Active Control of Helicopter Blade Stall

AIAA Meeting Papers on Disc, April 1996, pp. 492-501 A9630777, AIAA Paper 96-1221 Active control of helicopter blade stall

Khanh Nguyen NASA, Ames Research Center, Moffett Field, CA

AIAA, Dynamics Specialists Conference, Salt Lake City, UT, Apr. 18, 19, 1996

This paper describes the numerical analysis of an automatic stall suppression system for helicopters. The analysis employs a FEM and includes unsteady aerodynamic effects (dynamic stall) and a nonuniform inflow model. The stall suppression system, based on a transfer matrix approach, uses blade root actuation to suppress stall directly. The results show that stall can effectively be suppressed using higher harmonic blade root pitch at both cruise and high speed flight conditions. The control amplitude was small, less than 1 deg. In a high thrust, low speed flight condition, stall is fairly insensitive to higher harmonic inputs. In general, stall suppression does not guarantee performance improvements. The results also show the distinction between stall suppression and performance improvement with active control. When the controller aims to reduce the shaft torque, rotor performance improvement can be achieved with a small degradation in stall behavior. (Author)

Page 1 A96-30777

ACTIVE CONTROL OF HELICOPTER BLADE STALL

Khanh Nguyen* NASA Ames Research Center, Moffett FieldA C ,

forward flight blada , e encounter sdifferena t dynamic Abstract pressure due to the combination of blade rotation and rotor translation speed. Thus, the dynamic pressure is This paper describes the numerical analysis of an auto- greateadvancine th n ro g sid eretreatine thath n no g side. matic stall suppression system for helicopters. The r rolFo l moment balance blade th , e operate t anglea s f so analysis employs a finite element method and includes attack that are low on the advancing side and high on the unsteady aerodynamic effects (dynamica stall d an ) retreating side. At high blade loading or at high forward nonuniform inflow model. The stall suppression sys- speeds locae th , l blade section angl attacf eo becomn kca e tem, based on a transfer matrix approach, uses blade root large enough to stall. For untwisted blades, the stall area actuation to suppress stall directly. The results show occurs nea blade rth e tip, growing inboar loadine th s da g that stal effectiveln ca l suppressee b y d using higher har- forware oth r d speed increases r twiste[1]Fo . d blades, monic blade root pitch at both cruise and high speed effecte th reversee sar d stale —th l area spreads froe mth flight conditions controThe . l amplitud smallewas , less blade root outboard. than 1 deg. In a high thrust, low speed flight condition, stal s fairli l y insensitiv higheo et r harmonic inputsn I . Operating in an unsteady environment, the most severe general, stall suppression does not guarantee performance typ f staleo l encountere rotoa y b dr blad s dynamii e c improvements. The results also show the distinction be- stall forwarn I . d flight blade th , e experiences time-vary- tween stall suppressio performancd nan e improvement ing dynamic pressure and angle of attack changes arising with active control. Whe controllee nth r aim reduco st e from blade pitch inputs, blade elastic response nond an , - the shaft torque, rotor performance improvement can be uniform rotor inflow. If supercritical flow develops un- achieved with a small degradation in stall behavior. dynamir de c conditions, then dynamic stal initiates i l y db leading edge or shock-induced separation. Supercritical Introduction flow is associated with the bursting of the separation bubbl bubble th s ea e encounters tiie large adverse pres- Suppression of retreating blade stall has been proposed as sure gradient near the blade leading edge [2]. Dynamic a means of helicopter flight envelope expansion, thereby stal characterizes i l sheddine th y b d f stron go g vortices enhancin utilite gth f thesyo e aircraft. Unlike fixed-wing fro leadine mth g edge region leadine Th . g edge vortex aircraft, stall doe t limi loe no s wth t speed operatiof no produces a large pressure wave moving aft on the airfoil helicopters. Stal roton o l r blades, however, limite sth upper surface and creating abrupt changes in the flow helicopter maximum speed as well as the loading capa- field. The pressure wave also contributes to large lift and bilities. Stall places a loading limit on most of the heli- moment overshoots in excess of static values and signif- copter flight envelope at low and medium speed, and at icant nonlinear hysteresi airfoie th n si l behavior. high speed, either stal r compressibilito l y effectn ca s limit helicopter operations. A rotor experiencing stall e otheTh r typ f staleo l typically encountere rotoy db r can require more shaft power than is available from the blades involves trailing edge separation. The phe- engine. Also, the excessive control loads on a stalled ro- nomenon of trailing edge separation is associated with ei- tor blade, together with the changes in blade aerodynamic ther static or dynamic conditions. Separation starts from behavior, adversely affect aircraft handling qualities. the airfoil trailing edge, and with increasing angle of at- Stall-induced loads, possibl combination yi n with blade tack, the separation point progresses towards the leading dynamics as in stall flutter, can severely damage blade edge region. Trailing edge separation contribute nono st - structural components and cause excessive cabin vibra- linear behavior, suc hysteresiss ha liftn i , , dra pitchd gan - tion. in glose momen circulationth n s i o t e tdu contrasn I . o t t dynamic stall tha characterizes i t abrupy db t changen i s A unique characteristi f helicopteco roccure stalth s i l - airfoil behavior, trailing edge stall progresse moder-a t sa renc retreatine th f stal eo n o l rotoge sidth f r eo disk n I . ate rate. Passive control of blade stall typically involves the tai- loring of blade twist and planform for efficient blade load •Aerospace Engineer distribution. Another method employs blade construc- Copyright © American Institute of Aero- tion with multi-airfoil sections — thick, high-lift sec- nautic d Astronauticsan s , Inc., 1996H A . tions inboard and thin, transonic sections for the tip re- rights reserved. gion. These method provido t m sai e efficient rotor disk computed transfer functions relating higher harmonic draw loadinthusd lo gan d , employegan d primarilr yfo contro changeo t l bladn si e angl f attackeo , Arcidiacono performance benefits; however, they also provide stal- al l derived a blade pitch schedule that approximated an "ideal leviation. schedule" for stall alleviation. The analysis showed that the blade pitch schedule, which includeP 3 d botan P h2 As an alternative to passive methods, active control of components with a combined maximum amplitude of blade pitch has the potential to alleviate blade stall. deg3 capabls 4. wa , f avoidineo g retreating blade stall. Recent developmen high-frequencyf o t , blade-mounte- dac resultine Th g effects could rais speee eth d limihelia f o t- tuator ] make[3 s s this concept feasible e operatinTh . g coptepercen0 3 y b r t ove baseline th r e maximum speed. frequencies for blade pitch control are not limited by the additionae Th l power requiremen speee th do t gaie du tn blade-integer harmonics swashplatn i s a , e oscillationt bu , would be large, however, to compensate for the increase e bandwidtbth y e actuatorsth f o h . RecentlyF Z , in fuselage and rotor profile drag (about 100 percent). Luftfahrttechnik, GmbH of Germany built and wind tunnel tested, together with NASA Ames Research Center, In 1961, a flight test program was conducted to investi- an individual-blade-control system on a full-scale BO-105 gat feasibilite eth f usinyo g higher harmonic contron o l rotor. These actuators were tested at harmonics from 2P an UH-1A helicopter [7]. Using a rotor head mechanism to 6P (42.5 Hz) and amplitudes up to 3 deg. Although capable f generatino bladP g2 e pitch, Bell Helicopter no stall suppression study was attempted, the benefits of conducted a series of flight tests to determine the effects IBC input on rotor performance at high forward speed of active contro roton o l r performanc loadsd ean . Test (advance ratio p. = 0.4) were encouraging [3]. results indicated that the 2P control at different amplitudes and phases did not produce any reduction in rotor Previous Work shaft torque. Determined to resolve this variance with theoretical prediction investigatore ,th s conducte dposta - In 1952, Stewar ] suggeste[4 t d per-rethao tw t v (2P) test analysis. Analytical results indicated that the drag blade pitch applied to rotors in forward flight could be reduction in the retreating side due to 2P control was off- use delao dt onsee yth retreatinf o t g blade stall. Basen do set by an increase in profile drag in the fore and aft por- the analysis that included a rigid flapping blade, quasi- tions of the rotor disk. Such conclusions confirmed pre- steady aerodynamics and uniform inflow models, Stewart vious analytical predictions that 2P control could reshape derived an approximate transfer function relating the the rotor disk loading. change in 2P blade angle of attack due to 2P control. Results indicated that rotor disk loading coul effie db - Kretz [8, 9] reported the wind tunnel test results of a ciently re-distributed using higher harmonic Wade pitch. Stall Barrier Feedback (SBF) syste six-fooa n mo t diame- For a particular flight condition, the loading redistribu- ter two-bladed rotor. The salient feature of the system tion coul adjustee db avoio dt d retreating blade stalle Th . was the ability to detect and, through feedback control, resulting effects would be to raise the speed limitation of prevent blade stall. The SBF system employed three helicopters. According to his analysis, the helicopter pressure sensors percenmounte5 8 e th tt da blad e radial speed limit coul e increasedb 0. y advancdn b 1i e ratio. station and high-bandwidth hydraulic actuators to control However, Stewart did not consider the power requirement each blade. The pressure sensors provided feedback sig- speee duth o det increase. nals that activate actuatore dth attempn a n si preveno t t t stall. The system was configured such that once the Payne expanded Stewart's result includo st effecte eth f o s leading edge pressure exceeded a threshold value, the ac- active control using input harmonics higher than 2P [5]. tuators became active, generatin gshara p pulse (e.g.n a , arguee H d tha controP 2 t l alone sufficienwoule b t dno t nosg de e 8 down puls generates ewa f o d g withide 5 n7 to raise the speed limitation of helicopters, but a combi- rotor azimuth) to reduce the blade pitch. The threshold seconnatioe th highed f no dan r harmonic control would pressure value had been inferred from experimental data be more effective processe th n I . , Payne derived general- and used as an indicator of stall onset. Limited stall ized transfer functions relating change bladn si e anglf eo avoidanc achieves ewa systemF d SB wit e h,th whic- hre attachighee th o kt r harmonic contro hoverina f o l g rotor. sulted in some lift gain. Most significant was the per- However, Payne did not quantify the speed limit gain formance gain — an 8 percent reduction in shaft torque — from his approach. for the rotor operating at an advance ratio of 0.3 and blade loading (Cj/a) of 0.1. However, it was unclear Arcidiacono conducte dnumericaa l simulatio studo nt y whether the rotor was re-trimmed after the application of the effects of second and higher harmonic control on stair active coTrtroitamaintain identical rotor operating condi- [6]. This numerical analysis was more accurate and in- tions. cluded more realistic modeling of physical phenomena than previous analyses. The analysis was capable of in- As a leading advocate in individual-blade-control (IBC), cludin effecte gth f statio s c stalMacd an l h numbee th n i r Ham has also conducted experiments in active stall sup- for f two-dimensionamo l airfoil tables. e Baseth n do pression e methodTh . f sensino s g stall, however, dif- 2 fered from tha experimene f Kretzo t on n I . t reportey db solution, is mandatory for the analysis of stall control, Quackenbusd an m Ha h [10] e controlleth , r sensee dth Ames-modifiee th d versio Universite th f no Marylanf yo d blade pitch motions to modify the blade torsion dynam- Advanced Rotorcraft Code (UMARC adoptes i ] 12 r )[ d fo ics, and the feedback gain was adjusted to increase blade this investigation. UMARC/ finita s Ai e element code torsion damping e increasTh . dampinn ei g would pre- that includes advanced unsteady aerodynamic vortexd san - vent stall flutter, an indicator of retreating blade stall. wake modeling. The structural and aerodynamic model- The experiment was conducted in a non-rotating mode ing of UMARC/A makes the code an appropriate tool for and thus, was not validated in a simulated helicopter en- studying active control effects on rotor behavior. vironment n anotheI . r experiment performey b d McKillip [11], the controller successfully reduced 5P e rotoTh r blad s modelei e n elastica s a d , isotropic blade inplane accelerations, indicaton usea s da retreatf ro - Bernoulli-Euler beam undergoing small strain and'moder- ing blade stall. deflectionse at blade Th .e degree f freedoso flae mar p bending, lead-lag bending, elastic twist axiad ,an l deflec- Scope of Current Investigation tions finite-element-methode Th . base Hamilton'n do s principle allows a discretization of the blade model into a The objective of the current study is to evaluate the effec- numbe f beao r m elements, each with fifteen degreef so tivenes automatin a f so c stall suppression - systehe r mfo freedom. licopters using higher harmonic blade root input. The effect f stalo s l suppressio roton no r performance th d ean The blade airloads are calculated using a nonlinear un- control authority required are also investigated. steady aerodynamic model based on the work of Leishma Beddoed nan s [13]. This model consistn a f so An advanced rotorcraft analysis, capable of modeling the attached compressible flow formulation along wit hrepa - aeroelastic respons elastif eo c blades, dynamic stalld an , resentatio nonlineae th f no r trailineffecto t e du sg edge non-uniform rotor inflow, is adopted and modified for separatio dynamid nan cattachee stallth n I . d flow formu- this active control study nonlineae Th . r controller devel- lation, the normal force (or lift) and pitching moment in- opment is based on a transfer matrix approach with the cludes both circulator impulsivd yan e (noncirculatory) option for matrix updating at each controller cycle. The components. Physically, the circulatory components effect of stall reduction on rotor performance is investi- mode shee th ld wake effects, whil impulsive eth e com- gated resulte Th . s quantif distinctioe yth n between con- ponents originate from the pressure wave generated by trol of stall versus control for performance gain. the airfoil motion. For dynamic stall modeling, an artificial normal force CN is computed based on the attached Two aspects of the present study are unique. First, stall flodynamice th w pressure d lifth an tf so e distribution, suppressio formulates ni optimization a s da n problemn i represented by a time-lag model. This quantity incorpo- which the stall behavior of a rotor is quantified and sub- rates the effects of stall delay and is used in a criterion of sequently minimized using higher harmonic control stall onset. (HHC). Thus e systeth , m suppresses stall directly. Second range th , f fligheo t conditions considered varies The trailing edge separation model is based on from low to high speed flight, which helps evaluate the Kirchhoffs formulation that relates the separation point f effectiveness of higher harmonic control for stall sup- to the airfoil force and moment behavior. The variation pression when different physical phenomena dominate of the separation point with angle of attack is constructed e rototh r flow field, e.g.speew lo , d stall versus high from static airfoil data, then the results are curve-fitted speed shock-induced separation. using five parameters. The separation point value is a measur degree th f enonlinearitf o e o life tth behaviorn yi . In this paper, the term higher harmonic control refers to Information about the flow separation point also allows blade pitch input with harmonic contents greater than the reconstruction of the airfoil static behavior, a precur- per-reve on . aeroe Sinc th pape e focue -n th o eth f s ri o s modeline th airfoie o t th r f go so l dynamic characteristics. dynamic performance aspects of stall suppression, the effects of HHC on blade loads, control system loads, and r dynamiFo c stall stale th , l onse critee s basei tth n -do vibratory hub loads, which can be significant, are not rion such thaleadine th t g edge separation initiates only discussed. when the artificial normal force CN attains a critical Description of Analysis value, CNI, corresponding to a critical leading edge pressure. In this model, CNI 's tne airfoil maximum static lift coefficient (available from airfoil tables) and is a Aeroelastic analysis Since accurate representatio blade th f eno aeroelasti- cre function of the Mach number. Once initiated, the excess sponse complee th o st x rotor flow field, together witha lift due to dynamic stall is governed by the dynamics of robust and accurate numerical method for blade response vortee th x lift, define e differencth s a d lifn i e t between the attached (linear) and separated flow (nonlinear) regimes e vorteTh . x movement ove airfoie th r l upper surface induce larga s e chang pitchine th n ei g moment. where the double summation is over the 2880 airload The vortex induced pitching moment is computed based computation points ove rotoe th r r dispoint4 e k(2 th n si e vorteo nth positioe th centee x th d lif f f presan nto o r - radial directio n12x 0 azimuth steps)d ,an sure. infloe th r w Fo calculation prescribea , d wake modes i l (4) used for the high speed flight condition, and a modified 0 otherwise free wake model is used for the low speed flight condition. Both wake model e originallar s y adapted from Note defines thai F t d ove rotoe th r r disk, wit hr bein g CAMRAD [14]. A modification to the free wake model the blade radial station and If/ the azimuth angle. With improve convergence sth e behavio wake th f ero geometr y this definition, the stall index is a metric that measures computation by using a predictor-corrector updating the severity of stall on the rotor disk in term of the ex- scheme with non-reflective periodic boundary conditions. cess lift over the stall area. The excess lift is the amount couplee Th d blade response trid msan control settinge sar of artificial lift CN over the airfoil maximum lift CNJ, solve r simulatedfo d wind tunnel conditions r trimFo . , adapted from the dynamic stall model described earlier. the rotor shaft orientatio prescribeds ni blade th ed colan , - lectiv cyclid ean c pitch input automaticalle sar y adjusted controe th , 2 l. ratInEq e facto , witr r h value between0 desireo t d value momentsb f thrushu so d modaan tA . l an , limit1 d controe th s l update i denoterate d an ,e th s reduction techniqu employes ei blade th n edi respons- eso controller cycle. The transfer matrix updating is an op- lution to reduce the computational requirement. The tion in which Tj is updated at each controller cycle, based modal equations are solved iteratively using a robust fi- o secanna t metho matridT [15]e xTh . updating, when nite-element-in-time method in which the periodic used in combination with the control rate limit, helps boundary conditions are inherent in the formulation. The improv convergence eth controllee th f eo r when nonlin- converged solution satisfie governine th s g equationr sfo ear effects dominate. This approach was successfully ap- both rotor trim and blade responses, which include higher plie anotheo dt r control problem — vibration suppression harmonic control effects. of rotors under stalled conditions [16] — with significant nonlinearity in the model. Higher Harmonic Control System e controlleTh r algorithm, base transfea n do r function The vector u, represents the control input that includes matrix approach s i implemente, n UMARC/Ai d . harmonic revr pe :s6 froo t m2 Dependin controe th n go l objectives considered —supo t - press stall or to reduce rotor shaft torque ~ each element e transfeoth f r matrix represent sensitivite th s e th f yo (5) controlled paramete eaco t ) h (z rharmoni blade th f eco root actuation (u) thin I .s investigation transfee th , - ma r In e elementtermth f o s e highef ujo th s, r harmonic trix is computed using a finite-difference-method in schedule for thejth blade for is: which each harmonic of the control input (sine and co- sine components) is perturbed individually. The control la formulatews i optimization a s da n problem: (6) k=2 2 T min (qzf +Uj 0) wher amplitude eth : eis subjecteo dt (7) (2) anphase dth : eis For stall suppression, Zj is the stall index computed at each controller cycle by: ifr= tan 24 120 (3) factore . 1th ln, Eq (scalarsq (diagonaR d )an l matrixe )ar used to place relative weightings to the controlled paramete reacd zan ji h componen inpue th f to t vector, respec- schedule for stall reduction peaks at two regions of the lively. rotor azimuth — one between 90 to 135 deg and the other betwee 31o t 50 degn27 . This resul rathes i t r counter-in- Besides stall suppression, a second controller is also in- tuitive since Fig. 2(a), whic- h ex show e th e plo f th so t vestigated. This controller aim improvo t s rotoe th e r cess lift (F in Eq. 4) over the rotor disk, indicates that performance using higher harmonic blade root pitch. For stall occurs between 270 and 300 deg azimuth. this system, the controlled parameter (Eq. 3) is simply Interestingly, Fig. 2(b), which show stale th s l behavior the rotor shaft torque. Excepchange defie th th r -n fo tei at 240 deg of 2P phase, indicates that the rotor is almost nition of z, this controller retains the same structure as stall-free. These results imply thablade th t e aeroelastic e stalth tha lf o suppressiot n controller. Note that this responses to higher harmonic input are important consid- controller doe t restricsno inpue th t t harmonis a P 2 o ct erations in stall suppression for helicopters. in other investigation r [17] o st include ] (suc)bu [3 s ha s widea r rang inpuf eo t harmonic 6P)o t P . s(2 effecte amplitudP 2 Th f o s phaseg variatiode e0 24 t na on the stall index are shown in Figure 3 for the cruise Rotor Model speed flight condition resulte Th . s indicate thastale th t l rotoe Th r mode lstude usevariana th s yn i d i foure th t - index increases wit amplitudP h2 t thiea sabovg de 1 e bladed hingeless BO-10 e rototh f ro 5 helicopter beto T .- phase angle. Curve-fitting the results indicates an opti- ter captur effecte eth f stalo s l contro modern o l n rotors, mum amplitude at roughly 0.9 deg at this phase angle. two modification baselinmade e th sar o et e BO-105 rotor: HH-1e (1th ) 0 airfoi uses i l d instea NACe th f do A 23012 For the 2P phase sweep at the same operating condition, and (2) blade linear twist is decreased from -8 to -10 deg. die shaft torque variation exhibit differensa t trend than Beside these modifications, the blade geometry and struc- stale th tha lf indexo t resulte Th showe . sar Fign ni . 4 . tural properties are essentially the same as the BO-105 Althoug relative hth e chang shafn ei t torqu s smali e l rotor blade. The major characteristics of the rotor model compared to the change in stall index, a 2 percent reduc- are listed in Table 1. tio shafn ni t torqu , howevereis significana , t- gairo n ni tor performance. While minimum stall index occurs in Flight Conditions die range of 180 to 270 phase angle (Fig. 1), minimum Simulated flight conditions with significant blade stall torque is at 30 deg phase. In fact, in the phase region are selected at several forward speeds. These included a where stall inde minimus xi m deg)0 (18rotoe 27 th ,0o t r low speed condition at 63 knots (p. = 0.15, CT/a = shaft torque increases abov uncontrollee eth d valud ean 0.16), cruise speed conditio knot7 12 st na (n = 0.3, Gr/o even reache phaseg maximusa explanade n 0 A . 21 t ma - = 0.13)higa d h an ,spee d conditio knot8 14 st na (|i = tio thif no s phenomeno provides ni investigation a y db n of Fig . 5 Figure. s 5(a)-5(c) sho evolutioe wth e th f no 0.35, CT/ o0.12)= r all Fo fligh. t conditions steade th , y hub moment trimmee sar zeroo dt . blade drag coefficient over the rotor disk for the baseline case, minimum stall index case minimud an , m shaft Result Discussiod san n torque case, respectively. The results show that the drag behavior alon entire gth e blade span showregioe th n ni n Open Loop Study near 300 deg azimuth is responsible for this phe- An open-loop study is performed to evaluate the sensitiv- nomenon. Of the three cases shown, the minimum stall ity of the stall index to the amplitude and phase variation index case has the highest drag rise, while minimum of single harmonic inputs. The approach consists of a torqu draa s geha reductio n fro baselinee mth . Since eth phase variatio inpun a f no t harmoni fixea t ca d amplitude stall area is localized inboard, reducing stall does not and a subsequent amplitude variation about an optimum guarantee an improvement in rotor performance. phase wher controllee eth d paramete minimuma t a s i r . These results provide insight into the input-output be- Open loo speew plo resultde th fligh r sfo t condition (u= , havior of the control system and help define the type of 0.15, CT/O = 0.16) are shown in Fig. 6. The sensitivity controller (linear versus nonlinear) to use. The effective- stale oth f l indeexcitatioP 2 o xt s weakni . Figure 6(a) closed-looe nesth f so p syste malss i o estimated basen do shows diastale th l l index varie only sb percen0 y2 t with open-loop data. Representative results are presented in phasP 2 e eamplitudeg th sweede 1 t pe shafa Th . t torque this paper. variation with the same phase sweep is moderate, however, varyin percen6 y gb t abou uncontrollee th t d value. Figur showe1 variatioe sth stale a th o lt f no indee du xz e amplitudTh e variatio phase th minimur t nefo a m stall 2P phase sweep at 1 deg excitation for the cruise speed index (330 deg) show Fign ni . 6(b) exhibit same th s e flight condition (u,= 0.3, Or/a = 0.13). The results indi- low sensitivity. At this low speed condition, the stall cate thastale th t l index varies almost linearl t - thiya sam reducede indeb n xca t besta , only percenb ,0 1 y t with2 plitude of 2P excitation. Since the phase range for min inputP 2 -f o . g Opende loop result other sfo r harmonics imum stall is between 180 and 270 deg, the 2P pitch show similar result sstale ~th l inde fairls xi y insensitive to higher harmonic control at this low speed flight condi- Fig. 10 show that the controller is capable of relieving tion. drae mosth g f riseo t s ove rotoe th r r disk, resultin6 n gi percent reductio rotoe th rn ni shaf t torque. Closed Loop Study Closed loop results for the low speed flight condition (|i Control for Performance Gain 0.15= , C-r/ 0.16a= presentee )ar d first. Input harmon- For this pan of the study, the rotor shaft torque is the componentP 6 d an P e used5 ar se P th ;ic 4 so t fro P m2 controlled parameter cruise Th . e speed flight conditios ni are found to de-stabilized the closed-loop operation at this considered (|i = 0.3, CT/a = 0.13). The controller em- flight condition. The controller reduces the stall index ploy multi-harmonia s c input includincomP 6 o -t P g2 by 17 percent, with a control amplitude (root-mean- ponents e controlleTh . r reduce shafe th s t torqu5 y eb square value) of 0.6 deg. The stall behavior for the un- percent. The maximum control authority was roughly controlle controlled dan d case showe sar Figsn ni . 7(a) componentP 4 d an P 3 wit g se de dominanhth 6 0. t (see and 7(b), respectively. Compared to the uncontrolled Table 2, Case 5). The stall index, however, increased by case, the controlled excess lift (stall) region is narrower 1 percent. A comparison of two multi-harmonic wave- in azimuth range, t protrudeye s slightly outboardr Fo . forms — one for stall suppression (Case 2) and one for this flight condition, the stall index reduction is accom- torque reduction (Case 5) — at the same flight condition panied by an 8.5 percent reduction in shaft torque. The is shown in Fig. 11. An explanation for the difference input for stall suppression at this flight condition is in control waveform thas i sr performanc fo t e improve- shown as Case 1 in Table 2. ment e inputh , t requiremen s globali t , encompassing many different phenomena such as retreating blade stall For the cruise speed flight condition (fi = 0.3, CT/cr = and advancing blade compressibility othee th n r handO . , 0.13), the controller uses input harmonics from 2P to the requirement for stall index suppression is local, fo- stale Th l inde. 6P reduces xi ovey db percent5 7 r d an , cusin stalge onlth l n regioretreatinye o th n no g side. the control amplitud onls ei y 0.37 deg. Tabl showe2 s the amplitudes and phases of the blade pitch harmonics Concluding Remarks (Case 2). For the same flight condition, the open loop results shown previously that the same level of stall alle- resulte Th f thiso s investigation demonstrated that stall viation can be achieved with 1.0 deg of 2P input, and yet can be suppressed effectively with higher harmonic con- the shaft torque increases multi-harmonie th r Fo . c case, trol at 'both cruise and high speed flight conditions. The however reductioe th , staln ni accompanies i l 5 0. a y db control amplitude requirement e lesar ss tha deg1 n . percent reduction in shaft torque. With multi-harmonic However, sinc phenomene eth stalf o s onli e l - yon aaf inputs, Fig show8 . s tha reducee tb staln ca ld without fecting rotor performance, stall index suppression, as increasin blade gth eazimute drath n gi h 0 regio30 f no implemented here, does not guarantee a gain in rotor per- (comparg de e Fig wit8 . h Figs. 5(a), (b)). formance.

Effectiveness of the closed loop operation using only 2P speew Inlo d flight, open loop results indicate thae th t is evaluated. The controller converges to a minimum stall index was fairly insensitive to higher harmonic in- stall index usin f controgo 0.8 g 5de l amplitud0 22 t ea put. Althoug reductioe hth staln i n l inde s smalxwa l phasg de e (Tabl reductioe Th , Case2 . stale3) n ni s i l wit closee th h d loop multi-harmonic control sizabla , e simila multi-harmonie th o t r c cases, achievin per4 7 g-a gain in rotor performance was achieved. cent reduction in stall index. As in the open loop results, the 2P input increases the rotor shaft torque by 2.3 The blade pitch schedule that improved rotor performance percent r stalFo l. suppression, multi-harmonic inputs was different from the one that suppressed stall for the are more efficient than 2P input in terms of control am- cruise speed flight condition. Rotor performance im- plitude requirement. Furthermore, the multi-harmonic provement can be achieved, in fact, with a small degrada- input incur performanco sn e penalty. tion in stall behavior.

Closed-loop control with multi-harmonic inpu s alsi t o References effectiv hige th ht a espee d condition (|i= 0.35, C-p/o= 0.12). Since the system exhibits moderately nonlinear 1. Gessow, A. and Myers, C. Aerodynamics of the behaviors, this is the only flight condition that requires Helicopter. Frederick Ungar, New York, NY, 1981. transfer matrix updating e stalTh ^l inde reduces xi d by 2. McCroskey, W. J., "Some Current Research in Unsteady percen5 7 controf o g t usinde l 8 amplitudg0. e (see Table Fluid Dynamics," Journal f Fluido Engineering, Vol, 99 . 2, Case 4). Figures 9(a) and 9(b) show the stall behavior Mar 1977. for the uncontrolled and controlled cases, respectively. . Jacklin3 , NguyenS. , , K., Blaas, A., Richter , "FulP. , l Scale Wind tunnel TesHelicoptea f o t r Individual Blade All the stall areas, except for the one at the advancing Control System," Proceeding 50te th h f so Annua l Forum blad regionp eti suppressede ar , blade Th .e drag plotf so of the American Helicopter Society, Washington DC, 14. Johnson, W.ComprehensivA " , e Analytical Modef o l May 1994. Rotorcraft Aerodynamics and Dynamics, Part I: 4. Stewart, W., "Second Harmonic Control on the Helicopter Analysi d Development,an s " NASA TM-81182n Ju , Rotor," Aeronautical Research Council, Reports and 1980. Memoranda Number 2997 1952g Au . . 15. Dennis, J. E., Jr. and Schnabel. R. B. Numerical Method . Payne, 5 "HigheR. . P , r Harmonic Rotor Control," Aircraft for Unconstrained Optimization and Nonlinear Engineering, Vol , (354) 195830 g . Au , . Equations. Prentice Hall, Englewood Cliffs , 1983NJ , . 6. Arcidiacono , "TheoreticaJ. . P , l Performancf o e . Nguyend Chopra16 an . K , , I., "Applicatio f Higheo n r Helicopters Having Secon d Highean d r Harmonic Harmonic Control to Rotors Operating at High Speed Feathering Control," Journal Americane th f o Helicopter and Thrust," Journal of the American Helicopter Society, Vol. 6, (2), Apr 1961. Society, Vol. 35, (3), Jul 1990. d Wernickean . Drees. 7 M Experimentan . . K.J R ,"A , l . Nguyen Choprad 17 an . K , , I., "Effect f Higheo s r Harmonic Investigation of a Second Harmonic Feathering Device Contro n Rotoo l r Performanc d Controan e l Loads," on the UH-IA Helicopter," U.S. Army Transportation Journal of Aircraft, Vol. 29, (3), May-Jun 1992. Research Command, TR-62-109, Fort Eustis, VA, Jun 1963. Table 1. Blade Properties . Kretz8 , M., "Active Eliminatin f Stalo g l Conditions," Proceedings of the 37th Annual Forum of the American Number of blades 4 Helicopter Society 1981y Orleansw Ma Ne ., LA , Radius t f , 16.11 . 9 Kretz, M., "Active Expansio f Helicopteo n r Flight Tip speed, ft/sec 715 Envelope," Proceedings of the Fifteenth European Tip Mach number 0.6334 Rotorcraft and Powered Lift Aircraft Forum, Amsterdam, Chord n i , 10.63 Netherlandse Th 1989p Se , . 10. Ham, N. and Quackenbush, T., "A Simple System for Solidity ratio 0.0701 Helicopter Individual-Blade-Control and Its Application Root cut-out, ft 3.7 to Stall Flutter Suppression," Proceedings of the Seventh Linear twist -10 European Rotorcraf d Powerean t d Lift Aircraft Forum, Precone, deg 2.5 Garmish-Partenkirchen, Germany p 1981Se , . Lock number 5.40 11. Ham, N., "Helicopter Stall Alleviation Using Individual- Blade-Control," Proceeding e Tentth f ho s European Airfoil HH-10 Rotorcraft and Powered Lift Aircraft Forum, The Hague, Computed blade frequencies The Netherlands, Aug 1984. (425 rpm revr pe ,) 12. Chopra, I. and Gunjit, S. B., "University of Maryland Firs g la t 0.71 Advanced Rotor Code: UMARC," Proceedings of the First flap 1.125 Aeromechanics Specialists Conference n FranciscoSa , , CA1994n Ja , . First torsion 3.68 13. Leishman, J. G., and Beddoes, T. S., "A Semi-Empirical Secon g dla 4.53 Mode r Dynamifo l c Stall," Journale Americanth f o Second flap 2.82 Helicopter Society, Vol. 34, (3), Jul 1989. Third flap______5.10

Table 2. Closed-Loop Results

Cases Flight A2;2 AS; 03 A4;04 AS; 05 A6:06 AStall AShaft Condition (deg) (deg) (deg) (deg) (deg) Index (%) Torque(%) 1 Low Speed .10; -13 .372 11 ; .98; -99 -17 -8.5 2 Cruise .12; -140 .08; 77 .05; -143 .115 3 ; .325 12 ; -75 -0.5 3 Cruise .85; -140 -74 2.3 4 High Speed .267 11 ; .30; 1 .05; 180 .474 -2 ; .515 12 ; -75 -6 5 Cruise .04; -56 .23; 132 .39; 31 .09; 32 .13; 13 1 -5 O«J

50 -A

i f \ ' N40,. r \ : t

V 1 S £ 30 \ : / V ; J = ^ Uncontrolled ,

05 20 _...... -r - —• ' ' • »'• ...... /... .-. \ I / \ \ /* 10 y~ ^- ,., _^ -^i

, , , , 0, . , ..... I ...... i 0 27 0 18 0 9 360 1 2 2P Phaseg de , 2P Amplitude, deg

Fig. 1. Variation of stall index with 2P phase angle, 1 Fig. 3. Variation of stall index with 2P amplitude at deg amplitude (ji= 0.3, CT/d =0.13). . 24phasg 0.30= de e,(n CT/ a0.13)= .

§ ^_ -^

X „ 0.62- y. i . ^ ... .. - — o- " .

3-0.615 _ / : i>• c ' Uncontrolled a> \ = 0.05- S 0.61 0 r > \ - DC \

% 0.605 a 'F -^

O 0.7 Z 0.6 .....I..,,...... 0.8 90 180 270 360 0.9 2P Phase, deg 360 t r/R Fig . Variatio4 . f shafno t torque wit phasP h2 e angle, 1 deg amplitude (ji= 0.3, Gr/a = 0.13). (b) (a)

0.9 360 1 r/R

Fig . Evolutio2 . stalf o n l over rotor disk uncon) (a , - pig 5< Evolution of blade d over rotor disk uncon. amplitudg de 1 t a eg (|ade =trolled 0 phas P 2 24 ) f eo (b , trolle d fu3 Or/ =0 a013= ) ' ' 0.3, CT /0.13)a= . (b) x 10

1 2 2P Amplitude, deg Azimuthg ,de Fig. 6(b). Variatio f stalno l index wit amplitudP 2 h e at 330 deg phase (\i= 0.15, CT/a = 0.16).

x 10

§0.005-

270

360 1 Azimuth, deg

07 0.8 Fig. 5(cont.). Evolution of blade drag over rotor disk: 0.9 (b) minimum stall (2P phase 240 deg), (c) minimum 360 1 r/R torque (2P phase 60 deg) (|i= 0.3, CT/CT = 0.13). (b) 9 (a)

^A~ -i-— A 0.015^ ^ \ / ^ ' .. ^.-...... « 0.01- \ >f c / Uncontn lied •>\ Ui •o 1 _c r \ §0.005- / \ c . 55 7,i- "*•• ...... 4\ °> 0

6 iiii. -...,. - 0 36 0 27 0 18 0 9 0 2P Phaseg de , Azimuth, Fig. 6(a). Variation of stall index with 2P phase an- Fig. 7. Evolution of stall over rotor disk: (a) uncon- amplitudg glede 1 , e (n= 0.15, CT/O 0.16)= . trolled, (b) multi-harmonic control (n= 0.15, Gr/a = 0.16). 90

Azimuth, deg

Fig. 8. Evolution of blade drag over rotor disk with (b) multi-harmonic control (|J= 0.3, Gr/ 0.13)a= .

Fig. Evolutio10 . f bladno e drag over rotor disk) (a : uncontrolledj(b) multi-harmonic control (|i= 0.35, Cj/O

(b) = 0.12).

-0.4

360 1 - -• StalStalll buppressioSuppression \, Azimuthg de , - Torque Reduction . I _

-0.8 180 270 Fig . Evolutio9 . f stalo n l over rotor disk ) uncon(a , - Azimuthg ,de trolled, (b) multi-harmonic control (n= 0.35, C-r/a - Fig. 11. Comparison of HHC schedules for stall sup- O.I 2). pression and for torque reduction, (ji= 0.3, Gr/C = 0.13).