors extract energy from the free-stream.

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Case 12t - Tilt-Rotor Undergoing Aggressive Roll Reversal Maneuver in Low-Speed Descending Flight:

This case shows the rotor wake dynamics for a side-by-side (tilt-rotor) configuration when undergoing an aggressive roll-reversal maneuver in low-speed descending flight. The rate of descent is about 1/4 of the hover-induced velocity (or about 1,050 ft/min for a tilt-rotor in the weight class of the V-22) and the airspeed is about 40 kts. After establishing trimmed flight at these conditions, which is achieved by using rotor cyclic and collective pitch controls, the rotor system is given an aggressive roll rate about the longitudinal axis running between the rotors. The roll is first to starboard then the roll rate is reversed and the rotor system rolls to port. The maximum roll rate is about 40 degrees per second, and the maximum bank angle is 60 degrees. Notice how the wake is highly skewed and distorted in response to the roll rate. This effect, however, is clearly different on the two rotors. As a result of the roll rate, one rotor goes into a greater effective descent and the other rotor into a lesser rate of descent - that is one cause of the different wake distortion between the two rotors. Note that the wakes of the two rotors interact to a lesser or greater degree. Eventually, as the port roll develops, the wake distortion that takes place as a result of these wake instabilities causes one rotor wake to break down and to go into the VRS, and the wake vorticity then accumulates and convects through that rotor. This behavior causes large, unsteady, asymmetric aerodynamic forces and moments on the rotor systems, and the production of significant torque asymmetries. The results vividly demonstrate how standard types of maneuvers can affect the combination of rate of descent and airspeed where the adverse aerodynamic effects of VRS may be encountered. The problem is apparent on all types of rotors, but the nature of the side-by-side rotor configuration means that because the rotors are a relatively longer distance from the roll axis, the effects of roll-rate on the wake structure is amplified.

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Case 13t - Tilt-Rotor Undergoing Decelerating Roll Reversal Maneuver in Low-Speed Descending Flight:

Another case showing the interesting rotor wake dynamics for a side-by-side (tilt-rotor) configuration when undergoing a roll-reversal maneuver in low-speed descending flight. The rate of descent is about 1/4 of the hover-induced velocity (or about 1,050 ft/min for a tilt-rotor in the weight class of the V-22) and the airspeed is about 45 kts. After establishing trimmed flight at about 60 kts and 1050 ft/min rate of descent, with the nacelles tilted forward by 10 degrees, the rotor system decelerates to 40 kts and the nacelles are tilted back to zero degrees. The rotors  are simultaneously given a roll rate about the longitudinal axis running between the rotors, taking the bank angle to about 45 degrees. The roll is first to starboard then the roll rate is reversed and the rotor system rolls to port. The maximum roll rate in this case is about 25 degrees per second. Notice that during the level descending flight stage, the rotor wakes are well-behaved and trail well behind the rotors, essentially as separate independent wakes. As the airspeed drops and the roll starts to progress, the wakes show evidence of instabilities, which eventually cause the wakes to interact. After the roll reversal is initiated, the wakes become more and more unstable and the large distortions that take place cause both rotors to enter into a form of VRS.

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Case 14t - Tilt-Rotor Undergoing Roll Reversal Maneuver in Low-Speed Descending Flight:

Another case showing the interesting rotor wake dynamics for a side-by-side (tilt-rotor) configuration when undergoing a roll-reversal maneuver in low-speed descending flight. The rate of descent is about 800 ft/min, and the airspeed is about 40 kts. After establishing trimmed flight at these conditions, which is achieved by using rotor cyclic and collective pitch controls, the rotor system is given a roll rate about the longitudinal axis running between the rotors. The roll is first to starboard then the roll rate is reversed and the rotor system rolls to port. The maximum roll rate is about 25 degrees per second, and a maximum bank angle of 45 degrees is achieved. Although at a lower rate of descent that the other two cases (see cases 12t and 13t), notice again how the roll maneuver results in severe asymmetric aerodynamics between the two rotors, causing the rotors to enter into a form of VRS.

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