UNCLASSIFIED Nationaal Lucht- en Ruimtevaartlaboratorium National Aerospace Laboratory NLR Executive summary A Qualitative Introduction to the Vortex-Ring-State, Autorotation, and Optimal Autorotation Problem area survey relative to single-engine The main objective of this paper is helicopter optimal autorotation, and Report no. to provide the reader with some its associated problem formulation NLR-TP-2010-282 qualitative insight into the areas of as a nonlinear, constrained, optimal Vortex-Ring-State (VRS), control problem. Author(s) autorotation, and optimal S. Taamallah autorotation. Results and conclusions Presenting a complete survey of a Report classification Description of work field as diverse as helicopter VRS, UNCLASSIFIED First this paper summarizes the autorotation, and optimal Date results of a brief VRS literature trajectories in autorotation is a May 2011 survey, where the emphasis has daunting task. Hence the review been placed on a qualitative is from a common qualitative Knowledge area(s) description of the following items: approach, with emphasis on Helikoptertechnologie conditions leading to VRS flight, concepts rather than on details. the VRS region, avoiding the VRS, Descriptor(s) the early symptoms, recovery from Applicability Vortex-Ring-State (VRS) VRS, experimental investigations, This survey was essentially tailored Autorotation and VRS modeling. The focus of for researchers interested in Height-Velocity diagram the paper is subsequently moved designing control systems, for Optimal control towards the autorotation helicopter flight in the VRS and Optimal autorotation phenomenon, where a review of the autorotation, such as automatic following items is given: the VRS avoidance, automatic recovery maneuver, the height-velocity from VRS flight, and automatic zones, and factors affecting autorotation. autorotation. Finally the paper concludes by providing a literature This report is based on a presentation held at the 36th European Rotorcraft Forum, Paris, September 7-9, 2010. UNCLASSIFIED UNCLASSIFIED A Qualitative Introduction to the Vortex-Ring-State, Autorotation, and Optimal Autorotation Nationaal Lucht- en Ruimtevaartlaboratorium, National Aerospace Laboratory NLR Anthony Fokkerweg 2, 1059 CM Amsterdam, P.O. Box 90502, 1006 BM Amsterdam, The Netherlands UNCLASSIFIED Telephone +31 20 511 31 13, Fax +31 20 511 32 10, Web site: www.nlr.nl Nationaal Lucht- en Ruimtevaartlaboratorium National Aerospace Laboratory NLR NLR-TP-2010-282 A Qualitative Introduction To The Vortex-Ring- State, Autorotation, And Optimal Autorotation S. Taamallah This report is based on a presentation held at the 36th European Rotorcraft Forum, Paris, September 7-9, 2010. The contents of this report may be cited on condition that full credit is given to NLR and the authors. This publication has been refereed by the Advisory Committee AEROSPACE SYSTEMS & APPLICATIONS and AEROSPACE VEHICLES. Customer National Aerospace Laboratory NLR Contract number ---- Owner National Aerospace Laboratory NLR Division NLR Aerospace Systems and Applications Distribution Unlimited Classification of title Unclassified May 2011 Approved by: Author Reviewer Managing department NLR-TP-2010-282 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 3 NLR-TP-2010-282 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 [89]. 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 [89, 115]. 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 induced velocity curve. This curve can be Before addressing the areas of VRS and au- constructed on the basis of estimates of torotation, we start by giving a quick review of the profile power coefficient. Hence the in- the four rotor operating conditions in vertical duced velocity always shows some scatter, flight, see Fig. 1 for a schematic representation. due to errors in the profile power calcu- lation, and other aspects such as tip loss Fig. 2 shows the momentum theory1 solu- and blade twist [89]. Further in the VRS tions for a main rotor in vertical climb or de- region, a definite slipstream does not exist scent. The lines Vc = 0, Vc + vi = 0, and 2 anymore, since the flow in the far wake in- Vc + 2vi = 0 divide the (Vc, vi) plane into four side and outside the slipstream are in op- regions. The area of the plane right of line posite direction. At first for low descent Vc = 0 defines the normal working state rotor. rates −0.5 ≤ Vc/vh < 0, momentum the- The area of the plane between lines Vc = 0 ory is still valid [89]. As the descent rate and Vc + vi = 0 defines the VRS region. The increases Vtr/vh ≤ Vc/vh < −0.5, the flow area of the plane between lines Vc + vi = 0 and becomes turbulent and has large recircula- Vc + 2vi = 0 defines the turbulent wake state. tion, resulting in rotor vibrations and de- Finally the area left of line Vc + 2vi = 0 defines graded control [89]. In this region momen- the windmill brake state [99]. We provide next tum theory is not valid anymore. a succinct review of those four regions, a much more detailed discussion can be found in [89]. • 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 [89] 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 4 NLR-TP-2010-282 wake of a bluff body [89]. In this region, loss of control effectiveness [101, 100]. 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 [89]. 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 [125].