Model for Vortex Ring State Influence on Rotorcraft Flight Dynamics Wayne Johnson Army/NASA Rotorcraft Division NASA Ames Research Center Moffett Field, California [email protected] The influence of vortex ring state (VRS) on rotorcraft flight dynamics is investigated, specifically the vertical velocity drop of helicopters and the roll-off of tiltrotors encountering VRS. The available wind tunnel and flight test data for rotors in vortex ring state are reviewed. Test data for axial flow, nonaxial flow, two rotors, unsteadiness, and vortex ring state boundaries are described and discussed. Based on the available measured data, a VRS model is developed. The VRS model is a parametric extension of momentum theory for calculation of the mean inflow of a rotor, hence suitable for simple calculations and real-time simulations. This inflow model is primarily defined in terms of the stability boundary of the aircraft motion. Calculations of helicopter response during VRS encounter were performed, and good correlation is shown with the vertical velocity drop measured in flight tests. Calculations of tiltrotor response during VRS encounter were performed, showing the roll-off behavior characteristic of tiltrotors. Hence it is possible, using a model of the mean inflow of an isolated rotor, to explain the basic behavior of both helicopters and tiltrotors in vortex ring state. Notation Po rotor profile power a lift-curve slope Q rotor torque az vertical acceleration T rotor thrust A rotor disk area, πR2 v rotor induced velocity B tip loss factor 2 2 V total velocity, √Vx +Vz c blade chord √ ρ 3 vh velocity scale, T/2 A CP rotor power coefficient, P/ρ(ΩR) A 2 Vx rotor horizontal speed CQ rotor torque coefficient, Q/ρ(ΩR) RA V rotor vertical speed (positive in climb) 2 z CT rotor thrust coefficient, T/ρ(ΩR) A Vtip rotor tip speed, ΩR N number of blades VRS vortex ring state r blade root cutout c α rotor disk angle of attack (positive in descent) r blade radial station θtw blade twist R blade radius θ collective pitch (75% radius) P rotor power 75 κ empirical inflow factor Pi rotor induced power λ velocity scale, √C /2 ____________ h T ρ air density .Presented at the AHS 4th Decennial Specialist's Conference σ π on Aeromechanics, San Francisco, California, January 21– rotor solidity, Nc/ R 23, 2004. Copyright © 2004 by the American Helicopter τ time constant of inflow equation Society International, Inc. All rights reserved. Ω rotor rotational speed 1 Also shown in figure 2 is the stability boundary specified for Introduction the VRS model developed in this paper. The behavior of a rotor operating in vortex ring state It is remarkable that the flight test data for a helicopter (VRS) has long been familiar to aerodynamicists, and a and a tiltrotor define essentially the same VRS boundary in substantial number of VRS test programs have been reported figure 2, in spite of a different manifestation of the (Refs. 1–50). Yet vortex ring state is a complex instability (vertical velocity drop for a helicopter, roll-off for phenomenon, involving large-scale unsteady wake flow, and a tiltrotor), and large differences in twist and solidity between there is much to be done to thoroughly understand the the rotors of the two aircraft. This implies that basically the aerodynamics and develop accurate prediction methodologies. same aerodynamic mechanism is responsible for the behavior There has been renewed interest recently in vortex ring state, of both helicopters and tiltrotors in VRS. because of the possibility of operating rotorcraft in steep descent for approach to landing, and in particular because of The instability of the aircraft in vortex ring state is a the influence of VRS on tiltrotor roll control and response. consequence of the form of the rotor inflow as a function of descent rate. Figure 3 shows the total inflow through the The subject of the present paper is the influence of vortex rotor disk, Vz+v (where v is the induced velocity) for a rotor ring state on rotorcraft flight dynamics, specifically the in vertical descent. Momentum theory is not valid in descent vertical velocity drop of helicopters and the roll-off of until the total velocity is substantially negative (so the tiltrotors encountering VRS. The objective is to develop a velocity is again in the same direction throughout the flow model of vortex ring state that is suitable for flight dynamics field), although it provides a reasonable result for low calculations and real-time piloted simulation, including descent rate. The measured data show that at moderate descent training simulations. The model is based on existing flight rates (in VRS), the total velocity Vz+v increases as the test and wind tunnel test data, and is applicable to both descent rate increases. As the rotor descends into VRS, the helicopters and tiltrotors. energy losses resulting from the recirculating flow increase, hence the power (total inflow V +v) can increase. Where Overview z d(Vz+v)/dVz is negative (roughly Vz/vh = –0.5 to –1.5 in A rotor is operating in vortex ring state when it is figure 3), the vertical motion (and roll motion of a tiltrotor) descending at low forward speed with a vertical velocity that is unstable, because an increase in descent rate at constant approaches the value of the wake-induced velocity at the collective will produce an increase in total inflow and hence rotor disk. In this condition the rotor tip vortices are not a reduction in thrust — negative damping. This instability convected away from the disk rapidly enough, and the wake mechanism has been described by several authors (Refs. 18, builds up and periodically breaks away (figure 1). The tip 25, 34, 35, 43, 44). More investigations have been focused vortices collect in a vortex ring, producing a circulating flow on the unsteady nature of VRS aerodynamics. The instability down through the rotor disk, then outward and upward is defined by the character of the mean thrust and mean outside the disk. The resulting flow is unsteady, hence a power of the rotor in VRS, not the unsteadiness of the flow. source of considerable low frequency vibration and possible The challenge is to develop a model of the rotor mean control problems. For descent at forward speeds sufficiently inflow, applicable to simple calculations and real-time high that the wake is convected away from the rotor, vortex simulation, that includes this character that leads to the ring state does not develop. unstable flight dynamics. Vortex ring state encounter can produce a significant Rotor Inflow increase in the descent rate of a helicopter or a roll-off of a tiltrotor. Figure 2 shows helicopter Vz drop and tiltrotor The flow state of a helicopter is a global phenomenon, roll-off points measured in flight tests (Refs. 44, 46, 47, involving low speed wake velocities in a region on the order 51). In figure 2, Vz is the rotor vertical velocity and Vx is of the rotor radius. So rotor tip speed and Mach number are the rotor horizontal velocity. This motion is an instability not key parameters of the flow. It follows from dimensional of the helicopter vertical or tiltrotor roll dynamics. If the analysis (Ref. 52) that the appropriate velocity scale of the aircraft rate becomes sufficiently large as a result of the flow is vh = √T/2ρA, where T is the rotor thrust, ρ the air instability, it will not be possible to recover using collective density, and A the rotor disk area. The factor of 2 is included control for the helicopter or lateral cyclic control (differential for convenience, so vh is the ideal hover induced velocity collective) for the tiltrotor. While the response to control is (hence the subscript h). still a positive acceleration increment, the control authority The flow state depends on the rotor vertical velocity Vz is not sufficient to reverse the motion. Hence recovery from (positive for climb) and horizontal velocity Vx . VRS encounter requires a drop in collective and forward Alternatively, the rotor angle of attack α can be used (Vz = cyclic for a helicopter, or a forward nacelle tilt for a tiltrotor. –Vxtanα, so α = 90 deg for vertical descent). In the context Basically it is necessary to fly out of the instability region. 2 of momentum theory, the mean induced velocity through the flow, but still downward in the far wake (according to rotor disk is rigorously defined in terms of the rotor induced momentum theory assumptions). So the wake is once more power: v = Pi/T. The parasite and climb power of the rotor being convected away from the disk (upward now), although is given by TVz. Hence Vz+v = P/T represents the total momentum theory does not give a useful estimate of the power of the rotor, except for profile power Po. In power. Real autorotation of the rotor (zero total power, dimensionless terms, the mean induced velocity has the form including profile losses) occurs in the turbulent wake state. At ideal autorotation, P/T = V +v = 0, the flow through the v/v = P /P = function(V /v , V /v ) z h i h z h x h rotor disk is zero, and the momentum theory result for axial flow is singular. where Ph = Tvh is the ideal hover power. Momentum theory provides an estimate of the rotor Figure 4 shows momentum theory in terms of both total induced velocity (see Ref. 52). The rotor is modelled as a velocity Vz+v and induced velocity v, as a function of circular disk that sustains a pressure jump, so the vertical velocity Vz.