Calculations of pitch-link loads in deep stall using state-of-the-art

CALCCLATION OF PITCH-LINK LOADS IX DEEP STALL USING STATE-OF-THE-ART METHODOLOGY

JingG. YenandMithatYuce Bell Helicopter Textron, Inc. Fort Worth, Texas U.S.A.

Abstract

Pitch-link loads for bearingless rotors in deep stall are calculated using a unified state-of-the-art methodology. The methodology includes a modern free wake model for blade-vortex interaction, ad-vanced unsteady-aerodynamic and dynamic-stall models, and a state-of-the-art rotor dynamics mod-eling for redundant load paths on bearingless ro-tors. Validation of the methodology is briefly discussed. Correlations of theory with measured pitch-link loads are presented. The measured data are from wind tunnel tests of two 1/5 Mach-scaled rotor models with the same bearing less hub but with blades having different torsional rigid-ities, and from flight tests of three full-scale bearing less rotors with different torsional fre-quencies and solidities. Data are presented as functions of advance ratios and rotor thrust coef-ficients, and also in time-history waveforms. Effects of blade-vortex interaction, blade torsional stiffness, unsteady aerodynamics, and solidity on pitch-link loads in deep stall are discussed. Notation

c thrust-weighted chord, ft

cd

drag coefficient

Ce lift coefficient Cm moment coefficient

CT rotor thrust coefficient, T/[nR2 p (RQ)2] K reduced frequency of airfoil oscillation M Mach number

N number of blades R rotor radius, ft T rotor thrust, lb V airspeed, ftisec a angle of attack, deg J1 advance ratio, V/RQ p air density, slug/ft3 a rotor solidity, Nc/nR

'¥ blade azimuth, deg

n

rotor speed, rad!sec

w oscillating frequency, rad!sec

Wn first torsion natural frequency, per rev

Introduction

A reliable prediction of amplitude and waveform of pitch-link loads at high advance ratios and high

load factors has been a challenge for dynamics en-gineers. It is a well-known fact that proper repre-sentation of blade torsional rigidity and control system stiffness is important in such predictions. They directly affect the rotor torsional natural frequency and, hence, the pitch-link-load wave-form, particularly in deep stall. High pitch-link loads in deep stall result from an aeroelastic, self-excited, blade pitching motion precipitated by repeated submersion of a large portion of the blade into and out of stall. This phenomenon is the classical stall flutter. In addition to an accurate rotor dynamics representation, a reliable pre-diction of stall flutter depends on adequate modeling of wake-induced inflows and dynamic stall effects. A detailed investigation of these effects was conducted by Tarzanin (Ref 1). Based on analytical investigation and limited correla-tion, Tarzanin concluded that the magnitudes of pitch-link loads resulting from stall flutter were a function of torsional natural frequency, that inclusions of wake-induced inflows were essential to a better prediction of pitch-link-load magni-tudes, and that the dynamic-stall delay was the fundamental source of stall flutter.

Significant progress has been made in recent years in the development of free wake models to account for wake-induced inflow due to blade-vortex interaction (Refs 2 and 3). Extensive work has also been done on the correlation of theoretical blade-vortex interaction air loads with measured airloads (e.g., Refs 4, 5, and 6). The results are encouraging.

Classical unsteady-aerodynamic and dynamic-stall theories were developed in the early 1970s (Refs 1, 7, and 8) and have been used routinely at Bell. Gangwani developed an empirical model for dynamic stall (Ref9) which he used for a limited correlation with flight test rotor loads (Ref 10). A semi-empirical dynamic stall model developed by ON ERA (Ref 11) was used to make a correlation with flight test blade loads obtained from an Aerospatiale Gazelle SA 349/2 helicopter (Ref 12). As reported in Ref 12, the predicted time history of the pitch-link loads was poor and the most dis-crepancy was found in the retreating blade. A

more recent formulation of semi-empirical unsteady-aerodynamic and dynamic-stall

modeling using the indicia! method was developed by Leishman and Beddoes (Refs 13 and 14). Com-parisons of the theory with two-dimensional oscil-lating airfoil data on section lift force, pressure drag, and pitching moment hysteresis in deep dynamic stall showed good agreement. However, no rotor loads data have been found in the litera-ture using the Leishman!Beddoes dynamic-stall modeling.

Bell Helicopter Textron, Inc. has been developing COPTER, a second-generation global rotorcraft flight-simulation program (Ref 15), since 1979. COPTER (COmprehensive ,Erogram for Theoret-ical ~valuation of.!l,otorcraft) was developed from C81 (Ref16) by restructuring and modularizing. As did C81, COPTER analysis capabilities include rotor loads, forward flight performance, handling qualities, vibration, and aeroelastic stability. Drees inflow model (Ref 17) and BUNS unsteady aerodynamics (lift from Ref 1, drag from Ref7, and moment from RefS) were used successfully in C81 and are also available in COPTER. New tech-nology modules recently implemented in COPTER include the Johnson free wake model (Ref3) and Leishman unsteady aerodynamics (Ref 13). The rotor dynamics are represented by 20 elastic modes obtained from Myklestad analysis (Ref 18). The redundant load path of a bearing less hub is properly treated in the Myklestad analysis. This paper presents correlations of pitch-link loads for bearing less rotors in deep stall using COPTER with state-of-the-art methodology. The measured data were obtained from wind tunnel tests of two bearingless rotor models as well as flight tests of three full-scale bearingless rotors with different torsional frequencies and solidity. The present paper complements the previous work by Tarzanin (Ref 1) in that the effect of blade-vortex interaction on pitch-link loads in deep stall is re-examined using a modern free wake model, that the effect of rotor torsional frequency on the magnitude of stall-flutter pitch-link loads is reviewed, and that the effect of the dynamic-stall model of Leishman is compared with that of BUNS on pitch-link-load waveforms.

Validation of"Methodology

The unified state-of-the-art methodology avail-able in COPTER for rotor loads analysis includes the Johnson free wake model (Ref 3), BUNS (Refs 1, 7, and 8) and Leishman (Ref 13) unsteady aerodynamics models, and Myklestad rotor

dynamics analysis (Ref 18). Before the correlation of pitch-link loads in deep stall is presented, a brief discussion of the methodology is given.

Air loads Correlations

An experiment was conducted using a pressure-instrumented rotor in conjunction with a laser velocimeter system to measure air loads and rotor wake structure at high advance ratios (Ref 19). The model was a 1/5 Mach scale of the Bell Ad-vanced Light Rotor (ALR), a four-bladed bearing-less soft-in-plane rotor. The model was tested at the NASA Langley 14- by 22-ft subsonic wind tunnel in May 1989. Ninety-two pressure trans-ducers were installed on two opposite blades at five span wise locations: 0.69R, 0.73R, 0.81R, 0.87R, and 0.96R. The experimental vibratory airloads were obtained by integrating the individual pressures.

The measured blade sectional normal forces at 0.96R were compared with predictions using the Johnson free wake model in the COPTER rotor loads analysis. The free wake option used in this paper consisted of two circulation peaks, first-order lifting line theory, and 0.04R vortex core size. Results are shown in Figs l(a) and l(b) for

~ = 0.20, CTia = 0.117 and 11 = 0.37,

CTia = 0.085, respectively. The rotor thrust

coefficient, CTia, for the ALR at 1 g thrust is 0.055. At 11

=

0.20, the measured data show a vortex

interaction on the retreating side. At~ = 0.37, the lift at the advancing blade tip becomes negative to maintain a roll-moment trim. The COPTER predictions with the free wake model follow the same trend as the experimental data. Correlation of blade aerodynamic pitching mo-ments about the quarter-chord at 0.87R is shown in Fig 2. The theory was based on the Johnson free wake model and BUNS unsteady aerodynam-ics. At~= 0.20, CT!a

=

0.117, both the measured data and the theory show an on-set dynamic stall near an azimuth of240°. At~ = 0.37, CT/a

=

0.085, a strong retreating blade stall is predicted by the theory. A much milder stall, however, is shown by the measured data. As depicted, the lev-el of corrlev-elation for the pitching moment is not as good as that for the normal force. Further study of the effect of aerodynamic pitching moment on pitch-link loads in deep stall revealed that anini-tial nose-down disturbance in the pitching mo-ment due to stall is essential for the pitch-link-loads response on the retreating blade side and that a major portion of the pitch-link-loads wave-form is dominated by the blade yoke torsional stiffness and tennis racket moment. Hence, the less-than-desired correlation level in aerodynamic pitching moment depicted in Fig 2 does not signifi-cantly degrade the pitch-link-loads prediction. This is evident from the loads correlations shown later in this paper.

--Test -- - - Free wake (a) u = 0.20 15 10

"

_"

···.

7

-.,..._

_V"\

_..

_.

_/

v

""'

--;

\

•

..

\

·

...

/

0 -5 10t---r-~---+---+--~---r---r--4-~ -5~_.--~~--~--~~--~~b-~ 0 40 80 120 160 200 240 280 320 360 Azimuth (deg)

Fig. 1. Correlation of measured air loads at 0.96R on pressure-instrumented rotor with theory using free wake.

U nsteadv Aerodynamics

fhe BUNS unsteady aerodynamics was imple-mented in C81 in the early 1970s and has been used extensively at Bell for rotor loads analysis. The theoretical formulations for lift, drag, and moment coefficients of BUNS were obtained from Refs 1, 7, and 8, respectively. Correlations of the theories with two-dimensional oscillating airfoil data were good, according to these references. The aerodynamic forces al'ld moments calculated

using the Leishman unsteady aerodynamics mo-del were compared with McCroskey's two-dimen-sional airfoil data (Ref20) for a NACA 0012 airfoil at a Mach number of0.3 and a reduced frequency ofO.l. The McCroskey oscillating airfoil was con-strained to oscillate in such a way that a 10° sin-usoidal motion was superimposed on a 10° mean angle of attack. Results of the comparison are shown in Fig 3. Good correlation is evident.

--Test - - - - Free wake (a) u = 0.20 Crlcr=0.117 (b) u = 0.37 c,Ja = 0.085 1: ~ E ·._.,., 0 -1 t+---t--+--~t....,--t---t---t---t+---'+c---1 E

"•i

...

··· .. ·

...

C> I • c !

:s -

2 r---r--+---+----t---t--~---+t-:----t----1 B

!

..

~

I _g -3

r--1----+-+---t

!,

--+--+---t----i----1

v ,g: ~-4~~--~~--~~--~~--~~ 0 40 80 120 160 200 240 280 320 360 Azimuth (deg)

Fig. 2. Correlation of measured pitching mo-ments at 0.87R on pressure-instru-mented rotor with theory using free wake.

Bearingless Rotor Dynamics

The ability of the Myklestad analysis (Ref 18) to model a bearingless rotor is demonstrated by the frequency correlation shown in Fig 4. The bear-ing less rotor used for the demonstration is the Bell ALR (Ref21). Results show good correlation in frequencies up to 7/rev, including that of the first torsion mode.

Model Rotor Correlation

A 1/5 Mach-scaled baseline ALR was tested for high advance ratios and high thrust levels in the 8.5- by 12-ft low-speed wind tunnel of McDonnell Douglas Aircraft Corporation (MCAIR) in N ovem-ber 1988.

To evaluate the effect of blade torsional stiffness on pitch-link loads, a 1/5 Mach-scaled torsionally stiff rotor was designed, fabricated, and tested in

2 1.5 0.5 0 -0.5 0.6 0.4 c, 0.2 0.0 -0.2 0.1 0.0 -0.1 Cm -0.2 -0.3 -0.4 -5

v::

v

~

k

_"

a= 10°+ 10°sinwt •••• Test --Leishman $

0

v

•

~

~

/l

<i~"/

~

,-(8, ...

-.

_•

---.:

~

\'

~

0 5 10 15 20 25 Alpha (deg)

Fig. 3. Correlation ofNACA 0012 forces and moments data during strong dynamic stall with theory using Leishman for M = 0.302 and K = 0.0963.

the MCAIR wind tunnel in August 1989. The torsionally stiff rotor blades were designed to match the beam wise and chord wise stiffness and inertial properties of the baseline blades but have

Predicted 0

•

+ Measured • Out-of-plane • In-plane • Torsion 2800

.--~::;::==~=::;=::;:;=;:~

7/rev / + + /

I+ •;

J

+ + I _a~ 2400 + + I

I

a

.-/a o

I 2000

f---t----17:

i...;~"-.--J'-1---,1

5/rev

of

~I

/ / '

!

o.;/ /

/

1600

f---t--t---1--f--,1---h-'-~-I

//

v~

.

;/"e •

~

I t I

;f"

1200 l---tl-_,f-+_,-t

₀

-~·+--+-.-.-.--,.! 3/rev

I 1

·v

~

V+ • _r

~;.·

_/ /

/ i /

0....::___

// /

v:':

a a 800

1!/

~·q

400 1---11-;~+_._."--t---+-=.-1

_11;//

_I

_{.,..,...,.,...}

1/rev

~

/'" • 1J, ..il-T)...-!1'

-t •

r' · •

1!..~--~--.., 0~~~----~----~--~ 0 100 200 300 400 Ro<or speed (rpm)

Fig. 4. Correlation of analytical and mea-sured ALR cyclic mode frequencies. four times the torsional stiffness. The pitch-link static stiffness was measured. Frequencies of the first three cyclic modes and the first torsion mode of the torsionally stiff rotor are compared with those of the baseline rotor in Table l.

Analytical investigations of the effects of blade-vortex interaction, torsional stiffness, and Leish-man unsteady aerodynamics on pitch-link-load predictions in deep stall were conducted using the loads data measured on these two model rotors. The results are discussed below.

Effect of Blade-Vortex Interaction on Pitch-Link Loads

Both Johnson's free wake and Drees inflow models were used to compute oscillatory pitch-link loads for the baseline rotor. BUNS unsteady aerody-namics was used in both cases. The resulting loads are shown in Fig 5 as functions of rotor thrust coefficient for~= 0.25, 0.35, and 0.39. The measured loads are shown for comparison. The plots indicate that trends manifested by the free

TABLE 1. ROTOR CYCLIC MODE FRE-QUENCIES (PER REV)

Mode 1st in-plane 1st out-of-plane 2nd out-of-plane 1st torsion Mode 1st in-plane 1st out-of-plane 2nd out-of-plane 1st torsion 115 Mach-Scaled ALR Baseline 0.60 1.03 2.59 3.21 Torsionally Stiff 0.61 1.03 2.58 4.88 Full-Scale ALR 680 4BW 0.68 0.71 0.73 1.02 1.02 1.02 2.49 2.45 2.48 3.29 5.14 3.35

wake data correlate better than those by the Drees inflow data. The benefit of using the free wake model is particularly appreciated in deep stall, i.e., at higher ll and Cyla combinations.

Correlations of measured and computed pitch-link-load waveforms are shown in Fig 6 for the same advance ratios as Fig 5 and at the maximum

Cy/o values obtained by the analysis. The

theo-retical loads were calculated using the free wake model. Good agreement between the measured and theoretical data is evident.

Figs 7 and 8 show the same correlations for the torsionally stiff blades as Figs 5 and 6 do for the baseline blades. The plots for the torsionally stiff blades indicate that pitch-link-loads prediction

with the free wake model correlates better with the test data than the Drees inflow model (Fig 7) and that correlation of the waveform (Fig 8) is not as good as that for the baseline rotor.

As shown in Figs 5 and 7, there is a distinct dif-ference in trends between the results of the Johnson free wake model and the Drees inflow model. A close examination of the analytical data revealed that the influence of the blade-vortex interaction captured only by the free wake model was responsible for the better correlation results. Shown in Fig 9 are time histories of the induced velocity as computed by the Johnson free wake model for ll

=

0.35, Cy/a

=

0.11 at 0.75R, 0.83R, 0.87R, 0.91R, and 0.95R on the torsionally stiff blades. Strong blade-vortex interaction is seen at all these blade stations. The angle of attack at each of these stations is depicted in Fig 10. :"iotice

that the whole outboard region of the blade stalls simultaneously when the blade is near 270° az-imuth and that the dynamic-stall delay boundary (rate of change of the angle of attack equals zero) is found at 275° azimuth for the outboard 20% radius. The simultaneous stall and dynamic-stall delay were caused by the blade-vortex interaction (Fig 9). This simultaneous stall over the portion of the blade carrying the large air loading accounts for the initial nose-down stall spike in the pitch-link-load waveform (Fig 8). The negative pitch damping and elastic blade twist lead to the sub-sequent stall flutter spikes until angles of attack insufficient for stall are obtained and positive damping takes over.

Effect of Blade Torsional Stiffness on Pitch-Link Loads

As discussed earlier in this paper, the blade tor-sional stiffness of the tortor-sionally stiff rotor was four times that of the baseline rotor. The result-ing first-torsion frequencies are 4.88/rev and 3.21/rev, respectively, as shown in Table 1. Measmed pitch-link loads for the torsionally stiff and baseline rotors are shown in Fig 11 for

comparison. Notice that there is no significant difference in pitch-link loads due to blade tor-sional stiffness. Computed pitch-link loads for both rotors are shown in Fig 12. Again, the difference in blade torsional stiffness has no significant effect on the loads.

The effect of blade torsional stiffness on pitch-link loads was further studied using a simple analyti-cal model. This model included the following:

1. The blade aerodynamic loading was initiated by a step input in Cm of -0.1 on the outboard 40% radius between azimuth angles of 265° and 30°. This is depicted in Fig 13.

2. The blade dynamics was represented by the first torsion mode. A zero modal damping was assumed where the negative pitching moment was applied. A modal damping of 20% was used where the pitching moment became zero.

Three rotors with different blade torsional stiff-nesses were used for this study. The frequencies of the first torsion mode were 3.35/rev, 4.7/rev, and 6.7/rev. In a forward flight condition, an aerody-namic impulse pitching moment was computed using the step Cm input (Fig 13). Computed pitch-link-load responses of the three rotors to the same aerodynamic impulse pitching moment excitation are shown in Fig 13. Fig 14 shows the harmonic decomposition of the three pitch-link-load

0 Measured

- Theory, free wake/BUNS

- ~ ~ Theory, Drees inflow/BUNS

50 (a) \1 = o 25

g

"0 40

"'

.!l

""

30

Jf

.<:

·~

20

"'

-g ,£! 10 ·o ~ 0

1

0 ~

~-"'

0 - J).o -«>

---0 50 (b) \1 = 0.35

~

"0 40

"'

.!l 0

_•

""

30 ~ J: _v

·i

20 ~ 0 ~ 10 ,£! ·o ~ 0

'

lc

I I I

f

I

"

-~

_...-0 50 (c) \1=0.39

g

"0 40

"'

.!l

""

30 ~ .<: v

·a

20

"'

-g

~

10 ~ 0 0

,;.

~

I

'

I 0

I

,

_..~

0..-; ~-~ 0 0 0.025 0.05 0.075 0.1 0.125 0.15 c,la

Fig. 5. Correlation of measured and theoret· ical pitch-link loads for model ALR: baseline blades.

waveforms. Reviewing tiie data in Figs 13 and 14 leads to the following observations:

1. A nose-down aerodynamic impulse pitching moment resulting from retreating blade simultaneous stall with zero damping pro-duces stall-flutter characteristics.

2. An aerodynamic impulse loading is sufficient to excite all harmonics.

tv\AAAA Measured

Theory, free wake I BUNS

20 (a) jl- 0 25 -

.

c,Ja-o

-

.

115 10 0 -10

g

"0 -20

"'

.!l

""

-30 :E

J"

_"

"

....

f\.

A

'

k I~

'

J: -40 v

'"

a. _-50

),

J"' -60 -70 -80 20 (b) \1 = 0 35 c,io=011 10 0 :;;; -10

""

"0 -20

"'

.!l

""

-30 ~ _-40 .c _v

·"

..

-50 -60

""

'

-"'

:\

~

_:\..

\

'

/\,

I\

-'~

\

~~

"!

\. -70 -80 20 (C)jl-039 -

.

C/o-01 T - , 10 0

I

:;;; -10

""

..,

-20

"'

.!l

\1

I

_\

"'

""

-30 ~ J: _v -40

·"

..

-50 -60

I\_

_,\.

'

-'

!J/

"

~

v

I

-70 -80 0 90 180 270 360 Azimuth (deg)

Fig. 6. Correlation of measured and theoret-ical pitch·link-load waveforms for model ALR: baseline blades.

0 Measured

- - Theory, free wake/BUNS - - - Theory, Drees inflow/BUNS (a) )l-025 -

.

50 :0 0

"'

"

~ 40 .52

"'

co ~ 30 _lo .c _v ~ ·a 20

"'

5 ~ ~ 10 ·o _~ 0

I '

7 0 '

/

c- .. _' ~

~--...

0 (b) )! = 0.35 50 ~

r,.,oo

.,

40 ~ .52

""'

30 ~ .c v

·"'

0. 20

"'

5

~;

J

I I 0 _/ J ~ .!2 10 '5 '

...

~ 0 0 (<) )! = 0.39 50 :0

"'

,

40 ~ .52

""

~ 30 .c .~ 20 0. / ' 0

l~-c

f I

"'

-£ .!2 10 :0 _~ 0

/

N - I ' V,;-" l'"'e----0 0 0.025 0.05 0.075 0.1 0.125 0.15 CT/0

Fig. 7. Correlation of measured and theoret-ical pitch-link loads for model ALR: torsionally stiff blades.

3. The magnitude of the higher harmonic (3 and above) components depends on the frequency of the torsion mode.

4. With the same aerodynamic excitation, the effect of blade torsional stiffness on overall pitch-link-load response is insignificant.

~Measured

- - Theory, free wake/BUNS (a) )l-025 - . CT/o-o 115 -

.

20 10 0

g

-10

.,

-20 ~

"'

-30 :§ J: _v -40

·"'

0.. -50

(l

_it;

1\

·;

rv

\

lA

'

\

1/

\"

\

...A

'

_'

'

'-_f.-

_'

(\

....

1\

_'

'

'

•

_I

'

p

v

v

-60 -70 -80 20 (b))l-035 -

.

C/o-011 T - • ~ 10 0 -10

g

f\

_\

\\

loo.

lA

"

"'

"'

,

-20 ~ .52 -30

""

~ _-40 .c _v

·"'

0.. _-50

1\

In

_f

'

~

i

'

J\~

-60

t

.~ -70 -80 20 (<) )!--0 39

.

10 0 -10

~

,

-20 ~ -30

"'

c

"'

_J: -40 v

·"

..

-50

!\

~

~

_\

_~

!\\

I

1\

"U .\

_'

_'

~

_I

v

-60 -70 -80 0 90 180 270 360 Azimuth (deg)

Fig. 8. Correlation of measured and theoret-ical pitch-link-load waveforms for model ALR: torsionally stiff blades.

v ~ 150

i

100 .~ 50 v .2 !!: 0

3

,

-50 ] -100

~.

~

_""'

~

_c::Y

0 90 ---0.95 R - - - 0.91 R - · - 0.87 R ----0.83 R --0.75 R f', ,/···· ···.,

_iA.,

•' •,

~

~

_f\'\,

)

v

\

7

180 270 360 450 Azimuth (deg)

Fig. 9. Prediction of induced velocity for model ALR: torsionally stiff blades, ll

=

0.35, CT/ a

=

0.11.

g

50 -g 40 .2 "' 30 .s ]; 20 ~

·a.1o

v 0 0

g

50 -g 40 .2 ""30 ~ ..: 20 ~ ·a. 1 0 v 0 0

g

50 -g 40 .2 ""30 ~ ..: 20 -~ c.1o :;( 0 0 )l = 0.25 ll = 0 35 ll = 0.39 v 0 O.Q25 -+- Baseline

-A-Torsionally stiff

•

_1

l

__,_1

'

_£'/

;I

,,;;

. #"

'

//""'

I~

~I 0.05 0.075 Cr!O

i

l

0.1 0.125 0.15

Fig. 11. Comparison of measured pitch-link loads from baseline and torsionally stiff blades on model ALR.

- - 0 . 7 5 R ---- 0.83 R - · - 0.87 R - - - 0.91 R --- 0.95 R

""

~ 40 :!?. 30

""

u

"'

20 t:

"'

0 10 ('

I

~

b

_-

~~-

'\\!

\_/

r\

I'

....

~

~-

/

..

~ ~ 0

..

-10 0 90 180 270 360 450 Azimuth (deg)

Fig. 10. Prediction of blade angle of attack for model ALR: torsionally stiff blades,

Jl = 0.35, CTI a = 0.11.

g

50 )l = 0 25 "0 40

"'

r--· ' .2

""

30 ~ .r: 20 ~ '

·a.

₁₀ v ~ 0 0

g

50 )l = 0 35 ' "0

.9

40

.

~ 30 .r:. 20 E--· -~ v 10 ~ 0 0

g

50 "0 ..2 40 ~ 30 }. 20 .~ c. 10 :;( 0 0 0 )l = 0 39

i

' " ; 0.025 . 0.05 - + - Baseline - A - Torsionally stiff

i

. '

'

!

.

l .

rJ

I

_....-d"

;::;+- . . t

I.

.~

I .

,...,

/ /

_,...y

0.075 Crla 0.1 · -. 0.125 0.15

Fig. 12. Comparison of computed pitch-link loads from baseline and torsionally stiff blades on model ALR.

ljJ 265' 30' 1:!-_{~ E} 0.05 e!:!. 0 =

-

_;'~'=

~

0 ~ E c -0.05

"'

0'1'0 .E ~ -0.10 '§~

a:

v -0.15 -1000~---trr---·tt--~H----tt+---~ -2000~--~r---4*--~~---r~--+1 -3000~--~----~--~----~----~ 0 0.2 0.4 0.6 0.8 Time {sec) :;;- 2500

"'

,

₁₂₅₀

"'

_g

""

0 :S i:. _v -1250

·"

...

-2500 :;;- 2500

"'

,

₁₂₅₀

"'

_g

""

c 0 ~ -1250

f

_-2500

g

2500 , 1250

.9

~ 0 ~ -1250

...

_{-2500 0} (\

'\

(\ ' \ !\

1/\

A

I\

A

v

v

v

v

v

Wn :::4.7 ~

n

1

IL

IlL

v

v

v

v

v

v

A

~-

VL

II),

/l,

I' v v v v 0.2 0.4 0.6 0.8 Time (sec) Fig. 13. Pitch-link-load response to an aerodynamic impulse pitching moment.

1,000 900 800 700

@

600

,

.9

...

500 c 7 .c

"

·"

_...

400 300 200 100 0

Overall 1/rev 2/rev 4/rev

Harmonics

mm

Wn :a3.35

~ Wnm4,7

~ Wn=6.7

8/rev

Fig. 14. Harmonic decomposition ofpitch-link-load response to aerodynamic impulse pitching moment.

20 10 0

g

-10 "0 _m -20 .2

"'

-30 :§

1

'\

f,

"

~\

·'

I ff

't,

§

\

'

,;, _-40 v

f

-50

-5

t

IIi -60 -70 -80 0 90

f~

I~

_\.

"-..::

\

t.:.6D.6 Test - - - - Leishman --BUNS ~

..

1

r;,

'

~

180 270 360 450 Azimuth (deg)

Fig. 15. Correlation of measured pitch·link-load waveforms for model ALR with theory using Leishman and BUNS: baseline blades, 11

=

0.39, CTio

=

0.10. Effect of Leishman Unsteady Aerodynamics on Pitch-Link Loads

A brief assessment of the effect of Leishman un-steady aerodynamics on pitch-link loads was made using the 1/5 Mach-scaled ALR wind tunnel data. Shown in Fig 15 are pitch-link-load waveforms for the baseline rotor computed with Leishman un-steady aerodynamics and .Johnson free wake at 11

= 0.39 and CT/cr = 0.10. Also shown are measured and BUNS data for comparison pur-poses. The same comparison is made for the rotor with torsionally stiff blades in Fig 16 for 11 = 0.39 and CT/cr

=

0.10. Based on the limited data in Figs 15 and 16, a slight improvement over BUNS is observed when using Leishman's method. More correlation is needed so that the benefit of using the Leishman unsteady aerodynamics model can be assessed.

Flight Test Correlation

A pitch-link loads analysis using the Johnson free wake model and BU:\'S unsteady aerodynamics was performed for three full-scale bearing less rotors in maneuvering flight. The three rotors are Bell's ALR (Ref21), Model680 (Ref22), and Model 4BW (Ref23). The thrust-weighted chord and solidity of the three rotors are 1.55 ft, 0.0992; 1.14 ft, 0.073; and 1.966 ft, 0.1015, respectively. Rotor

20 10

~

0

g

-10 "0 -20 m

.·1A

\

\

\\

~ .2

"'

-30 ~ ,;, v -40

·"'

..

-50 -60 -70 -80 0 90

J

r\

~

_J

'~ 180 270 Azimuth (deg) D.66t.:. Test - - - - Leishman --BUNS

-'"

~ I

9

I,

,,

360 450

Fig. 16. Correlation of measured pitch-link-load waveforms for model ALR with theory using Leishman and BUNS: torsionally stiff blades, 11 = 0.39, CT/o = 0.10.

frequencies of the first four cyclic modes of the three rotors are tabulated in Table 1.

ALR Pitch-Link Loads

Predicted pitch-link loads using the free wake model and BU;-.iS were correlated with flight test data from the ALR during a symmetric pull-up. Results are shown in Fig 17. The theory cor-relates well in trend and slightly underpredicts the magnitude in high-thrust conditions. 680 Pitch-Link Loads

Predicted pitch-link loads using the free wake model and BUNS were correlated with flight test data from the 680 during a symmetric pull-up. Results are shown in Fig 18. The theory corre-lates well for high thrust conditions and slightly overpredicts the magnitude for lower thrust coeffi-cients.

4BW Pitch-Link Loads

Correlation data for the 4BW in a symmetric pull-up are depicted in Fig 19. The theory correlates well when the rotor is in deep stall. However, it overpredicts at the lower end of the thrust coeffi-cients. A close examination of harmonic content

0 Flight test Free wake/BUNS 1200 1000 ~ 0

..,

"'

800 .2

"'

.5

'

"'

v 600 .1: Q, 2':' 0 400 ~ ,\¥ '0 ~ 0

!j

/

0

/

0 200 0 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 Cr/0

Fig. 17. Correlation of measured and theoret-ical pitch-link loads in symmetric pull-ups: ALR, 11

=

0.28 to 0.31. of the loads data revealed that the discrepancy was largely due to the overprediction of the 1/rev component. The overprediction was partially attributed to the yoke torsional stiffness repre-sentation.

Pitch-Link-Loads Normalization

The measured or predicted pitch-link loads shown in Figs 17, 18, and 19 for the ALR, 680, and 4BW rotors at u " 0.3 have different slopes because the rotors have different solidities and thrust-weighted chords. If the oscillatory pitch-link loads are normalized with respect to solidity and chord-square, the resulting data from the three rotors would fall into a relatively narrow band. Fig 20 shows the measured loads normalized by solidity and chord-square for the three rotors. Notice that the normalized loads have nearly identical slopes, with a slight difference in magnitude. Since the theory correlates well with the measured data (Figs 17, 18, and 19), the characteristics depicted in Fig 20 are also simulated by the analysis.

Cone! us ions

Calculations of pitch-link loads in deep stall were conducted on bearing less rotors using a unified state-of-the-art methodology. The theory was cor-related with data measured on five different rotors. Results presented in this paper reveal the following: 1200 1000

g

.,

"'

800 .2

""

_~ .c 600 l:!

·a

2':'

s

,\¥ 400 '0 ~ 0 200 0 0 Flight test -Free wake/BUNS

~

-~

0 0 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 Crla

Fig. 18. Correlation of measured and theoret-ical pitch-link loads in symmetric pull-ups: 680 rotor, 11 = 0.28 to 0.31. 2800 2400 ;; 2000 .2

"'

~ 1600

~

_c. 2':' 1200

s

.!!! ~ 800 0 400 0 0 Flight test - Free wake/BUNS

8

~

v

/o

/

0

/

0 0 0.025 0.05 O.o75 0.1 0.125 0.15 0.175 Cr/0

Fig. 19. Correlation of measured and theoret-ical pitch-link loads in symmetric pull-ups: 4BW rotor, 11 = 0.29 to 0.31.

1. Strong blade-vortex interaction in deep stall is predicted using the Johnson free wake model.

70 X

.,

..2

40

.,.

:.5 ~ 030

·au

"'

!

20 '5{ 0 10 0 10.

oo

0 0,025 0.05 0.075 0.1 c,ta [ 10. UQ 0 0 ALR 10. 680 0 4BW ::J

c8

r8

b

0.125 0.15 0.175

Fig. 20. Comparison of measured ALR, 680, and 4BW pitch-link loads in symmet-ric pull-ups, normalized hy solidity and chord square: Jl = 0.28 to 0.31. 2. Blade-vortex interaction contributes

significantly to the dynamic stall delay. 3. Both measured data and analytical

predic-tions suggest that the effect of blade torsion-al stiffness, and hence the torsiontorsion-al frequen-cy, on overall pitch-link-load response is insignificant.

4. Both BUNS and Leishman unsteady aero-dynamic models serve well for predictions of pitch-link loads in deep stall.

5. The level of correlation presented in this paper using the COPTER state-of-the-art methodology is encouraging.

References

1. Tarzanin, F. J., Jr., "Prediction of Control Loads Due to Blade Stall," Journal of the

American Helicopter Society, Vol. 17, (2),

April1972.

2. Scully, M.P., Computation of Helicopter

Rotor Wake Geometry and its Influence on Rotor Harmonic Airloads, Massachusetts

Institute ofTechnology, ASRLTR 178-1, :vlar. 1975.

3. ,Johnson, W., Wake Model for Helicopter

Rotors in High Speed Flight, NASA CR

177507, Nov. 1988.

4. Johnson, W., "Calculation of Blade-Vortex Interaction Air loads on Helicopter Rotors,"

Journal of Aircraft, Vol. 26, (5), May 1989.

5. Bousman, W. G., eta!., Correlation of Puma

Airloads ·Lifting-Line and Wake Calcula-tion, NASA TM 102212, Nov. 1989 . 6 .

7.

Bousman, W. G., "The Response of Helicop-ter Rotors to Vibratory Airloads," American Helicopter Society National Specialists' Meeting on Rotorcraft Dynamics, Arlington, TX, Nov. 1989.

Harris, F. D., et al., "Rotor High Speed Per-formance, Theory vs. Test," Journal of the

American Helicopter Society, Vol. 15, (3),

July 1970.

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Stall and Unsteady Airloads for Rotor Blades," Journal of the American Helicopter

Society, Vol27, (4), Oct. 1982.

10. Gangwani, S. T., "Development of an Un-steady Aerodynamics Model to Improve Cor-relation of Computed Blade Stresses with Test Data," 2nd Decennial Specialists' Meet-ing on Rotorcraft Dynamics, NASA Ames, Nov. 1984.

11. Tran, C. T., and Petot, D., "Semi-empirical Model for the Dynamic Stall of Airloads in View of the Applicatio11: to the Calculation of Responses of a Helicopter Blade in Forward Flight," Sixth European Rotorcraft and Pow-ered Lift Aircraft Forum, Bristol, England, Sept. 1980.

12. Gaubert, M., and Yamauchi, G. K., "Predic-tion of SA 349/2 GV Blade Loads in High Speed Flight Using Several Rotor Analysis," American Helicopter Society 43rd Annual National Forum, St. Louis, :\10, May 1987. 13. Leishman, J. G, and Beddoes, T. S., "A

Gen-eralized Model for Airfoil Unsteady Aerody-namic Behavior and DyAerody-namic Stall Using the Indicia! :VIethod," American Helicopter

Society 42nd Annual .\' ational Forum, Wash- 19. Wood, T. L., et al., "An Experimental lnvesti-ington, D. C., June 1986. gation of Rotor Blade Airloads and Wake

Structure at High Advance Ratio," American 14. Leishman, J. G., and Beddoes, T. S., "A Semi- Helicopter Society 46th Annual N a tiona!

Empirical Model for Dynamic Stall," Journal Forum, Washington, D. C., May 1990. of the American Helicopter Society, Vol. 34,

(3),July 1989. 20. McCroskey, W. J., eta!., An Experimental

Study of Dynamics Stall on Advanced Airfoil 15. Corrigan, J. J., et al., "Developments in Sections, Vols 1-3, NASA TM 84245, July

Dynamics Methodology at Bell Helicopter 1982. Textron," American Helicopter Society 44th

Annual National Forum, Washington, D. C., 21. McEntire, K. G., eta!., "Flight Test of an

June 1988. Advanced Rotor System for Future Combat

Helicopter Applications," American Heli-16. Van Gaasbeek, J. R., eta!., Rotorcraft Flight copter Society Specialists' Meeting on Rotary

Simulation, Computer Program C81, Volume Wing Test Technology, Bridgeport, CT, Mar. I- Engineer's Manual, USARTLTR 77-54A, 1988.

1979.

22. Alsmiller, G. R., eta!., "The All-Composite 17. Drees, J. M., "A Theory of Airflow Through Rotorcraft," American Helicopter Society

Rotors and Its Application to Some Helicop- 39th Annual N a tiona! Forum, St. Louis, MO, ter Programs," Journal oft he Helicopter As- May 1983.

sociation of Great Britain, Vol. 3, (2), July

1949. 23. Harse, J. H., "The Four-bladed Main Rotor

System for the AH-1W Helicopter," Amer-18. Schlomach, R. C., and May, J., Rotor Blade ican Helicopter Society 45th Annual

Natural Frequency Analysis for Complex National Forum, Boston, MA, May 1989. Hub Configuration, USAA VSCOM TR

85-D-22, July 1989.