36th European Rotorcraft Forum, Paris, France, September 7-9, 2010 Paper Identification Number 089 A Qualitative Introduction to the Vortex-Ring-State, Autorotation, and Optimal Autorotation Skander Taamallah ∗† ∗ Avionics Systems Department, National Aerospace Laboratory (NLR) 1059 CM Amsterdam, The Netherlands ([email protected]). † Delft Center for Systems and Control (DCSC) Faculty of Mechanical, Maritime and Materials Engineering Delft University of Technology, 2628 CD Delft, The Netherlands. Keywords: Vortex-Ring-State (VRS); autorotation; Height-Velocity diagram; optimal control; optimal autorotation Abstract: The main objective of this pa- 1 Introduction per is to provide the reader with some qualita- tive insight into the areas of Vortex-Ring-State This paper summarizes the results of a brief (VRS), autorotation, and optimal autorota- literature survey, of relevant work in the open tion. First this paper summarizes the results literature, covering the areas of the VRS, of a brief VRS literature survey, where the em- autorotation, and optimal autorotation. Due phasis has been placed on a qualitative descrip- to time and space constraints, only published tion of the following items: conditions leading accounts relative to standard helicopter to VRS flight, the VRS region, avoiding the configurations will be covered, omitting thus VRS, the early symptoms, recovery from VRS, other types such as tilt-rotor, side-by-side, experimental investigations, and VRS model- tandem, and co-axial. Presenting a complete ing. The focus of the paper is subsequently survey of a field as diverse as helicopter VRS, moved towards the autorotation phenomenon, autorotation, and optimal trajectories in where a review of the following items is given: autorotation is a daunting task. Hence the the maneuver, the height-velocity zones, and review is from a common qualitative approach, factors affecting autorotation. Finally the pa- with emphasis on concepts rather than on per concludes by providing a literature survey details. relative to single-engine helicopter optimal au- torotation, and its associated problem formu- The paper is organized as follows: in lation as a nonlinear, constrained, optimal con- Section 2, a review of the four rotor operating trol problem. conditions in vertical flight is given. In Section 3, the VRS is presented, including a review of aspects affecting the VRS, the VRS region, and VRS modeling. In Section 4, a review of published accounts in the field of 1 autorotation, aspects affecting the maneuver, • The normal working state region 0 ≤ and the associated height-velocity diagram Vc/vh. It includes climb and hover. Here are provided. In Section 5, a literature survey the velocity throughout the main rotor relative to the optimal autorotation problem, flow field is always downwards, hence a and its solution through constrained optimal wake model with a definite slipstream3 is control, is presented. Finally, conclusions and valid for this rotor state, resulting in good future directions are presented in Section 6. estimates of rotor performance, in climb and hover, by momentum theory [90]. As a final introductory note, many inter- • The VRS region Vtr/vh ≤ Vc/vh < 0, esting and important contributions or founda- 4 where Vtr refers to the transition veloc- tional works related to the VRS and autoro- ity between the VRS and the turbulent tation have not been surveyed in this paper. wake state regions. Over the years, several In this, and many other respects, we sincerely transition velocities or transition velocity ask for the kind understanding of readers and ranges have been reported, for example authors alike. in [90, 116]. There is indeed no clear-cut value for Vtr as can be seen from measure- 2 Vertical flight ments scatter reported in Fig. 3, where the figure shows the universal empirical Before addressing the areas of VRS and au- induced velocity curve. This curve can be torotation, we start by giving a quick review of constructed on the basis of estimates of the four rotor operating conditions in vertical the profile power coefficient. Hence the in- flight, see Fig. 1 for a schematic representation. duced velocity always shows some scatter, due to errors in the profile power calcu- 1 Fig. 2 shows the momentum theory solu- lation, and other aspects such as tip loss tions for a main rotor in vertical climb or de- and blade twist [90]. Further in the VRS scent. The lines Vc = 0, Vc + vi = 0, and region, a definite slipstream does not exist 2 Vc + 2vi = 0 divide the (Vc, vi) plane into four anymore, since the flow in the far wake in- regions. The area of the plane right of line side and outside the slipstream are in op- Vc = 0 defines the normal working state rotor. posite direction. At first for low descent The area of the plane between lines Vc = 0 rates −0.5 ≤ Vc/vh < 0, momentum the- and Vc + vi = 0 defines the VRS region. The ory is still valid [90]. As the descent rate area of the plane between lines Vc + vi = 0 and increases Vtr/vh ≤ Vc/vh < −0.5, the flow Vc + 2vi = 0 defines the turbulent wake state. becomes turbulent and has large recircula- Finally the area left of line Vc + 2vi = 0 de- tion, resulting in rotor vibrations and de- fines the windmill brake state [100]. We pro- graded control [90]. In this region momen- vide next a succinct review of those four re- tum theory is not valid anymore. gions, a much more detailed discussion can be found in [90]. • The turbulent wake state −2 ≤ Vc/vh < Vtr/vh. Here the flow pattern above the 1 Momentum theory refers to the conservation of rotor disk is very similar to the turbulent mass, momentum, and energy in the case of an inviscid, incompressible, steady, irrotational, and 1-D flow [90] 3The stream of air forced downwards by rotating 2 With Vc being the climb velocity, vi the main rotor blades 4 induced velocity, and vh the main rotor induced velocity In this paper we will assume that Vtr/vh ∈ in hover [−1.9, −1.6] 2 wake of a bluff body [90]. In this region, loss of control effectiveness [102, 101]. when compared to the VRS, flow recircu- lation through the rotor has diminished 3.1 VRS: a hazardous flight condi- and rotor vibrations have also decreased. tion But the rotor still experiences some rough- ness due to the (high) turbulence [90]. It For a helicopter main rotor, VRS may occur is also in this region that equilibrium au- for example in a descending flight, while for a torotation occurs. Note also that here too helicopter tail rotor, VRS may occur during momentum theory is invalid. a sidewards flight, or while in hover with a crosswind. For the case of a main rotor VRS • The windmill brake state Vc/vh < −2. In condition, the symptoms are generally exces- this region the flow is again smooth with a sive vibrations, large unsteady blade loads, definite upwards slipstream, and momen- thrust/torque fluctuations, excessive loss of tum theory is applicable, providing good altitude, and loss of control effectiveness [126]. rotor performance estimates [90]. Hence flight in the VRS is a dangerous flight condition, especially if entered at low altitude. 3 The Vortex-Ring-State For the case of a tail rotor VRS, it is the vehicle yaw control (i.e. heading) that may A horizontal rotor creates a downward flow become difficult or impaired. induced by the thrust generation. If the ro- tor moves along the direction of its induced For the 1982 - 1997 time frame, data from 5 flow, i.e. down, the downward induced flow the U.S. NTSB , U.S. Navy & Army, and the will compete with the upward flow due to the U.K. Air Accidents Investigation Branch show descent motion. As a result, the smooth slip- that 32 helicopter accidents were caused by stream around the rotor disk is gradually de- flight into the VRS, most of them at altitudes stroyed. In particular, when the descent rate less than 200 feet and at low airspeeds [141]. approaches the rotor induced velocity, the ro- In April 2000, a Marine Corps V-22 Osprey tor enters its own wake, resulting in blade tilt-rotor crashed in Arizona, resulting in the tip vortices recirculation. These vortices will tragic loss of all 19 Marines on board. It was then tend to pile up at the disk plane to cre- later determined that a contributing cause of ate a so-called doughnut-shaped vortex ring that accident was flight into the VRS [49, 43]. [102, 101, 43]. Moreover, the onset and devel- opment of this so-called vortex ring state can It is nowadays well known that a signifi- be viewed as a spatial and temporal wake insta- cant number of VRS accidents were the result bility. By instability one means vortex rings as of accepting slight tailwinds or downwind ap- a result of wake recirculation in the plane of the proaches, hence reducing the actual horizontal 6 rotor [102, 101]. Periodically however the char- air velocity . acter of this recirculation changes, as a partial 5National Transportation Safety Board vortex collapse causes flow asymmetry at the 6This is often a point of concern for helicopter pilots, rotor disk. This phenomenon results in large since the airspeed indication on most civil helicopters is fluctuations in rotor lift and torque [33]. More somewhat ineffective below 35 to 40 knots [141]. This specifically these include high amplitude, low problem however can be solved by algorithmic methods, which use an internal model, available control inputs, frequency blade flapping, low frequency verti- and sensors measurements to infer airspeed and sideslip cal bounce of the helicopter, and substantial angle see [55, 60, 108, 71] 3 Figure 1: Helicopter axial flight (from [127]) Figure 2: Axial flight: induced velocity variation as a function of vertical velocity (from [100]) 4 Figure 3: Axial flight: induced velocity scatter in descending flight through the VRS (from [101]) 3.2 Flight conditions leading to the For a helicopter tail rotor, VRS may occur VRS in the following conditions For a helicopter main rotor, VRS may occur in • In sidewards flight the following conditions • While hovering in a crosswind • In an axial descent with the rate of descent being about equal to the hover induced • During a hover, turn over a spot [127] velocity 3.3 The VRS region • At low speeds and steep descent angles Knowledge of the location of the VRS onset • When descending downwind into a land- boundary, see Fig.