BLADE TWIST EFFECTS ON ROTOR BEHAVIOUR IN THE VORTEX RING STATE R. E. Brown J. G. Leishman† Department of Aeronautics, Dept. of Aerospace Engineering, Imperial College of Science, Technology & Medicine, Glenn L. Martin Institute of Technology Prince Consort Road, University of Maryland, London SW7 2BY. College Park, MD 20742, USA. S. J. Newman‡ F. J. Perry§ Dept. of Aerospace Engineering, FJ Perry Rotorcraft Consultant, University of Southampton, Yeovil, Somerset BA20 1NU. Highfield, Southampton SO17 1BJ. θ § Abstract r§ z Cylindrical polar coodinates, m, rad., m r Position vector of a wake marker, m Results are shown that give a better understanding of the R Rotor radius, m 2 factors that influence the initiation and subsequent devel- S Vorticity source, s ¨ opment of the vortex ring state (VRS). It is suggested that t Time, s the onset of VRS is associated with the collapse of the or- T Rotor thrust, N ¡£¢ ¤ 1 derly structure of the rotor wake into a highly disturbed, vh Hover induced velocity, T 2ρA , ms ¨ 1 irregular, aperiodic flow state. An analysis of the stabil- vi Induced velocity, ms ¨ 1 ity of the wake is presented to show that the location of the Vc Climb (out-of-plane) velocity, ms ¨ 1 boundary of the VRS is influenced by the detailed structure V∞ Forward (in-plane) velocity, ms ¨ 1 of the rotor wake prior to its breakdown. Time-accurate V Velocity vector, ms ¨ § calculations of the evolution of the rotor wake in the VRS x § y z Cartesian coordinates, m are then presented to obtain more insight into the flows ex- 1 perienced by the rotor in the VRS. These calculations sug- αP Wake perturbation growth rate, s ¨ ¡ ¡ gest that the location of the boundary of the VRS, and the 2 α © α Γ π P Non-dim. growth rate, P v 4 R depth of the VRS regime, is sensitive to the blade spanwise 2 1 Γv Tip vortex strength (circulation), m s ¨ loading distribution, which is influenced by blade twist. δCT Perturbation to thrust coefficient The effects are significant even at low disk loading, but ζ Wake (vortex) age, rad at high thrust where rotor stall may be encountered, rotors θtw Effective linear blade twist per radius, degrees with and without significant blade twist show marked, and ¡ λh Non-dim. hover induced velocity, CT 2 somewhat counterintuitive, differences in their behaviour λi Induced velocity, scaled by vh under VRS conditions. µW Effective wake transport velocity, scaled by vh ¡ µx Non-dimensional forward speed, V∞ vh ¡ µz Non-dimensional climbing speed, Vc vh Nomenclature 3 ρ Air density, kg m ¨ σ Rotor solidity, N c ¡ πR A Rotor disk area, πR2, m2 b ψ Azimuth angle, rad c Rotor blade chord, m ¡£¢ ω Wake perturbation wave number 2 2 ¤ CT Rotor thrust coefficient, T ρAΩ R 1 ¡£¢ ω Vorticity vector, s ¨ 2 3 ¤ CQ Rotor torque coefficient, Q ρAΩ R 1 Ω Rotor angular velocity, rads ¨ k Vorticity transport parameter Q Rotor torque, Nm Abbreviations ¥ Lecturer. BVI Blade Vortex Interaction † Professor. FVM Free-Vortex Model ‡ Senior Lecturer. TWS Turbulent Wake State § Consultant. VRS Vortex Ring State Presented at the European Rotorcraft Forum, Bristol, England, ¦ VTM Vorticity Transport Model c September 17–20, 2002. Copyright 2002 by R. E. Brown, WBS Windmill Brake State J. G. Leishman, S. J. Newman and F. J. Perry. Published by the Royal Aeronautical Society with permission. All rights reserved. 76.1 “settling with power,” and adversely affects flight safety (Ref. 2). The rotor thrust fluctuations in the VRS lead to low-frequency vertical accelerations of the helicopter, and the associated blade flapping can lead to a substan- tial reduction of control effectiveness and thus to high pi- lot workload. While operation in the VRS is obviously undesirable, it can be entered inadvertently through poor piloting technique. Recently, there has been renewed interest in understand- ing and predicting the flow mechanisms that lead to the on- set of the VRS, both for helicopters and for other rotating- wing aircraft such as tiltrotors. For traditional helicopters with low disk loading, the region of the flight envelope af- fected by the VRS is generally small, and has not overly constrained practical operations. However, it has been sug- Figure 1: Smoke flow visualization of a rotor operating gested (Refs. 3–6) that modern helicopters and tiltrotors, in the VRS, showing the characteristic recirculation of the with their very much higher disk loadings, may be suscep- flow in the rotor plane. tible to the VRS over a greater proportion of their low- speed flight envelope. Furthermore, modern military ro- Introduction torcraft are required to fly a wide range of manoeuvres at low airspeed, including rapid pull-ups, which can increase While the accurate prediction of rotor flow fields is dif- the upward component of velocity through the disk and ficult under most flight conditions, the prediction of the may bring the rotor(s) closer to the VRS (Ref. 6). The be- wake dynamics during descending flight has proven to be haviour of side-by-side configurations, such as tiltrotors, at a particularly challenging problem for the analyst. This is high rates of descent has come under particular scrutiny be- partly because of blade vortex interaction (BVI) and a gen- cause the VRS may be encountered more severely on one eral susceptibility to unsteadiness and aperiodicity of the rotor compared to the other (Refs. 5–7), possibly requiring rotor wake structure. Under conditions where the upward large asymmetric loads to be overcome by the aircraft’s component of velocity normal to the rotor disk plane is a control system. substantial fraction of the average induced velocity down- The highly nonlinear physics of the VRS is further com- ward through the rotor disk, such as when descending at plicated by the likelihood of flow separation and blade high rates or steep angles, the rotor can encounter an ad- stall on more highly loaded rotors during descending flight. verse condition known as the vortex ring state (VRS). Un- This can occur because of the higher aerodynamic angles der VRS conditions, the wake vorticity produced by the of attack produced on the inboard parts of the blades dur- blades cannot convect away from the rotor and accumu- ing descent, or, when in the VRS, the blades chop through lates near the rotor plane, clumping or bundling together the accumulations of vorticity engulfing the rotor (Ref. 6). and producing large, aperiodic airloads. In aerodynamic Flight tests (Ref. 8) show that in partial power descent terms, the onset of the VRS is associated with the collapse near the VRS the rotor can operate without evidence of of the orderly structure of the rotor wake into a highly dis- blade stall and at relatively low power, but that another turbed, irregular, recirculating flow. state can be reached at the same airspeed and rate of de- A representative example of the complex topology of scent where the rotor requires much higher power because the flow surrounding a steeply descending helicopter rotor of blade stall. This observation suggests that, in addition operating in the VRS is shown in Fig. 1, which is taken to the nonlinear behaviour of the wake within the VRS, from the work of Drees & Hendal (Ref. 1). This smoke nonlinearity in the aerodynamics of the blades also plays flow visualization image was taken by illuminating a cross- an important role in governing helicopter behaviour in the section through the rotor wake. Deeply into the VRS, the VRS. flow near the rotor resembles that of a three-dimensional The results of the present paper confirm that the suscep- bluff body operating at low Reynolds numbers, and there tibility to wake breakdown, and the potential onset of the is clear evidence of separation and unsteady recirculation VRS, depends on several factors that are a consequence of the flow near the rotor. of the rotor configuration as well as of its operating state. When a helicopter enters the VRS, it experiences sig- In particular, it is suggested that, in addition to the disk nificant rotor thrust fluctuations and an increase in average loading effects mentioned above, the high levels of blade rotor shaft torque (power required). Power must be applied twist inherent in modern helicopter rotor and tiltrotor de- to overcome the high aerodynamic losses associated with signs may expand the VRS regime to a wider range of op- the rotor operating inside its own recirculating wake. Most erational descent velocities and to higher forward speeds helicopters have minimal excess power available at low air- than is the case for rotors with more lightly-twisted blades. speeds, so these losses usually manifest themselves as an Furthermore, numerical calculations show changes in ro- uncommanded increase in descent rate. This behaviour of tor behaviour, once rotor wake breakdown has occurred, the helicopter is referred to by pilots as “power settling” or which result from the introduction of high blade twist. 76.2 Previous Work problem of wake stability has been examined under various operating conditions using a linearized, eigenvalue analy- Experimental work is fundamental to understanding the sis of the rate of growth of perturbations to the vortical VRS, but instrumented flight tests with helicopters oper- structure of the rotor wake (Ref. 5). The stability analysis ating in the VRS are sparse, mainly because it is a diffi- suggests that the helicopter rotor wake is inherently unsta- cult flight condition in which to sustain equilibrium flight. ble in most flight regimes, including in hover, and shows The flight tests of Scheiman (Ref. 8) revealed the highly that increasing the rate of descent makes the wake more unsteady blade loads and high rotor power requirements prone to instability.