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Nonlinear Aeroelastic Response Simulation of Rotor Blades with Trailing Edge Flap Controls

Y. Kemal YILLIKCI*, Mesut YILMAZ† and Rahmi AYKAN‡ Turkish Airlines, Istanbul, TURKEY

In the study, a numerical simulation tool to capture major vehicle flight and blade dynamic characteristics has been developed. A generic compound helicopter configuration which utilizes broader range of rotor rpm changes, auxiliary lift, and tail propulsion as additional flight control inputs is considered. Rotor of the helicopter is controlled by trailing edge flaps. The major flight characteristics and nonlinear rotor blade aeroelastic response are obtained starting from constant rotor speed forward flight to rotor rpm change quasi-steady forward flight phases. For trim conditions, nonlinear aeroelastic partial differential equations (PDE’s) are solved numerically by a conditionally stable explicit finite difference scheme developed by previous studies. The major introduced result of this study is the development of a numerical simulation tool which enables designers to capture vehicle flight characteristics and blade dynamic responses. The simulation tool is primarily used to generate blade and hub components stresses, flow field perturbations due to maneuver and blade deflections and blade dynamic stall conditions. These simulations are aimed to be the replacement of outputs of different sensors on vehicle and rotor systems as well as physical effects of aeroelastic interactions around the blade in a real compound helicopter. Simulated sensor outputs are utilized as parameters in objective functions and as physical constraints on the flight control problem. As the first step of study, trim equations with vector notation for conventional control inputs are used. Additional to these conventional control inputs, left and right canard and horizontal tail incidences as well as longitudinal and lateral components of the tail propulsion are also considered as additional control inputs. Rotor rpm variations are allowed in a broad bandwidth to expand the design space for the optimization procedure. Main rotor as well as total power/torque required of the compound vehicle is governed to maintain the flight. Numerical solutions are obtained for vehicle trim and rotor blade aeroelastic nonlinear PDE’s simultaneously. Nonlinear aeroelastic rotor blade PDE’s are solved to obtain time dependent motion of the elastic axis where blade is modeled as long slender beam deflecting with geometric nonlinearities. Three dimensional deformation of the blade, stresses at blades and another load bearing parts, flow field fluctuations both due to blade deflections and vehicle motion and dynamic stalling effects are obtained. The tool is used to generate simulations of blade and hub stresses, flow field around blade and blade stalling conditions which can be used to generate the necessary design parameters closely related with the rotor slowing flight and blade dynamic characteristics needed for analysis and design. With this approach “Response Surfaces” generated for parametric design and optimization can reflect these important dynamic effects in the early stages of the Concept Exploration and Design studies.

Nomenclature a = lift curve slope α = angle of attack αs = angle of attack of the rotor shaft relative to vertical c = nondimensional blade section chord which can vary spanwise

* Engineering Director, Technical Department † Design and Development Manager, Technical Department ‡ Engineer, Technical Department

American Institute of Aeronautics and Astronautics

1

AIAA Atmospheric Flight Mechanics Conference and Exhibit15 - 18 August 2005, San Francisco, California

AIAA 2005-5809

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

CL = lift coefficient CT = nondimensional thrust coefficient Dcan = drag of canard Df = drag of fuselage Dtw = drag of tail wing h = offset distance of the helicopter center-of-gravity location in vertical H = rotor drag Lcan = canard lift Ltw, = tail wing lift MYF = aerodynamic pitch moment of the fuselage; U = the resultant velocity acting to the blade section. Up and UT = velocity components acting to blade cross section, Tmr = main rotor trust Tpr = pusher propeller thrust, xcg = offset distances of the helicopter center-of-gravity location in longitudinal W = weight of helicopter θ0 = collective pitch angle θ1s and θ1c = cyclic pitch angles. θri = the rigid angle of attack of the blade, Λ = trailing edge flap angle σ = blade solidity, Abbreviations

AFCS = Automatic flight control system CRW = canard rotor wing IBC = individual blade control UAV = unmanned aerial vehicle VTOL = vertical takeoff and landing

I. Introduction

A. Stopped Rotor/Rotor-Wing Concept CHWARTZ1 et al have developed a new concept for an unmanned aerial vehicle (UAV) configured with a tipjet- driven, two-bladed, stoppable rotor and circulation control airfoils. The vehicle’s high-aspect ratio wing

converts to a tipjet-driven helicopter rotor for vertical takeoff and landing (VTOL). The conceptual design is presented for a 1200-lb Tipjet VTOL UAV. Vehicle performance predictions are included for the key flight regimes of hover, low-speed rotary wing flight, and conversion between rotary wing and fixed wing flight.

S Boeing’s Phantom Work will design build and flight-test two canard rotor-wing “dragonfly” unmanned aerial

vehicle prototypes. Objectives include validation of the aeromechanical performance of the canard rotor wing (CRW) concept. The

1,300-lb. aircraft is intended to takeoff and like helicopter from confined areas such as small ship decks. Once in flight, transition to wing-borne, powered forward flight. Estimated top speed is in excess of 375 kt. with its thick, blade-tip jet-powered rotor locked in the side to side position and acting as an added wing. Potential CRW uses include reconnaissance, communications weapons delivery and “urban operation” as indicated in Ref. 2.

Preliminary CRW configuration estimates call for a 17.7- ft. long airframe that is 8.5ft. wide at its horizontal, lift-producing tail. That CRW’s forward canard will measure just under 8ft., and the vehicle will stand 6.5 ft high from the ground to the top of the rotor mast. The artist’s concept of CRW is shown in Fig. 1.


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Unlike conventional rotor system that requires use of a bulky and heavy transmission, the CRW turns its rotor using a reaction drive system. It ducts engine exhaust up through the rotor mast and into rotor blade passages. The pressurized gasses are vented out blade-tip jets.

Rotor diameter is about 12 ft., and there are no lead-lag or flapping mechanisms, although there is a pitch hinge. No anti torque tail rotor is required, since the main rotor is not driven by a mechanical system producing torque.

Rutherford et al3 have investigated a configuration of a “Rotor/Wing” or as also called “Stopped Rotor” for demonstrating capabilities and concept effectiveness for Close Ground Attack VTOL aircraft. The selected configuration with 28,000 lb. gross weight, the considered VTOL aircraft is intended to combine Close Ground Attack fixed wing military aircraft with Heavy Attack helicopters in one aircraft.

The rotor wing consists of a warm cycle, reaction-driven rotor, with a large triangular center body/hub and three short-span, wide-chord blades. For vertical and low-speed flight, the rotor is powered by ducting mixed flow turbofan engine exhaust gases through the hub and rotor blades out to tip jets. The rotor autorotates during conversion until the aircraft reaches conversion speed (170 kt), and the center body provides enough lift to achieve 1-g conversion. At this point, the rotor, off loaded stops to become a swept forward wing for cruise and high-speed flight. For simplicity, the use of airfoils with blunt leading and trailing edges and a feathering hinge eliminates the need for circulation control. Due to the amount of initial concept exploration in the mid-60’s, including whirlstand, wind tunnel, dynamic model conversion and transonic tests, much is known about this configuration.

The XH-17 and XV-9A technology demonstrators incorporated reaction drive rotors in their designs. Since no new engine technology is required-such as convertible engines development-the risk and cost should be less than any of the folding concepts.

The rotor/wing attaches to the fuselage through a rigid mounting on a bearing, which allows only rotational motion. The stub blades can only feather. The flexibility of the structure provides the necessary flapping motion for helicopter flight. A reaction drive system eliminates the heavy transmissions common to high-speed rotorcraft and provides a very simple system for both rotary and fixed-wing operation. During conversion, diverter valves redirect engine exhaust gases aft for conventional forward thrust. A small thruster located in the tail boom provides yaw control in helicopter mode (no anti-torque is required).

Ref. 3 indicated one of the major problems to be solved of the rotor/wing concept, rotor blade vibrations during the rotor stopping transition. As the advance ration becomes very large, rotor vibrations increase. It is expected that unloading the blades significantly reduce the vibrations using cyclic pitch control. Also indicated in Ref. 3 additional oscillations occur due to the triangular center body. As the center body carries the lift during conversion, the center of lift oscillates in an elliptical pattern with a frequency three times the rotor rotational speed, causing pitch and roll inputs during the last few revolutions. As indicated in Ref. 3, the use of cyclic pitch control, elevon deflection and a four-bladed configuration are suggested by Huston and Shivers4.

Figure 1. Concept Boeing Canard Rotor Wing in Flight. (Ref. 2)

Control mechanism used to control the rotor blade during helicopter forward flight and the rotor slowing down transition becomes the critical flight mechanic problem of rotor/wing (or stopped rotor). Yillikci and Hanagud5 have introduced a simplified trim procedure to calculate the required pilot control inputs for helicopter and rotor slowing down transition modes of stopped rotor configuration. The introduced trim formulation accounts a series of steady state forward flight conditions with changing rotor speeds and trim formulation for the flap controlled case is based on the formulation introduced by Yillikci6.

Blade transient vibrations are also addressed by Yillikci and Hanagud7-9 and a method for numerically simulating rotor blade nonlinear transient response is introduced. For calculated trim inputs for successive rotor slowing down maneuver the corresponding blade vibrations are calculated by an explicit finite difference method introduced in References9-11. Karamisir and Yillikci13 investigated the rotor slowing down maneuver for a 8,000-lb stopped rotor


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configuration where the effects of different level of auxiliary lift (canard and tail wing) and tail propulsions on trim requirements are investigated.

B. Flap Controlled Rotor Concept In forward flight the dynamic pressure on the

blade changes as the function of the blade azimuth position, if the angle of attack of blade sections is kept constant, the resultant lift on the retreating blade will be much less than the advancing blade. As a result of this unbalanced lift, a rolling moment would be produced on the rotor hub, which will cause the helicopter fuselage to roll towards the retreating side. Introducing a periodic pitch angle of change to the blade solves this problem. This pitch change is applied through the pitch bearing by pilot as a combination of control inputs. These control inputs consist of the mean and the first harmonics of

θ ψ θ( )= +0

The mean angle θ0 is called the collective pitch called the cyclic pitch angles. Primarily, collective pcyclic inputs θ1s and θ1c control the thrust vector orie

Introduction of this sinusoidal blade pitch anglebalance the aerodynamic lift distribution but also tolift coefficient of the lifting surface like a rotor blade

Where a is the lift curve slope of the profile whiand α is the effective angle of attack of the airfoil. cyclic pitch change to change the lifting capability Ca instead of the blade section angle of attack α is ththe rotor blades. A downward motion of a hinged camber of the blade. This results in the change in lift

sin 110 Λ+Λ+Λ=Λ ψ CS

Trailing edge flap control concept was first introand the concept called servo-flap was successfully usrotors the idea of using trailing edge flaps on bladKaman servo-flap. On the other hand, with the newactive control technologies, it is now becoming incedge mounted flaps on rotor blades as a means of infeedback strategies, active controlling of the blade lifthe rotor performance, as well as for the reduction merging new technologies and demand for advanced

With this new rotor control system with approprichanged with the blade azimuth position and non-problems such as; dynamic stall, tip vortex generatintroduced to the rotor blades by the use of electromemicrocomputer processors.

American Institute o

θ θri

Λ

θ = θ0+ θ1s sψ +θ1c cψ Λ = Λ0 + Λ1ssψ + Λ1c cψ

Classical periodic pitch control Proposed periodic flap control

Figure 2 Rotor Blade With trailing Edge

the pitch angle variation of the rotor blade as,

θ ψ θ ψsin cos+1 1S c (1)

and 1/rev harmonics of the pitch control inputs θ1s and θ1c are itch controls the average blade lift - thrust of the rotor - while

ntation in longitudinal and lateral directions respectively. is basically used to change the blade sectional lift not only to augment the rotor hub control forces and moments. .Sectional can be written in the simplest form as;

C aL = α (2)

ch basically defines the lift generating capability of the surface Conventionally, the angle of attack α has been changed by the L of the blade section. The idea of changing the lift curve slope e basic idea behind the “trailing edge flap control” concept for trailing edge flap, (Λ), expressed with Eq. 3, can change the generating capability of the airfoil, CL.

.....2cos2sincos 22 +Λ+Λ+ ψψψ CS (3)

duced by Charles Kaman13 a distinguished helicopter pioneer, ed in several Kaman helicopters for many years. For helicopter es has found use only for 1/rev. cyclic pitch control, e.g. the ly developing smart materials/ structures and high bandwidth reasingly feasible to use compliant airfoil surfaces or trailing dividual blade control (IBC). Coupled with real time adaptive t distribution offers several possibilities for the improvement of of blade loads and vibrations. Developments in related fields, rotor systems have reactivated the flap control concept. ate trailing edge flap motions varied span wise on the blade and pitching rotor tips, rotor blade aerodynamic and aero elastic ions can be reduced significantly. These new controls can be chanical servo and actuator systems activated and controlled by

f Aeronautics and Astronautics

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C. Scope of the Present Study Previous studies have addressed the primary rotor control and blade vibration problems of rotor/wing (or CRW)

configurations and introduced several computational methods for trim and blade response calculations. The scope of this study is to extend these previous efforts towards more comprehensive formulation of the rotor blade aerodynamics in trim and rotor blade nonlinear blade response formulations. A typical CRW-stopped rotor flight mission is depicted in Fig. 3 where the vehicle takeoff from confined areas like ship decks and climb vertically to certain altitude. CRW also fly in helicopter mode to certain altitude and maneuver as helicopter configuration.

Rotor slowing down transition is will be performed by successive steady state forward descending forward flight segments. At each interval rotor speed is kept constant and it is reduced with certain decrements in rotor rpm, vehicle forward flight and descending (flight path angle). These decrements are kept small to maintain the steady state flight conditions. Rotor is expected to slow almost to the one third of its initial helicopter mode rotor speed. At this lowered rotor speed rotor system possesses much less angular momentum therefore it can be braked and locked. At these rotor speeds the rotor can no longer produce practical level of thrust and starts vibrating severely.

At this fourth stage of the CRW flight mode the rotor is braked as rapidly as possible and CRW will be quickly switched to the fixed wing mode at the fifth stage of the flight as illustrated in Fig. 3

Takeoff fromconfined area likeship decks

A- Verticalclimb

B- Flyinghelicopter

C- Trasitionmaneuver

D- Rotor finalbreak and lock

ying with 300-nt cruise speed

Figure 3 Canard Rotor Wing (CRW) Flight Modes

II. Trim Formulation As also indicated by Rutherford3 one of the major problems of stopped rotor (rotor/wing) configuration is the

possible severe vibration of the rotor during rotor slowing down transition mode. This phenomenon is primarily due to the softening of the blade while the centrifugal force acting on the blade decreases as the rotation rpm of the stopped rotor is reduced. To over come this problem to rotor is needed to be unloaded and the vehicle must perform a proper transition maneuver. For this purpose auxiliary lift and tail (vectorized) propulsion is proposed. Rutherford3 has explained the CRW rotor slowing down and stopping transition as helicopter auto-rotation maneuver. In present study, vehicle transition maneuver trimming conditions and the required control inputs are investigated for a selected CRW configuration.

Thrust coefficient of a flap controlled rotor has been approximated by Yillikci6 as;

Where CT is defined as nondimensional thrust coefficient, Up, UT are velocity component acting to blade cross

section, θri is the rigid angle of attack of the blade, σ blade solidity, a lift curve slope of the blade profile and c is the nondimensional blade section chord which can vary spanwisely. U is the resultant velocity, acting to the blade section. First and second derivatives with respect to nondimensional time, Ωt, is expressed as ( )* and ( )** respectively.

The first term in Eq. (4) represents blade airfoil aerodynamics resultant of its relative speed due to its rotation, plunging and pitching. The used formulation is reduced from the blade aerodynamics representation of standard trim formulation given by Johnson14. Flap geometry aerodynamic parameters; f1,f2,f3 and f4 are given in Ref 7.

[ ]

( ) dxUfa

fa

cUffac

dxUUURR

Ta

CTpriT

T

⎥⎥⎦

⎤Λ+Λ−Λ⎢

⎣

⎡−+

−=Ω

=

∫

∫

21

**4

2*

1

032

1

0

222

184

21

)(θ

ρπσ

(4)


5

Trim settings of the rotor blade configuration where all conventional collective and cyclic pitch controls are replaced with the suggested cyclic trailing edge flap controls are calculated by a two step procedure. At the first step, trim settings for the cyclic pitch case for the selected helicopter and the same blade geometry configuration are calculated by the use of standard trim equations given by Johnson14. Since the overall configuration and the rotor blade geometry are kept identical for the both pitch and flap control configurations; trim settings such as; β1s, β1c , αv, ∅v , CTmr , CH, CY, Cp are calculated for the pitch controlled configuration are assumed to be identical for the flap control case.

Stopped rotor slowing down and transition to fixed wing aircraft mode expected to require highly complex rotor and vehicle controls. At this stage the scope of this study is narrowed only to the basic flight path definition along with the estimation of the ranges at the rotor control inputs both for the conventional pitch control and the suggested flap control case.

For this purpose an approximate trim formulation for the stopped rotor with trailing edge flap control surfaces is developed. Transition from helicopter mode to fixed wing mode is modeled as descending maneuver with successive rotor rpm reductions. Rotor slowing down stage is modeled as simultaneous steady descending forward flight segments. Rotor angular speed is kept constant during these successive segments but it is reduced with constant decrements between these flight segments. At this stage of the study, static longitudinal equilibrium for each flight segments is investigated and required trim settings are calculated. Main objective of this study is to model this transition mode and define the basic maneuver of the stopped rotor as well as determine the levels of required controls, both conventional pitch and the trailing edge flap controls.

By integrating equation (4) along rotor blade span and arranging the terms mean (average) of the rotor thrust of a flap controlled rotorcan be written as,

T

M

H

W

L

D

V

T

h

h

l

l

h

h

α

αα

θ

X

MR s

MY

tw

L

Dtw

twpr

pr

tw

can

can

can cg

FP

s

canDf

yf

Figure 4 Stopped Rotor Longitudinal Equilibrium. Modeling Acting Forces and Moments

( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++−+⎥⎦

⎤Λ+

⎢⎣

⎡Λ⎟⎟

⎠

⎞⎜⎜⎝

⎛++Λ++Λ−=

ri

T

skd

twkdkdckda

C

θµλµ

µµµ

σ

461

4132

42

41

302

31

31122

0 (5)

Where d1k, d2k, d3k, are related with the spanwise varying flap geometry and given in Ref. 6.

Stopped rotor reaches to trim condition by expressions based on the newly defined flap controlled rotor configuration, and blade dynamics, rigid blade flapping dynamics are considered at this stage.

Longitudinal force equilibrium considers the forces in the vertical longitudinal plane of the helicopter as seen in Fig. 4. The helicopter has speed V and a flight path angle θfp, so that it can climb or descent. The acceleration effects of during rotor slowing down transition are neglected and steady unacelerated flight conditions are assumed.

The forces on the rotor are the main rotor trust Tmr , and the rotor drag H are defined relative to reference rotor hub plane. This reference to the plane has angle of attack α respect to the forward speed. The forces acting on the helicopter are the weight W, canard and tail wing lift Lcan, Ltw, drags of fuselage; Df, canard and tail wing, Dcan and Dtw respectively. A pusher propeller thrust, Tpr, is also applied in the direction of the hub reference plane from aft rear and of the tail boom.

Vertical force equilibrium is written as,


6

0sincossin

sincos=−+−

++−

sPRFPTFPT

ssMR

TLDHTW

αθθαα

(6)

Where,

tcanT

twcanT

DDD

LLL

+=

+=

Similarly the horizontal force equilibrium can be written as:

0coscossin

sincos

=+−−

+

ssPRsMR

FPTFPT

HTT

LD

ααα

θθ (7)

The equilibrium of pitch moments acting on the helicopter determines the angle of attack of the rotor shaft relative to vertical, αs. Moments are taken about the rotor hub so that the rotor forces are not involved and the rotor reference plane is not entered to the problem. The rotor hub moment equilibrium about the rotor hub, for small angles, can be written as,

(8) ( )

0sin

coscossin

=+′−′−

′−′+−

−−++

+ tpTPtwtwtw

cancanCcgfus

fusscgsYFY

hThDlLhDlLxD

hDxhWMM

α

ααα

where resultant lift and drag of the auxiliary horizontal aerodynamic surfaces in the rotor hub reference direction is written as;

αααα

sincossincos

LDDDLL

+=′−=′

where MYF is the aerodynamic pitch moment of the fuselage; h and xcg are offset distances of the helicopter center-of-gravity location in vertical and longitudinal directions respectively as shown in Fig. 4.

Eq. (6), (7) and (8) are solved in nondimensional form to calculate CTmr , αs and CMY respectively. Main rotor thrust coefficient, CTmr represents the main rotor thrust required to maintain the vertical equilibrium of the CRW which is varied during the rotor slowing down transition maneuver with the utilization of auxiliary lifts of the canard and the tail wing. The second quantity αs is the angle of attack of the helicopter which is important in defining the transition maneuver. The third quantity CMY represents the pitching moment required at the hub to keep the helicopter in static balance around its center of gravity. The required hub pitching moment CMY is maintained primarily by the longitudinal cyclic rigid flapping component of blade, β1c.

A. Aeroelastic Analaysis Second objective of this study is to investigate CRW rotor blade nonlinear elastic responses during the rotor

slowing down transition mode. Yillikci and Hanagud10,11 has developed a numerical scheme for integrating the rotor blade partial differential equations based on a conditionally stable explicit finite difference formulation. Rotor blade nonlinear partial differential equations derived by Hodges and Dowell15 are modified by Yillikci et al9 for trailing edge flap controlled rotor blade case.

The used rotor blade nonlinear aeroelastic equations of motions are written in nondimensional form, the blade crossectional inplane and out of plane bending as well as the torsional stiffneses are represented by nondimensional stiffness parameters,


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ΛΩ

ΛΩ

∆Ω1 2 4 2 2 4 2 4= = =

EIm R

EIm R

GJm R

y z, , (9)

Where blade stiffness parameters are divided by mΩ 2 which physically means that blades gets softer as the rotational speed is reduced. For example if the rotor angular speed Ω is reduced to half, the blade stiffnesses are reduced to one fourth of their initial values. This simply explains the rotor vibration problem of the stopped rotors. To overcome this problem either blades are designed to be very stiff or the blade loading should be reduced during this slowing down. This nature of the stopped rotor softening during slowing down transition possible stopped rotor blades causes them to vibrate at increasing levels. From this aspect , an engineering tool is required for simulating the aeroelastic response of the slowing stopped rotor blade during this transition maneuver.

Figure 5 The 7000 lb. CRW Configuration.

III. Results and Discussions Results are presented as three groups whereas trim settings for the selected helicopter configuration are presented

first. Results for different flight angle path, auxiliary lift and tail propulsion utilization are compared. Second group of results is presented for the comparison of the required pitch control inputs with the proposed trailing edge flap control inputs for the same helicopter and flight conditions. Elastic blade responses simulated by the solution of nonlinear elastic rotor blade partial differential equations of motion are presented as the third group of results.

A. Trim Results First set of results is obtained both for pitch and flap control cases where identical rotor blade and helicopter

configurations are considered for both control cases. Basic rotor and vehicle parameters of the considered 7000 lb. stopped rotor helicopter configuration are given in Table 1. Conceptual design for the 7000 lb. stopped rotor helicopter configuration is based on AH-1G Cobra Light Attack Helicopter configuration. The assigned role for the proposed 7000 lb CRW is ship based Light Attack and Reconnaissance Navy Missions as introduced in Ref. 12.

The considered rotor blade has a rectangular planform with average chord width c=2.0 ft, and uniform flap along the rotor span with nondimensional flap hinge offset from center chord, cf=0.4. A rigid pitch setting is taken as, θri=0.06 for flap control case.

Considered stopped rotor is considered to have four bladed configuration with blade solidity σ=0.1107. Main rotor with radius Rmr=23 ft with blade average blade chord width c=3.0ft. Trailing edge flap geometry is selected as follows; rigid part of the blade is taken as C0 =3.0 ft starting from the blade span location r = 0.2 Rmr . and the trailing edge flap is started from r = 0.7 Rmr with width Cf0=0.4 ft. Flap reaches its maximum width Cf0=0.5 ft at r=0.85Rmr and then reduces to Cf0=0.4 ft at the rotor tip.

Vehicle trim and rotor response calculations are initiated from hover condition with and flight conditions are defined with advance ratio µ, rotor angular speed Ω for the conventional helicopter configuration in increasing forward speed conditions. Forward flight conditions are introduced with advance ratio increments ∆µ = 0.025 starting from hovering condition, µ = 0.0 to µ = 0.125 whereas the rotor angular speed has been kept constant at its nominal value of Ω=32 rad/sec during this conventional pure helicopter flying mode.


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After this pure helicopter configuration reached to steady-state forward flight condition at µ = 0.125 where for the selected flight conditions VT =80 knots, helicopter assumed to start using its auxiliary canard and tail wing lifts as well as its tail propulsion. Total nondimensional auxiliary lift and tail propulsion are modeled as;

CTcan =KTcan (VT )2

CPprop =KPprop VT (10)

where CL and CPR are total auxiliary lift and tail propulsion coefficients generated by the aerodynamic lifting surfaces like canard-tail horizontal wing and by the tail propulsion respectively. Total auxiliary lifts and tail propulsion coefficients nondimensionalized similar as main rotor thrust coefficient CTMR.

Stopped rotor is assumed to fly in helicopter mode until its forward cruising speed reaches to VT =135 knots. After this forward speed which rotor slowing down transition is initiated. Auxiliary lift and forward propulsion are increased gradually by the increased forward speed. above For each rotor-slowing interval parameters are changed as;

Ωk+1 = Ωk - ∆Ω

Clk+1 = Clk + ∆CL

CPRk+1 = CPRk + ∆CPR

θFPk+1 = θFpk - ∆θFP

Vhk+1 = Vhk + ∆VH

Blade elastic stiffness parameters are nondimensionalized with rotor angular speed, they are updated with the new Ωk+1 at each (k+1) th flight interval. Since blade nondimensional stiffness parameters are changed significantly, time step ∆t of the conditionally stable explicit finite difference scheme is also checked and changed based on the

nn

BT

dcc

Table 1 The 7000 lb. CRW Configuration.

Number of blades b = 4

Main rotor radius RMR = 23.0 ft Main rotor angular speed ΩMR = 32 rad/sn Main rotor chord (average) cMR = 2.25 ft Flap width ratio (average) cf = 0.43 cMR Hub-cg offsets xcg = 0.125 ft h = 1.8 ft Gross weight Wg = 7000 lb 2-D lift curve slope a = 2π Blade main drag coeff. CD0 = 0,01 Solidity ratio σ = 0.1107 Lock number γ = 9. Blade rigid pitch angle θri = 0,06 to 0 11 (rad) .

0,002

0,0025

0,003

0,0035

0,004

Mai

n R

otor

Thr

ust C

oeff.

0,0015

umerical stability criteria of the umerical scheme.

. Numerical Results for Transition rim Analysis

Trim results are obtained for four ifferent CRW configuration and flight onditions. First the pure helicopter onfiguration which flew up to 170 knt forw

American I

0

0,0005

0,001

0 20 40 60 80 100 120 140 160 180Forward Speed (knt)

CTm

r

Figure 6 Main Rotor Thrust Variation with Forward

StopRot_2PureHeli_SStopRot_1PureHeli

Pure Helicopter CRW CRWRotor Slow Down

ard speed without any auxiliary lift and tail propulsion with level flight

nstitute of Aeronautics and Astronautics

9

without descending condition. The proposed CRW is flown as standart helicopter without any canard and tail wing lifts and tail proposulsion utilization and rotor slowing down transition. Pure helicopter is considered as a baseline for the analysis and also as the reference for comparing the results and labeled as “PureHeli” in figures. The second considered case labeled “PureHeli_S” represents the standard helicopter configuration slowing its rotor without any canard and tail wing lifts and tail proposulsion utilizations. “PureHeli_S” only uses descending flight condition with ∆θfp= 0.0035 rad per each rotor slowing flight segment with ∆ Ω=1.0 rad/sec rotor rpm reduction after VT =135 knots.

The third considered case is “StopRot_1” represents the CRW configuration with auxiliary lift and tail propulsion and with a descending flight condition where ∆θfp is taken as equal to 0.0025 rad for every ∆ Ω=1.0 rad/sec rotor angular speed reduction. The only difference between “StopRot_1” and the fourth case labeled “StopRot_2” is the placement of the tail wing. In the “StopRot_1” case tail wing is placed

above the rotor hub whereas in the “StopRot_2” case the tail wing is placed below the rotor hub with equal distances in both cases.

For both of the stopped rotor cases auxiliary lift utilization parameter KTcan = 2.0E-8. The descending condition is taken as ∆θfp = 0.0025 rad, and the tail propulsion is introduced with its coefficient KPprop = 0.6E-8. These considered cases are also outlined in Table 2.

Fig. 6 shows the main rotor thrust coefficient variations respect to the helicopter forward speed

respectively for the considered four configurations. As seen from Fig. 6, the main rotor thrust coefficient is almost stayed steady for pure helicopter mode and “PureHeli” case but it is decreased in the other three cases where auxiliary lift and tail propulsion are utilized along with the descending flight condition. In stop rotor ‘CRW’ cases auxiliary lift and tail propulsion have significantly reduced the main rotor thrust loading.

Fig. 7 shows collective pitch input variation with respect to forward flight speed for the considered cases. For the pure helicopter rotor slowing case “PureHeli_S” collective and cyclic pitch controls represent not practical ranges, and they are only presented here for comparision purposes. Utilization of auxillary lift significantly reduces the collective input requirement and maintains enough time for pilots to transite to level flight with higher speeds on a lower altitude. For pilot’s rotor commands decending flight and the utilization of canard and tail wing lifts as wel as the tail forward propulsion gives a better improvement. The best configurations are presented by “StopRot_1” and “StopRot_2”cases where the only difference is the placement of the tail wing. In CRW configurations the required collective pitch controls are within the ranges of hovering conditions. CRW configuration results in easier adaptation to higher speeds at lower altitude. This suitable transition maneuver parameters are obtained after several iterations, where different flight conditions, rotor blade configurations as well as auxillary lift and tail propulsion utilizations are considered.

Table 2 Flight Condition Parameters for Different Flight Cases

CASE KTcan

PureHel 0.0 PureHel_S 0.0 StopRot_1 2.0x10-8

StopRot_2 2.0x10-8

0,15

0,2

0,25

0,3

0,35

0 20 40 60 80 100 120 140 160 180

Forward Speed (knt)

Col

lect

ive

Pitc

h (r

ad)

StopRot_2

StopRot_1

PureHeli_S

PureHeli


Figure 7 Sine Component of the Cyclic Pitch Variation

with Forward Speed.


10

It should be noticed in the considered rotor slowing down cases, rotor is controlled by collective, cyclic and collective controls as well as the canard flaps and tail propulsion is also introduced as new control features. These controls are proposed to be integrated by an autopilot system which can be over ruled by pilot and/or copilot.

The cosine and sine components of the first harmonics of cyclic pitch inputs are represented in Fig. 8 and 9 respectively. As illustrated, the cyclic inputs of pitch control are significantly affected by the utilization of the auxillary lift and tail propulsion, and the flight path descending conditions. The cyclic inputs are identical until 95 knts forward speed for all flight cases. After canard and tail propulsion is applied, cyclic control inputs are lowered.

As indicated in Introduction we propose VTOL capabilities. In Figures 8 and 9 pilomaneuver pilot controls and it is applicable by

Angle of attack variations of the helicopteconfiguration angle of attack is increased as fobserved for this case. Angle of attack of the “as seen in Fig. 10. In the CRW configurationutilization of the auxiliary lift and the tail significant difference between the placement of the tail wing is observed for the vehicle angle of attack. As shown in Fig. 10. Placement of the tail wing above the rotor hub is reduced the vehicle angle of attack which results in reducing the parasite drag of the vehicle.

Nondimenional main rotor thrust and the auxiliary lift variations with forward speed are shown in Fig. 11. As canard and tail wing lifts are introduced the main rotor thrust is decreased for the CRW considered configuration. In the considered configuration and the flight condition the rotor thrust is reduced to half. In further studies this reduction is expected to reach at least 80 % for more efficient CRW fixed wing transitions.

American Ins

-0,25

-0,2

-0,15

-0,1

-0,05

0

0,05

0 20 40 60 80 100 120 140 160 180

Forward Speed (knt)C

yclic

1s

Pitc

h (r

ad)

StopRot_2StopRot_1PureHeli_SPureHeli


Figure 9 Sine Component of the Cyclic Pitch Variation with Forward Speed.

to reach to 450 knts forward speed regime while we are preserving t cyclic control inputs are identical to an autorotation emergency

any pilot. r and CRW configurations are shown in Fig. 10. For the “PureHeli” orward speed is increased and highest change in the angle of attack is PureHeli_S” is decreased sharply with the descending flight condition

s the angle of attach is changed in similar fashion, decreased with the propulsion and increased with the increasing forward speed. The

-0,06

-0,04

-0,02

0

0,02

0,04

0,06

0,08

0 20 40 60 80 100 120 140 160 180

Forward Speed (knt)

Cyc

lic 1

c Pi

tch

(rad

)



Figure 8 Cosine Component of the Cyclic Pitch Variation with Forward Speed.

titute of Aeronautics and Astronautics

11

C. Comparison of the Pitch and Flap Control Inputs

Control Input types are also compared for pitch and the flap controlled cases. Fig. 12 represents a typical comparison of the collective pitch and the trailing edge flap control inputs along with the rigid pitch angle applied for the flap control case. Although the rigid pitch angle is shown as varying in Fig. 12, a fixed value can be optimized for the selected flap geometry. With

-0,05

0

0,05

0,1

0,15

0,2

0,25

0 20 40 60 80 100 120 140 160 180

Forward Speed (knt)

Col

lect

ive

Inpu

ts (r

ad)

Thet0Gamma0Thetri

Figure 12 Comparison of Collective Pitch and Flap

0,04

0,06

0,08

0,1

0,12

0 20 40 60 80 100 120 140 160 180Forward Speed (knt)

Alp

ha V

ehic

le A

ng. O

f Atta

ck (

rad)


Figure 10 Angle of Attack Variation with Forward Speed.

Controls for “StopRot_1” Case

various applicable flap geometry and rigid pitch setting combinations the required flap control input can be reduced. Illustrated result for the range of the flap control input is found to be in applicable limits.

-0,0005

0

0,0005

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

0 50 100 150 200

Forward Speed (knt)

CTm

r and

Ctc

an C

oeff.

StopRot_2

StopRot_2

CTmr

CLaux

Figure 11 Comparison of Main Rotor Thrust and Auxiliary Lift Variations with Forward Speed.


12

Similarly the sine and cosine components of the cyclic pitch and trailing edge flap controls are also compared in Fig. 13 and 14 respectively. Sine component of the flap control input found to be quite high compared with the pitch control case as shown in Fig. 13. Cosine component of the cyclic flap control input is in the range of the pitch control case.

D. Aeroelastic Response Simulations. In this section sample results are presented for

the transient blade responses throughout helicopte forward fligth and the rotor slowing down sections. Blade stiffness parameters are nondimensionalized with rotor angular speed, they are updated with the new Ωk+ at each k th flight interval. Since blade nondimensional stiffness parameters are changed significantly

, time step )4(3216 11 =Ω=Ω

Λ=Λ ∆ t of the conditionally stable explicit finite difference scheme is also checked and changed based on the numerical stability criteria of the numerical scheme.

Blade configuration for the selected gross weight anddesign for 3g maneuver loads and blade bending and torsiblade stiffness properties are assumed to be constant throug

Rotor angular speed variation is presented in Figure 14defined. Blade required flap control input variation during fflight condition are presented in Fig. 15 which the levels ofSimilarly blade elastic lead-lag tip deflection transient timetip deflections are also illustrated in Fig. 17.

-0,05

-0,025

0

0,025

0,05

0 20 40 60 80 100 120 140 160 180

Forward Speed (knt)

1st S

ine

Inpu

ts (r

ad) Thet1c

Gamma1c

Figure 14. Comparison of Cosine Component of the Cyclic Pitch and Flap Controls for “StopRot_1” Case

-0,6

-0,5

-0,1

0

0,1

0 20 40 60 80 100 120 140

Forward Speed (knt)

(rad

)

Figure 13 Comparison of Sine Component of the Cyclic Pitch and Flap Controls for “StopRot_1”

American Institute of Aero

13

160 180

Omega

14

16

18

20

22

220 225 230 235 240 245 250

Blade Revolution

Rot

or O

meg

a (r

ad/s

ec)

Omega

Figure 15

-0,4

-0,3

-0,2

1st S

ine

Inpu

ts

Thet1s

Gamma1s

Table 3. Blade Nondimensional Stiffnesses For The Selected Rotor Configuration Λv ΛzFlap Lag 0.0306 0.04

number of blades stopped rotor blades are structurally onal stiffnesses are calculated. At this level of study the hout the blade spanwise direction. which also gives the idea of how the flight condition is orward flight speed increase and the rotor slowing down the flap control during this predecribed flight condition. history is shown in Figure 16. Blade vertical flapping

Case

nautics and Astronautics

w

-1,50E-01

-1,00E-01

-5,00E-02

0,00E+00

5,00E-02

1,00E-01

1,50E-01

220 225 230 235 240 245 250

Blade Revolution

w/R

Fla

p D

efle

ctio

n

w

Figure 17

-30

-20

-10

0

10

20

30

40

50

60

70

80

234 236 238 240 242 244 246 248 250

Blade Revolution

Gam

ma

Con

trol

Inpu

t (de

g)

Gamma Theta

Figure 18

Gamma

-10

-5

0

5

10

15

220 225 230 235 240 245 250

Blade Revolution

Flap

Con

trol

Inpu

t (de

g) Gamma

Figure 16

-1,00E-01

-5,00E-02

0,00E+00

5,00E-02

1,00E-01

1,50E-01

2,00E-01

234 236 238 240 242 244 246 248 250

Blade Revolution

v/R

Lea

d La

g D

efle

ctio

n

v_crw w_phel

Figure 19


14

-1,50E-01

-1,00E-01

-5,00E-02

0,00E+00

5,00E-02

1,00E-01

1,50E-01

2,00E-01

234 236 238 240 242 244 246 248 250

Blade Revolution

w/R

Fla

p D

efle

ctio

n

w_crww_phel

Figure 20

REFERENCES 1Schwartz, A. W., Reader, K. R. and Rogers,

E. O; “An Unmanned Air Vehicle Concept With Tipjet Drive'’ Specialists'’Meeting on Vertical Lift Aircraft Design, San Francisco, CA, USA, January 1990.

2Proctor, S; “Boeing To Test ‘Dragonfly” UAV”, AV&ST December 7, 1998, pp 48.

3Rutherford, J. W., O’Rourke, M. J., Lovenguth, M. A. and Mitchell, C. A. “Conceptual Assessment o Two High-Speed Rotorcraft”, Journal of Aircraft, Vol. 30, No.2, March-April, 1993.

4Huston, R. J., and Shivers, J. P., “The Conversion of the Rotor/Wing Aircraft,” NASA TM-X 60448, Sept. 1967.

5Y.K. Yillikci and S. V. Hanagud; “An Initial Evaluation of Blade Dynamics of A Stopped/Flipped Rotor With Flap Controls”, 19th European Rotorcraft Forum, Cernobbio, Italy, 14-16 September 1993.

6Yillikci, Y.K; “Trimming Rotor Blades with Periodically Deflecting Trailing Edge Flaps”, 17th European Rotorcraft Forum, Berlin, Germany, September 24-26, 1991.

7Y.K. Yillikci, S. V. Hanagud and D. P. Schrage; “Blade Response Simulations of Flap Controlled Stopped Rotors”, 1993 AIAA International Powered Conference, San Francisco, USA, 1-3 December 1993.

-1,00E-02

-5,00E-03

0,00E+00

5,00E-03

1,00E-02

1,50E-02

234 236 238 240 242 244 246 248 250

Blade Revolution

Elas

tic T

wis

t (ra

d)

fi_crw fi_phel

Figure 21

8Y.K. Yillikci, S. V. Hanagud and D. P. Schrage; “Transient Response of Stopped Rotor Blades with Flap Controls”, ICAS’94, 20th Congress of the International Council of the Aeronautical Sciences, Anaheim, USA, 18-23 September 1994.

9Y.K. Yillikci, S. V. Hanagud and D. P. Schrage; and J. Higman, “ Aeroelastic Analysis of Rotor Blades with Flap Controls”, 18th European Rotorcraft Forum, Avignon, France, September 15-18,1992,.

10Y.K. Yillikci and S. V. Hanagud “ Finite Difference Techniques aand Rotor Blade Aeroelastic P.D.E” 15th European Rotorcraft Forum, Amsterdam, Holland, Sept. 12-15 1989,.

11Y.K. Yillikci “Finite Difference Techniques and Rotor Blade Aeroelastic Partial Differantial Equation with Quasisteady Aerodynamics”, Doctoral Dissertation, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia, December 1988.

12T. Karamisir and Y.K. Yillikci; “Modeling the Transition Maneuver of Stopped Rotors” AIA’98 Second Ankara International Conference, 13-15 September, 1998, Ankara TURKEY

13Stuller, J, “The Taming of the Copter”, Air & Space, Vol, 5, No.5, December 1991, January 1992 14Johnson, W. “Theory of Helicopter”, Princton Press. 1980. 15Hodges, D.H and Dowell, E.H, “Nonlinear Equations of Equilibrium for Elastic Bending and Torsion of Twisted

Nonuniform Rotor Blades”, NASA TND-7818 , 1974


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