Correlation of SA349/2 helicopter flight test data with a comprehensive rotorcraft model

TWELFTH EUROPEAN ROTORCRAFT FORUM Paper No. 74

CORRELATION OF SA349/2 HELICOPTER FLIGHT TEST DATA WITH A COMPREHENSIVE ROTORCRAFT MODEL

Gloria K. Yamauchi and Ruth M. Heffernan NASA Ames Research Center

Moffett Field, California, U.S.A. and Michel Gaubert Aerospatiale-Division Helicopteres Marignane, France September 22-25, 1986 Garmisch-Partenkirchen Federal Republic of Germany

Deutsche Gesellschaft fur Luft-und Raumfahrt e.V. (DGLR) Godesberger Allee 70, D-5300 Bonn 2, F.R.G.

Abstract

CORRELATION OF SA349/2 HELICOPTER FLIGHT-TEST DATA WITH A COMPREHENSIVE ROTORCRAFT MODEL

Gloria K. Yamauchi and Ruth M. Heffernan NASA Ames Research Center

Moffett Field, California, U.S.A. and

Michel Gaubert

Aerospatiale - Division Helicopteres Marignane, France

A comprehensive rotorcraft analysis model was used to predict blade aerodynamic and structural loads for comparison with flight test data. The data were obtained from an SA349/2 helicopter with an

advanced geometry rotor. Sensitivity of the correlation to wake geom-etry, blade dynamics, and blade aerodynamic effects was investigated. Blade chordwise pressure coefficients were predicted for the blade transonic regimes using the model coupled with two finite-difference codes.

SYMBOLS

e.g. center of gravity

c~ blade section lift coefficient

en blade section normal force coefficient

cP

blade chordwise surface pressure coefficient CT/a ratio of rotor thrust coefficient to solidity r blade radial station

R rotor radius

r₀/c ratio of tip vortex core size to blade chord

a blade angle of attack

a time derivative of blade angle of attack ~ advance ratio

1. INTRODUCTION

~ joint rotorcraft research program has been established between the National ~eronautics and Space ~dministration (N~S~) and the French Ministry of Defense. The purpose of the program is to correlate the N~S~ prediction code Comprehensive ~nalytical Model of Rotorcraft ~era­ dynamics and Dynamics (C~MR~D) with flight test data from the French

S~349/2 Helicopter and an advanced geometry rotor system.

Structural and aerodynamic loads and performance were measured for several thrust levels and advance ratios. From the flight envelope, 16 flight conditions were selected by N~S~ and ~erospatiale for documen-tation. In addition, data from three of these flight conditions were chosen for detailed correlation with C~MR~D. These conditions provided an opportunity to exercise various modeling features within C~MR~D.

The pressure data from this flight test are a valuable addition to the limited data base of helicopter rotor blade pressures in forward flight, especially in the transonic regime. Predictions of shock forma-tions near blade tips using C~MR~D coupled with a finite-difference code have been restricted to comparisons with several model rotor data sets using rigid blades (described in Ref. 1). Chordwise pressure compari-sons presented here aid in further validating the coupling procedure.

The flight test, the comprehensive model, the assumptions and approximations in modeling the aircraft and rotor in C~MR~D, and the resulting theoretical predictions compared with the data are described in this paper. Finally, recommendations for improving the correlation are given.

2. ~IRCR~FT DESCRIPTION

The flight tests were performed on an ~erospatiale Gazelle

S~349/2 helicopter (Fig. 1) dedicated to experimental research. The

S~349/2 belongs to the Gazelle family of helicopters, but differs some-what from the 342 line of aircraft. The S~349/2 includes a comprehen-sive on-board data acquisition system. Table 1 provides general char-acteristics of the helicopter. For this flight test program, the

aircraft was fitted with the ~erospatiale advanced geometry rotor. The rotor includes the classical articulated Non ~rticule en Trainee (N~T) hub (Fig. 2) and three research Grande Vitesse (GV) blades. The N~T hub, which is the standard Gazelle hub, is fully articulated and has a lag damper with nonlinear characteristics (stiffness and damping).

The GV blades were developed to achieve a better understanding of rotor aerodynamics and dynamics. Features of the blades are (Fig. 3)

0~209 advanced airfoils (9% thickness), a removable tip, and an

adjust-able blade section e.g. location. For this flight test, a rectangular tip and a blade e.g. location of 24.7% chord were used. The 0~209 airfoil is discussed in Ref. 2. The twist distribution (Fig. 3b) is

constant at the tip, linear on the main part of the blade, and varies 11.5 degrees from the root to the first airfoiled section.

The tail rotor for the SA349/2 is a Fenestron. The Fenestron is a shrouded 13-bladed rotor with one control input (collective pitch

control).

Detailed technical data on the aircraft and rotors are available from Heffernan and Gaubert, to be published by NASA.

3. FLIGHT TEST INSTRUMENTATION

The rotating frame instrumentation included both blade pressure transducers and strain gages. Strain gages for measuring pitch-link loads and flap and lag angle were also available.

The blade pressure data analyzed in this paper were obtained from 51 pressure transducers distributed between two blades, as shown in Fig. 4. Three groups of 20 chordwise transducers (upper and lower surface) were located at 75%, 88%, and 97% radial stations. The number of functional transducers were 18, 15, and 18 for 75%, 88%, and 97% radial station, respectively.

The blade structural data in this paper were obtained from 15 strain gages, also shown in Fig. 4. The gages (four flap-bending, seven lag-bending, and four torsion gages) are located at eight radial sta-tions on two blades. Data from additional blade strain gage instrumenta-tion installed on these two blades were not recorded because of slip-ring limitations.

Instrumentation in the fixed frame included strain gages on the primary rotor control system servos and main gear box struts. Pilot and copilot seat vertical acceleration were also measured. The following flight condition parameters were recorded: ground pressure and tempera-ture, altitude, velocity, static temperature (in flight), static pres-sure (in flight), collective pitch stick position, lateral and longi-tudinal cyclic pitch stick position, load factor, rotor speed, sideslip angle, aircraft pitch, roll and yaw speed, engine power and fuel

consumption. 4. DATA REDUCTION

A total of 18 consecutive rotor revolutions were required to obtain all of the blade pressure data. Data from each of the three groups of 20 pressure transducers were acquired as time-histories over a period of six consecutive rotor revolutions (starting from 0 degrees azimuth). The pressure signals were digitized at a frequency of

180 samples/rotor revolution. The data were then converted into physi-cal units and transformed into aerodynamic coefficients. The strain gage signals were obtained as harmonic analysis coefficients (10

were acquired during one of the 18 revolutions of pressure data acquisi-tion. The blade strain gage data were next transformed into blade-bending and torsional moments after accounting for the blade weight contribution and flap/lag/torsion interaction components. "igure 5 illustrates the data reduction procedure.

5. "LIGHT CONDITIONS

Various operating conditions were included in the orignal flight test envelope: (1) hover out-of-ground-effect; (2) level flights at 305m, 1524 m, and 3048 m (1000 ft, 5000 ft, and 10000 ft) with speeds from 100 km/hr to 300 km/hr; (3) steady turns at 305 m, 1524 m, and 3048 m (1000 ft, 5000 ft, and 10000 ft) corresponding to a range of load factor from 1.4 to 2.0; (4) autorotation at 200 km/hr; and (5) high speed dive at 350 km/hr.

"rom this flight envelope, 16 flight points were chosen for docu-mentation purposes. The selected points provide a large range of

advance ratios (0.13

<

~

<

0.36) and thrust-to-solidity ratios

(0.062

<

CT/a

<

0.133), as shown in Fig. 6. The data are documented in Heffernan and Gaubert; in addition, further details of the flight test

instrumentation and data reduction process are explained in their report.

6. DESCRIPTION 0" THE COMPREHENSIVE ROTORCRAFT MODEL

CAMRAD is an analysis designed to calculate rotor performance, aerodynamic and structural loads, aircraft vibration and gust response, flight dynamics and handling qualities, and aeroelastic stability. The analysis development is discussed in Refs. 3-5. Summaries of the vari-ous structural and aerodynamic models used in CAMRAD are described in Ref. 6. A general two-rotor aircraft with either articulated, hinge-less, gimballed, or teetering rotors can be modeled using CAMRAD. The rotor structural model is based on engineering beam theory for rotating wings with large pitch and pretwist. The rotor aerodynamic model is based on lifting-line theory, and uses two-dimensional airfoil charac-teristics and a vortex wake. Three levels of aerodynamic analysis exist in CAMRAD: uniform inflow (linear variation of inflow over the rotor disk), nonuniform inflow with prescribed-wake geometry, and nonuniform

inflow with a free-wake geometry. "igure 7 outlines the aircraft trim solution procedure in CAMRAD.

7. APPROACH

The strategy for the correlation effort was to first develop a baseline model of the SA349/2 aircraft and rotor for CAMRAD. Much time and effort was spent obtaining detailed information about the GV blades, NAT hub, and aircraft geometry. Also, definitions, sign conventions, and reference systems for the data and theory were constantly checked for consistency.

Preliminary comparisons of theory with data were then

Per-formed. CAMRAD predictions were performed for seven flight conditions; the flight parameters for these conditions are shown in Table 2.

Detailed results for the first three of the seven conditions will be presented here. These three flight points represent forward flight extremes: low speed, low thrust; high speed, low thrust; and high

speed, high thrust. As a result of the preliminary CAMRAD calculations, several approximations and assumptions about both theory and data were necessary. The results presented in this paper are qualified by the following:

1. Measured mean values of blade loads proved to be unrealistic; therefore, all strain gage time-history data presented in this paper have the mean value removed.

2. Measured blade flap and lag angles are not presented since their accuracy is suspect, especially at high forward speed.

3. Measured lift coefficient is actually the normal force coef-ficient en (the force perpendicular to the chord line). At small blade angle of attack, the difference between C~ and Cn is insignificant. For flight conditions where the blade experiences large angles of inci-dence, the error that is caused by the difference between C~ and en will be a small part of the overall error in predicting C~. Large angles of incidence occur when the blade experiences dynamic stall, and as will be shown, this phenomenon is not well-predicted.

4. Measured blade moment coefficient values are unreliable, probably because of an insufficient number of chordwise pressure mea-surements.

5. The steadiness of Condition 3 data is questionable. tions in the flight parameters were noticed during a period of revolutions of static data acquisition.

Varia-18 rotor

6. Fuselage aerodynamic characteristics used in CAMRAD were obtained from a wind tunnel test of a one-seventh-scale model of the SA349/2 fuselage.

7. The same aircraft e.g. location was used for all flight conditions.

8. CAMRAD normally calculates the blade-bending loads at a given radial station, r, by computing the difference between the total aerody-namic and inertial moments on the blade surface outboard of r. Using this method for the advanced-geometry rotor, the flapwise bending moments were found to be very sensitive to the blade mass distribu-tion. This sensitivity is numerical, not physical. The blade-bending moments were, therefore, calculated directly from the blade curvature and stiffness. This method significantly improved the correlation of the blade loads; however, this method is not accurate where discontinui-ties in the blade stiffness distribution occur because of the modal

structural model in CAMRAD. For the GV blades, jumps in the flapwise and edgewise stiffness occur near the 10% and 90% radial stations. Poor correlation for bending moments near these radial stations is therefore expected.

9. The measured control inputs were used as initial control settings in the free-flight trim analysis in CAMRAD. In the trim itera-tion, the control settings were adjusted until force and moment equilib-rium on the aircraft were achieved. For Condition 3, however, the aircraft was also trimmed to the measured power (descent). When trim-ming Condition 3 to force and moment equilibrium alone (level flight),

the trimmed power level was unrealistically high.

Baseline modeling conditions were next developed for the seven flight conditions. Table 3 provides baseline values used in CAMRAD. Modeling parameters in CAMRAD were then varied to assess the sensitivity on the correlation; these parameters included: number of blade-bending and torsion modes; wake geometry; tip-vortex core size; lifting-surface correction; and blade stall model.

8. RESULTS

8.1 Prediction of control inputs and power required

Figure Sa presents predicted collective pitch as a function of advance ratio. The collective pitch is overpredicted by approximately 3 degrees for all conditions. The nearly constant offset in collective pitch results from a tension-torsion coupling caused by the jump in blade twist at the inboard radial station (Fig. 3b). This steep jump in twist was discovered to be the source of a steady, nose-down blade

pitch. CAMRAD calculates a pitch increment from the tension-torsion coupling associated with the pretwist. A small positive pitch increment results from the negative twist that is inherent over most of the GV blade, and a large negative pitch increment results from the large positive pitch change at the root. The net elastic pitch change is large, negative and occurs at the blade root. The pitch increment is also steady because the change is produced by the centrifugal force. Since the analysis trims the helicopter to equilibrium flight, the primary effect is on the main rotor collective pitch.

This tension-torsion coupling is modeled in CAMRAD using a method that is similar to that of Ref. 7. Reference 8 presents a more general theory to account for this effect. Because of lack of mean torsion moment and pitch-link load data, the predicted elastic pitch increment could not be checked directly. Figure Sa indicates that the magnitude of the elastic pitch increment is overestimated. Increasing the number of elastic torsion modes from one to three, however, reduced the steady, nose-down pitch increment from 4.6 to 3.5 degrees.

Figures 8b and Be present lateral and longitudinal cylcic pitch, respectively, as a function of advance ratio. Except for the low speed

cases of Conditions 1 and 4, cyclic pitch is not accurately predicted with discrepancies typically less than 2 degrees.

The prediction of total power required is shown in Fig. 9a. Condition 3 is not shown since measured power was used to trim the aircraft. Except for Condition 7, predictions for the remaining

condi-tions are within 8% of measured values. Aircraft attitude is also not well-predicted for most of the flight conditions (Fig. 9b), probably because of an inaccurate representation of the fuselage aerodynamics. 8.2 Condition 1: low speed, low thrust(~= 0.14, Cr/a = 0.065

At low forward speed, the rotor wake tends to remain in the vicinity of the blades and strongly influences the blade aerodynamic environment. A detailed wake geometry is needed therefore for good aerodynamic load correlation.

Figure 10 presents C~ as a function of azimuth for r/R = 0.75, 0.88, and 0.97. Uniform inflow is not able to predict the details of the lift variation. The prescribed wake results are better, but still do not predict the details of the distribution. The free-wake geometry, however, is able to predict the trend and magnitude of the lift. At this low speed, the rotor wake is slowly convected away from the rotor allowing time for interaction between the blade and shed tip-vortices. This interaction is evident in figure 10 for r/R = 0.97 on the

retreating side of the rotor disk (note sharp peaks in C~ near

270 degrees azimuth). Figure 11 shows the effect of varying tip-vortex core size on C~. A ratio of core size to blade chord of 0.525 was found to be optimum. The core size used in CAMRAD includes other

effects of blade/vortex interaction which are not modeled by the theory; therefore, the core size in CAMRAD is larger than the physical tip-vortex core size.

For cases where the blade passes close to a tip-vortex (as in Condition 1), lifting-line theory usually cannot predict blade loads accurately, especially at the tip. A lifting-surface solution is required for these cases. CAMRAD uses a correction based on a linear, lifting-surface theory to adjust the solution for the vortex-induced loading on the blade which is calculated by lifting-line theory.

Because of computation time constraints, this correction is only applied when the blade and vortex are a specified distance apart. Figure 12 shows C~ predictions using the lifting-surface theory correction. When using this correction, a more realistic tip-vortex core size is allowed (rc/c = 0.10 was used for this figure). For this flight condi-tion, the calculated correction to lifting-line theory is small. The effect of tip-vortex core size is greater than the effect of the lifting-surface correction on C~.

The flapwise bending moment is well-predicted at the 54% radial station, but not at the 20% and 80% stations (Fig. 13). Although the free-wake geometry results are a significant improvement over the

uniform inflo~ results, the free ~ake provides only a small improvement in the predictions as compared to the prescribed ~ake results. The edge~ise bending moment is predicted both in magnitude and trend for r/R = 0.20, predicted in trend for r/R = 0.54, and not ~ell-predicted for r/R

=

0.80 (Fig. 14). The difference bet~een ~ake geometries

becomes more significant near the blade outboard regions. The torsional moments are not ~ell-predicted for any radial station, as sho~n in

Fig. 15. If the one-half peak-to-peak values for data and theory ~ere compared, ho~ever, the correlation ~auld be quite reasonable. The data

sho~ a 5/rev - 6/rev influence that is not accounted for by the

theory. CAMRAD calculates the first torsion frequency to be 3.9/rev. The predicted pitch-link loads sho~ a large 1/rev influence for both uniform and nonuniform inflo~, ~hereas the data do not (Fig. 16). A possible explanation is the value used for the control system stiff-ness in CAMRAD (a very large value ~as used). A better estimation of the stiffness may improve the correlation.

8.3 Condition 2: high speed, lo~ thrust (~

=

0.36, CT/a

=

0.071) At high for~ard speed, the rotor ~ake is rapidly convected do~n­ stream, and so ~ake effects on blade loading are smaller. Figure 17 sho~s that the nonuniform inflo~ predictions of lift are slightly better than are the uniform inflo~ predictions. Ho~ever, the difference

bet~een the free-~ake and the prescribed-~ake geometry results are insignificant. Henceforth, predictions for this flight condition are based on nonuniform inflo~ ~ith a prescribed ~ake geometry.

The flap~ise bending moments are reasonably ~ell-predicted; better correlation is achieved at the outboard radial stations than at the inboard radial stations (Fig. 18). Using six blade-bending modes provides better predictions at the outboard radial stations than using five blade modes. The difference bet~een using five and six blade modes is significant; however, there is no difference in results from using six, seven, or eight bending modes. The seventh and eighth bending modes are dominated by edgewise motion; therefore the flapwise moment predictions are not affected by these modes. The edgewise moments are not well-predicted on the advancing side of the rotor disk (Fig. 19), probably reflecting compressibility effects for this high-speed case. For the retreating side of the disk, the moments are better predicted at the inboard radial stations. Using five or six blade modes appears to provide the closest correlation. Figure 20 shows that pitch-link loads are badly predicted. Varying the number of blade modes does not improve the correlation.

Reasonable correlation is obtained for torsional moments at 20% and 54% radial stations (Fig. 21). Increasing the number of torsion modes from two to four does not improve the predictions. The 5/rev -6/rev influence present in Condition 1 is absent here.

8.4 CAMRAD/Finite-difference predictions of surface pressures With an advancing tip Mach number of 0.87, chordwise surface pressure data for this flight condition reveal shocks forming near the blade tip. Reference 9 describes a method for predicting transonic flows on rotors in forward flight. The predictions are made via a loose coupling (file transfer) between CAMRAD and a small-disturbance, finite-difference code (FDR). Recently, comparisons were made of results from FDR and several other finite-difference codes coupled with CAMRAD

(Ref. 1). Results obtained by using one of these codes, a full-potential rotor code (FPR), in addition to results from FDR, will be presented here. FPR is described fully in Ref. 10. The code solves a three-dimensional, conservative, full-potential equation to calculate unsteady rotor flows.

As explained in Ref. 9, CAMRAD first computes the blade partial angle of attack for the advancing side of the disk. The

finite-difference code then computes the blade lift (for r/R ~ 0.5) for the advancing side of the disk. This is defined here as the end of the first iteration. The C~'s computed by the finite-difference code are then used by CAMRAD to compute new blade angles, which are used by the finite-difference code to compute a new C~ distribution (end of second iteration). The iteration continues until the difference between the C~ calculated by CAMRAD and the finite-difference code becomes small.

Results from Ref. 1 are for rigid blade motion. As shown in Table 3, five bending modes and four torsion modes were used for the calculations presented here in Figs. 22 to 25. Using four torsion modes reduced the steady twist value (as discussed earlier) and improved the chordwise pressure predictions.

Figures 22 and 23 present lift coefficient predictions for the advancing side of the rotor disk for FPR and FDR, respectively, for Condition 2. The difference between the C~ calculated by CAMRAD and by FPR for iteration 2 is smaller than the difference for iteration 1 (Fig. 22). Similar results are shown in Fig. 23 for FDR. Using the coupling procedure between CAMRAD and FPR (for this flight condition) does not improve the prediction of C~, except perhaps for the second quadrant of the rotor disk for r/R

=

0.97. Figure 23 shows that FDR underpredicts the lift near 0 degrees and near 180 degrees azimuth for all three radial stations. The coupling between CAMRAD and FDR appears to improve the lift prediction only in the 90-degrees-azimuth region of the rotor disk. In general, lifting-line theory does an adequate job of predicting the section lift. The reason for the underprediction of the lift in Figs. 22-23 when using both finite-difference codes is difficult to determine without a tip-path-plane angle-of-attack measurement.

Figures 24 and 25 show chordwise surface pressure coefficient (Cp) predictions for the three radial stations at three azimuth stations for FPR and FDR, respectively.

Condition 2. As shown in Fig.

The pressure predictions 24, the shape of the CP

are again for distribution as

predicted by FPR compares well with the data for all locations; however, the upper surface pressure peak is consistently underpredicted (because the calculated lift is is too low). For the azimuth stations shown, a second iteration between CAMRAD and FPR produced improvements only at ~ = 150 degrees. The predictions of upper surface pressure peaks were improved, but the lower surface peak predictions were degraded at this azimuth. FDR does not predict the Cp distribution shape as well as FPR does (Fig. 25). A second iteration between CAMRAD and FDR improved the correlation slightly. FPR reasonably predicts the shock locations for r/R

=

0.88 and 0.97 at ~

=

150 degrees (Fig. 24b) and c)). FDR, however, does not predict these shock locations (Fig. 25b) and c)).

8.5 Condition 3: high speed, high thrust (~

=

0.34, CT/a

=

0. 125) Although not shown here, there is little difference between the prescribed- and free-wake results for this condition. Since the

prescribed-wake analysis is computationally less expensive than the free-wake analysis, calculations were performed using the prescribed-wake geometry. The high thrust level of this flight condition leads to stall on the retreating side of the rotor disk (especially near the blade inboard region). The rapid blade pitch motion causes a delay in the occurrence of separated flow. Once the blade has reached stall, a vortex is shed from the leading edge resulting in large transient blade loads. Therefore, a dynamic stall model is used in the calculations for this flight condition. Several models of dynamic stall are available in CAMRAD. In the model used here (based on Refs. 11-13), a correction that is proportional to

a

is applied to a before the blade section lift, the drag, and the moment coefficients are evaluated. This model accounts for the hysteresis of dynamic stall, but not for the leading-edge vortex effects.

For the 75% radial station, Fig. 26 shows that the static stall model is not able to predict the complex C~ behavior on the retreating side of the rotor disk. The dynamic stall model provides a better

prediction in this region of the disk. The difference between the two stall model predictions on the retreating side of the disk becomes less significant for the outer radial stations since the blade becomes less stalled near the blade tip. As an additional comparison, one revolution of unaveraged data is included. Attempts were made to improve the

predictions by varying the correction term to the blade angle of attack; however, significant improvements were not obtained. A more sophisti-cated stall model will be necessary to predict the detailed behavior of c~.

Figure 27 shows that the flapwise moments are reasonably well-predicted. No significant improvement is gained by using the dynamic stall model instead of the static stall model. On the other hand, the edgewise moment at 20% radial station is greatly overpredicted by the static stall model at ~

=

270 degrees (where the blade is most

stalled); using dynamic stall improves the predictions (Fig 28). The edgewise moments at the outer radial stations are not well-predicted by

either stall model. For all three radial stations shown in Fig. 29, the torsional moments are not well-predicted by either model. Figure 30 again shows the poor correlation of pitch-link loads. Using the dynamic stall model does not improve the correlation.

9. RECOMMENDATIONS FOR CORRELATION IMPROVEMENT

1. Since the one-seventh-scale data does not represent the full-scale fuselage aerodynamic characteristics exactly, additional calcula-tions were performed to assess the sensitivity of the correlation to fuselage drag. For Condition 2, changing the fuselage drag had a pro-nounced effect on the trimmed control inputs, power required, and blade loads. The predictions were also somewhat sensitive to the fuselage moment characteristics. For future correlations with this data set, using full-scale fuselage aerodynamic characteristics would improve the accuracy of the predictions.

2. Since the blade flap angle measurements were suspect, the rotor position relative to the fuselage was unknown. If CAMRAD were trimmed to the measured tip-path-plane angle, the resulting predictions could improve.

3. Incorporating a more sophisticated dynamic stall model into CAMRAD may improve the predictions of C~ for stalled regions of the blade.

10. CONCLUSIONS

A summary of the correlation results for aircraft performance and trim and the three flight conditions are listed below.

10.1 Aircraft performance and trim

1. CAMRAD is able to predict aircraft performance to within 8% for the low speed cases analyzed; performance for high-speed cases is not well-predicted.

2. degrees. the blade

The collective pitch is consistently overpredicted by about

3

This overprediction is caused by the steep jump in twist at

inboard section which produces a large, nose~down, steady blade pitch increment.

3. Cyclic pitch (for high speeds) and aircraft attitude are not accurately predicted.

10.2 Condition 1 (~

=

0.14, CT/a

=

0.065)

1. Blade tip-vortex interactions dominate the wake effects on blade loads. Tip-vortex core size has pronounced effects on the C~ predictions.

2. The free-wake geometry is able to model the blade tip-vortex interactions.

3. Use of a lifting-surface theory correction has little effect on the C~ prediction.

4. Nonuniform inflow is required to predict blade structural loads. The free wake is not important in predicting flapwise moments, but is required for calculating edgewise bending moments. Torsional moments and pitch-link loads are not well-predicted.

10.3 Condition 2 (~

=

0.36, CT/a

=

0.071)

1. Nonuniform inflow is required for reasonable predictions of blade aerodynamic and structural loads; however, there is little or no difference between the free- and prescribed-wake results.

2. Use of five or six blade-bending modes provide the best predictions of bending moments. Flapwise moments were well-predicted for all radial stations. Edgewise moments are not well-predicted on the advancing side of the rotor disk; better correlation is achieved on the retreating side of the disk at inboard stations.

3. Variation of the number of blade-bending modes had no effect on the poor prediction of pitch-link loads.

4. Torsional moments were reasonably predicted at the inboard radial station. Increasing the number of torsion modes had a small effect on the predictions.

5. Near the blade tip in the second quadrant of the rotor disk, coupling CAMRAO with either FPR or FOR provided a better esimation of the blade lift than did lifting-line theory.

6. In general, the FPR code provided better predictions of blade surface pressures than the FOR code. The shape of the pressure distri-butions were well-predicted by FPR. However, both FPR and FOR underpre-dicted the magnitude of the upper surface pressures.

·7. Shock locations were reasonably well-predicted by FPR.

10.4 Condition 3 (~

=

0.34, CT/a

=

0. 125)

1. The difference between prescribed-wake and free-wake results is small.

2. A dynamic stall model provides a better prediction of C~ on the retreating side of the rotor disk for the blade inboard sections than a static stall model. The detailed behavior of C~, however, is not well-predicted by using the dynamic stall model.

3. The flapwise moments are well-predicted, although the dynamic stall model does not offer significant improvements over the static

model results. The edgewise moments at the inboard radial statiqns are more sensitive to the stall model used; the edgewise moments at the outboard radial stations are not well-predicted.

4. Torsional moments and pitch-link loads are not well-predicted by either stall model.

11. VALUE OF PERFORMING CORRELATION STUDIES

The benefits of performing extensive correlations, such as pre-sented here, can be assessed in several ways.

1. The theoretical model is checked for validity over a wide range of flight conditions.

2. Limitations of the analysis are identified.

3.

The data set is validated somewhat by the analysis. Data reliability can be verified by rechecking instrumentation, data acquisi-tion systems, and data reducacquisi-tion processes; however, gross errors in the data are easily identified by performing correlations with analyses. Errors made consistently throughout the data reduction process can also be identified by thorough correlation with a validated analysis.

Acknowledgements

The authors would like to thank Dr. Wayne Johnson for his invalu-able guidance throughout this joint project. We would also like to

thank Dr. Chee Tung of the U.S. Army Aeroflightdynamics Directorate for his assistance with the finite-difference codes and useful

discus-sions. Finally, we would like to thank Dr. William Warmbrodt of NASA Ames and Mr. Olivier Lambert of the French Ministry of Defense who are the technical representatives for this project; their continued efforts have made this project possible.

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J. American Helicopter Soc. (1970) 15 (3) Prediction of Control Loads due to Blade Stall.

J. American Helicopter Soc. (1972) 17 (2) A Mathematical Model of Unsteady

Aerodynamics and Radial Flow for Application to Helicopter Rotors. USAAVLABS TR 72-67 (May 1973)

TABLE 1. SA349/2 AIRCRAFT CHARACTERISTICS

Aircraft gross weight Main rotor number of blades radius blade chord solidity rotational speed

Tail rotor rotational speed Engine type 2000 kg 3 5.25 m 0.35 m 0.0637 387 rpm 5919 rpm Astazou XIV H rated at 550 kw

TABLE 2. FLIGHT PARAMETERS FOR SELECTED FLIGHT CONDITIONS

Flight condition number

2

3

4

5

6

7

__, Altitude, m

317

1521

235

320

336

308

292

-'= _{True air speed, km/h}

_106.85

_{277. 15}

_258.41

_{199. 14}

_263.20

_289.74

_271.76

I ~ Load factor

1.0

1.0

2.0

1.0

1.0

1.0

1 . 5

"'

_{Advance ratio}

_{0. 140}

_0.362

_0.338

_0.2599

_0.3441

_0.3783

_0.3552

Thrust coefficient/solidity

0.065

0.071

0. 125

0.0645

0.0649

0.0645

0.0940

Helicopter weight, kg

1985

1934

1951

1979

1973

1967

1961

Static pressure, mbar

975.7

843.4

985.3

975.3

973.5

976.7

978.6

TABLE 3. BASELINE CAMRAD CONDITIONS

Tip vortex Number of Number of Stall model, Wake Condition core size, bending torsion _{MR/TR geometry}

rc/c modes modes 1 0.525

6

2 static/static free 2a _0.525

₆

_{2 static/static prescribed} 3b 0.525

6

2 dynamic/none prescribed 4 0.525

6

2 static/static prescribed 5 0.525

6

2 static/static prescribed

6

0.525

6

2 static/static prescribed 7 0.525

6

2 dynamic/none prescribed

afor CAMRAD/finite difference computations, 5 bending modes and 4 torsion modes were used.

Fig. 1. SA349/2 Helicopter.

.1

~

~========:::::=-"' 0 S2 :c I--.1L-__ _ L _ _ _ _ L _ _ _ _ L _ _ _ _ ~--~----~--~----~--~----~ 0 u. ROTOR~ SHAFT I 0 (a)

~

f - =

I

0.545

"'

3.75 Q) "tJ t-' 0 (/)

s:

1--7.75 LCl

"'

"'

0 (b) Fig.

3.

profile.

"'

,.... 0

I

;

.2 .4 -' 0.35 .6 .8 CHORD

"'

FEATHERING AXIS ~

/

(25')( CHORD) 0 "'

i

CONSTANT AIRFOIL OA209

-7.3922°/m RADIAL LOCATIONS, m I 175% I I

+

I I 1.0

"'

"'

N

""

I

I

· +

-I

_I

I

REMOVABLE TIP REMOVABLE TIP -1.28

I

"'

N ui

Grande Vitesse (GV) blade characteristics. (a) OA209 airfoil (b) Blade twist distribution.

STRAIN BLADE NO. 1 F: FLAP BENDING L: LAG BENDING T: TORSION

(IJ

GAGES 2 (15) PRESSURE 3 I \F)

~SQ

0.,12 0.,20

'8"

BLADE' NO. 1 1 -\F) L \F) T

cp

(\)

®

u

0.46

~~

0.54 0.63 0.87 0.85

I

0.75 0.88 0.97 TRANSDUCERS 2--1---~---~---+----(51) 3--1----0 .1 .2 .3 .4 .5 r/R .6 .7 .8 .9

Fig. 4. Blade pressure transducer and strain gage locations.

-.l -"' I N N SA 349 2

r>~

~ j\..-<1

=--10

FLIGHTTAPE

00

b

PCM MESSAGE ~ (NUMERICAL)

~

PRESSURE DIGITALIZATION

__;

---", HARMONIC ANALYSIS (STRAIN GAGES) n~;;.unl.lMIItiL.I:U PRESSURE DATA PRESSURE

PRESSURE/PCM PROCESSING DATA FILE _SOFTWARE AERODYNAMIC HARMONIC _ANALYSIS TAPE SOFTWARE

_/

o-

e ORGANIZE DATA 1- 1-- • CONVERT

_{I -}

• Cp. CN• CM P(mv)-+ P(mbar)

• REFERENCE _{e CALCULATE} -+

AZIMUTH HARMONIC

• AVERAGE DATA • Cp. CN· CM COEFFICIENTS

CORRECTED STRAIN GAGE SIGNAL

HARMONIC _{PROCESSING SOFTWARE} BLADE MOMENTS

ANALYSIS TAPE DATA FILE

rOD-

• ACCOUNT FOR INTERACTIONS

HARMONIC • ACCOUNT FOR WEIGHT ANALYSIS-" RECONSTITUTE SIGNAL MOMENT TIME

HISTORIES

.13r---.---.---.---,---.---, .12 f.. .10 .09 f.. .08 f.. .07 3 1111

Ill CALCULATIONS PERFORMED FOR

THESE FLIGHT CONDITIONS

I

I

I

THRUST

I

SWEEP

I

~l

I

~

o

I

0 0

p

I

I

VELOCITY

I

SWEEP

I

2

I

0

I

1111 0

~--- ---~---5·---11116

₀ .06L_ ______ ~ ______ _ L _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ .10 .15 .20 .25 .30 .35 .40 ADVANCE RATIO

Fig. 6. Thrust and speed range of flight conditions.

en f-:c (!) ...J u.. (!) z z a: ::> f-~ :c (!) ...J u.. ...J UJ

>

UJ ...J

TRIM

UNIFORM INFLOW

I

TRIMMED SOLUTION

l

NONUNIFORM INFLOW

PRESCRIBED WAKE GEOMETRY WAKE INFLUENCE COEFFICIENTS TRIMMED SOLUTION

(REPEAT IF WAKE GEOMETRY CHANGES)

~

NONUNIFORM INFLOW FREE WAKE GEOMETRY

WAKE INFLUENCE COEFFICIENTS TRIMMED SOLUTION

(REPEAT IF WAKE GEOMETRY CHANGES)

(a) Inflow Analysis Levels TRIMMED SOLUTION

ITERATE CONTROLS TO TRIM PERIODIC MOTION AND AIR LOADS

CIRCULATION ITERATION

(INDUCED VELOCITY FROM LOADING) MOTION ITERATION

ROTOR MOTION AZIMUTHAL STEP

RADIAL INTEGRATION SECTION AERODYNAMICS UPDATE MOTION HARMONICS TOTAL ROTOR LOADS

BODY VIBRATION

TEST MOTION CONVERGENCE TEST CIRCULATION CONVERGENCE TEST TRIM CONVERGENCE

(b) Trim, Circulation, and Motion Iterations

Fig. 7. CAMRAD solution procedure.

0 MEASURED 7 18.0

•

CALCULATED

•

"'

G6

"'

e3 "0 :r: 82 u _{15.0 5e} t- _{7 06} c.. 3'8Eb2 w

>

_12.0 t- 04 5 u w G1 ..J ..J _9.0 0 04 u 01 6.0 (a) 31&1 06

"'

2

"'

2.0 "0 ₀ :r: 50 u _{70 1116} t-c.. 1.6 Ill u 5ED 2 ..J 01 u 30

>-

1.2 ₁₁₁₁ 40 u

•

..J <( 4 cc _.8 w t-<( ₇ ..J .4 (b)

"'

2.6

"'

"0 01 :r: _Ill u ₀ 1 t-c.. u _~4 ..J -2.6 u

>-

7 u 0 3 ..J <( _-5.2 5~0

z

7 2 Cl _{50 8 G6} ::J t- -7.8 ~2 c.:l 3

z

₀₆ 0 ..J _-10.4 .12 .18 .24 .30 .36 .42 ADVANCE RATIO (c)

Fig. 8. Trimmed control inputs (numbers correspond to flight

condition). (a) Collective. (b) Lateral cyclic. (c) Longitudinal cyclic.

1080 0 MEASURED 0 CALCULATED 900 4~ 84 04 .18 .24 .30 ADVANCE RATIO 87

1;16

70 50

02

•

5 50be2 50 2 0 06 30 87

i

60 .36 .42

Fig. 9. Trimmed aircraft characteristics (numbers correspond to flight condition). (a) Performance. (b) Aircraft attitude.

CL

CL

CL

--UNIFORM INFLOW

---NON-UNIFORM INFLOW: PRESCRIBED WAKE ---NON-UNIFORM INFLOW: FREE WAKE

·-·DATA- AVERAGED .78 _{r/R = 0.75} .66 .54 .42 .30 .18 .66 _{r/R = 0.88} .54 .42 .30 ~ .18

\~

(b) , .06 .60 _{r/R = 0.97} .48 .36 r--. .24

'

--

' .12 0 80 I '--...·

.:

' ' 160 240 AZIMUTH. deg 320 400

Fig. 10. Effect of wake geometry on lift- Condition 1. (a) r/R

=

0.75. (b) r/R

=

0.88. (c) r/R

=

0.97.

Fig. 11 . tion 1 • - - rc/c = 0.225 - - - r clc = 0.375 - - - r clc = 0.525 1.1 r/R = 0.75 .9 .7 .5 .3 ··-·· rc/c = 0.675 ···-··· rc/c = 0.825 ·-·DATA- AVERAGED .1 +-r-r~-,-,,..,-~.,...--,,..,-~.,...--,-,-~.,-.-,---.--, .90 r/R = 0.88 .72 .54 .36 .18 (b) 0~~~ ... -.~ ... -.~ ... - . -... -.~ .70 r/R = 0.97 .56 .42 .28 .14 0 80 160 240 320 400 AZIMUTH, deg

Effect on lift of varying tip vortex core size -(a) r/R "0.75. (b) r/R

=

0.88. (c) r/R

=

0.97.

74-28

Condi---LIFTING SURFACE, rc/c = 0.10 - - - Ll FTING LINE, rc/c = 0.10 ---LIFTING LINE, rc/c = 0.525 ·-·DATA- AVERAGED 1.35 _{r/R = 0.75} 1.05 .75 .45 .15 (a) -.15 +-,-.,~-.~.-..--.-~-.-~ ... -.~.-...-,r--"-, 1.20 _{r/R = 0.88} r/R = 0.97 320 400 AZIMUTH, deg

Fig. 12. Effect of lifting surface correction on lift- Condition 1. (a) r/R

=

0.75. (b) r/R

=

0.88. (c) r/R a 0.97.

Fig. 13. tion 1.

--UNIFORM INFLOW

---NON-UNIFORM INFLOW: PRESCRIBED WAKE ---NON-UNIFORM INFLOW: FREE WAKE

0 z - E Cl, zz w - OJI-wZ (J)W -:;;: S:o ~:;;: _J u. ·-·DATA 150 r/R = 0.20 90 -.30 -.90 -.150"--~-~---~ 60 0 30 z - E Cl, zz 0 w -OJf-, wZ ~ ~ -30 S:o ~:;;:

u:

-60 r/R = 0.54 (b) -90"--~-~---~ 100 0 50 z - E Cl, z z 0 w - OJI-wZ (J)W -:;;: -50 S:o ~:;;: _J u. -100 r/R = 0.80

-150~(-c)

_ _ _ _ _ _ _

~---~

0 80 160 240 AZIMUTH, deg 320 400

Effect of wake geometry on flapwise bending moment - Condi-(a) r/R

=

0.20. (b) r/R

=

0.54. (c) r/R

=

0.80.

--UNIFORM INFLOW

---NON-UN I FORM INFLOW: PRESCRIBED WAKE ---NON-UNIFORM INFLOW: FREE WAKE

·-·DATA 250 (!) 150 2 Ci E 2 ' w 2_ ₅₀ ali-w2 VJW -:;: ~0 ~:;: 0 w _-150 -250 300 (!) 2 200 Ci E 2 ' w2 ₁₀₀ !!) t-' w2 VlW - 2 ₀ ~0 ~2 0 -100 w -200 250 (!) 150 z Ci E 2 ' w z 50 !!) t-' w2 VJW - :;: -50 ~0 ~2

6l

-150 r/R = 0.20 (a) r/R = 0.54 I (b) r/R = 0.80

&---,

if . \ ' . '

I

\

. '

---/~/

J

/v, .

\V-~

\l

I \

v

-250~(-c_l

__

~---~

0 80 160 240 AZIMUTH, deg 320 400

Fig. 14. Effect of wake geometry on edgewise bending moment - Condi-tion 1. (a) r/R

=

0.20. (b) r/R

=

0.54. (c) r/R

=

0.80.

--UNIFORM INFLOW

---NON-UNIFORM INFLOW: PRESCRIBED WAKE ---NON-UNIFORM INFLOW: FREE WAKE

·-·DATA 35 E 2 21

t-:

z

w ~ ₇ 0 ~ _J <(

z

-7 0 (/) cc -21 0 1-(a) r/R = 0.20 -35 35 ~

z

₂₁ ~--·

z

w ~ 7 0 ~ _J <( -7

z

0 (/) cc -21 0 1-(b) r/R = 0.54 -35 42 ~

z

28 ~--·

I

z

w

(

~ ₁₄

I

0 ~ _J

\I\-f

<( ₀

z

0 (/)

t,j

cc -14 0

J

1-(c) -28 r/R = 0.87 0 80 160 240 320 400 AZIMUTH, deg

Fig. 15. Effect of wake geometry on torsional moment- Condition 1. (a) r/R

=

0.20. (b) r/R

=

0.54. (c) r/R

=

0.87.

z c:i <! 0 ..J >e: z ..J J: 800 400 0 ~ -400 0.. -800 0 --UNIFORM INFLOW

---NON-UN I FORM INFLOW: PRESCRIBED WAKE ---NON-UNIFORM INFLOW: FREE WAKE

·-·DATA- BLADE 1

·.._,r·

80 160 240 320 400

AZIMUTH, deg

--UNIFORM INFLOW

---NON-UNIFORM INFLOW: PRESCRIBED WAKE ---NON-UNIFORM INFLOW: FREE WAKE

·-·DATA- AVERAGED 1.40 r/R = 0.75 1.12 .84 .56 .28 o+-~-~~---~-.-~-.--.~ 1.35 r/R = 0.88 1.05 .75 .45 .15 (b) -.15

+-...

-,...::...,-.-,--,..._-..,.--,-.--~ 1.17 r/R = 0.97 .91

r"'

. / -~

(/

.65 .39 . / .13 (c) -.13 +-.,....-,~--~~---~---r---

...

-0 80 160 240 AZIMUTH, deg 320 400

Fig. 17. Effect of wake geometry on lift- Condition 2. (a) r/R

=

0.75. (b) r/R

=

0.88. (c) r/R = 0.97.

- - 5 BENDING MODES - - - 6 BENDING MODES ··-·· 7 BENDING MODES - - - 8 BENDING MODES ·-·DATA 150 r/R = 0.20 (!) ₉₀

VI

z

- E Cl,

y

zz

₃₀ w

Ole-:

I

wZ (/)W -::.;: S:o ~::2: --' -90 LL -150 (a)\j 125 r/R = 0.54 (!) ₇₅

z

- E Cl,

zz

w Ill t-' wZ (/)W -::.;: S:o ~::2: --' LL _-75 (b) -125 80 r/R = 0.80 (!) ₄₀

(V'

z

- E Cl,

zz

₀ w Ill t-' wZ (f)W -40 -::.;: S:o ~2 --' -80 LL -120 (c) 0 80 160 240 320 400 AZIMUTH, deg

Fig. 18. Effect of number of bending modes on flapwise bending moment -Condition 2. (a) r/R = 0.20. (b) r/R = 0.54. (c) r/R

=

0.80.

Fig. 19. Condition - 5 BENDING MODES .. - .. 7 BENDING MODES ·-·DATA - - - 6 BENDING MODES 750 (!) 450 z

o

E z ' w z 150 a:l t-' wZ t/lW ~ 2 -150 wO (!)2 0 w -450 - - - 8 BENDING MODES r/R = 0.20 -750~~---1050 (!) 750 z

Ci

!:: z ' w z 450 a:l t-'

wz

(I)W - 2 150 S:o ~2

8

-150 r/R = 0.54 -450~~---~---660 (!) 440

z

Ci

E z ' w z 220 a:l t-'

wz

t/lW - 2 0 S:o ~2

8

-220 -440 0 80 Effect of number of 2. (a) r/R

=

0.20. r/R = 0.80 160 240 320 400 AZIMUTH, deg

bending modes on edgewise bending (b) r/R

=

0.54. (c) r/R

=

0.80.

74-36

-z

0 <( 0 ..J

"'

z

:::; :I: u 1-<>. 1600 800 0 -800 -1600 0 - - 5 BENDING MODES ··-·· 7 BENDING MODES ·-·DATA- BLADE 1 - - - 6 BENDING MODES - - - 8 BENDING MODES ~

.·

_./ 80 160 240 320 AZIMUTH, deg

Fig. 20. Effect of number of bending modes on pitchlink loads -Condition 2.

(!) z 0 E 125 75 Z • wZ 25 co • _,I-~~

Q

~ -25 "'::,;: _a: 0 -75 1-r/R = 0.20 (a) - - 2 TORSION MODES - - - 3 TORSION MODES · - · 4 TORSION MODES ---DATA -125+-~---~-~-~----~~ (!) z o E Z •

wz

co • _,I-~~ Z::,;:

Qo

"'::,;: _a: 0 1-(!) z o E Z •

wz

co • _,I-~~ z::,;:

Qo

"'::,;: a: 0 1-100 r/R = 0.54 60

/\

20 -20 -60 (b)

!('

,_)

-100+--.--.-~-T~--~---~-~ 50 r/R = 0.87 30

/\

10 -10

\

-30 (c) 80 160 240 320 400 AZIMUTH, deg

Fig. 21. Effect of number of torsion modes on torsional moment-Condition 2. (a) r/R

=

0.20. (b) r/R

=

0.54. (c) r/R

=

0.87.

.81 .63 .45 CL .27 .09 -.09 .80 .64 .48 CL .32 .16 0 .70 .56 .42 CL .28 .14 0 - - CAMRAD- 1st ITERATION - - - CAMRAD- 2nd ITERATION - - - CAMRAD/FPR- 1st ITERATION · - · CAMRAD/FPR- 2nd ITERATION ··-··DATA- AVERAGED r/R = 0.75

/,

!/

./"

/ (a) r/R = 0.88 ' '

~

!

\

.. /'..

, /

I

. "'·

_{·'--._}

_-~J;

/ r

(b) '~-·

. - . I

.. r/R = 0.97

l

';

:-,.

-;;/~/

~·

.. ,aP

·:0-..

•"/

(c)

~?:'l

40 80 120 160 AZIMUTH, deg 200

Fig. 22. ~ift predictions using CAMRAD and CAMRAD/FPR - Condition 2. (a) r/R

=

0.75. (b) r/R

=

0.88. (c) r/R

=

0.97.

.80 .64 .48 .16 .64 .48 .32 .16 --CAMRAD -1st ITERATION - - - CAMRAD- 2nd ITERATION - - - CAMRAD/FDR- 1st ITERATION - - · CAMRAD/FDR- 2nd ITERATION ··-··DATA- AVERAGED r/R = 0.75

/

j

'

/

--·

//._

...

·-·-r/R = 0.88 (b) 0+-~~-.--~-.~--~~--~--~-.~ .70 r/R = 0.97 .56 .42 .14 (c) 0 40 80 120 160 200 AZIMUTH, deg

Fig. 23. Lift predictions using CAMRAD and CAMRAD/FDR - Condition 2. (a) r/R

=

0.75. (b) r/R

=

0.88. (c) r/R

=

0.97.

1.8 r/R = 0.75 · - · 1 s t ITERATION- FPR 1.4 ---2nd ITERATION- FPR to----e DATA 1.0 ~ _{ljJ = 30°} .6

...

_

-CP ·-...

_____

·--

. . 2

--·

·--:::.:...

-.2 \ ~ -.6 -1.0 1.8 ljJ = 90° 1.4 1.0 -CP .6 .2 -.2 -.6 1.8 _{ljJ =} 150° 1.4 1.0 -C _{p .6} .2 -.2 -.6 0 .2 .4 x/c .6 .8 1.0 (a) r/R = 0.75: azimuth = 30, 90, 150 degrees.

1.8 1.4 1.0 .6 -CP .2 -.2 -.6 r/R = 0.88 ·-·1st ITERATION- FPR ---2nd ITERATION- FPR .,_.__.DATA

\

.'-' -1.0 1.8 1.4 1.0 -CP .6 .2 -.2 -.6 1.8 1.4 1.0 .2 ,. __ ,-;:::.:...:::-::..---==-~·---.;.

----.2

\./

-.6 L , . _ _ - l , _ _ __.J.. _ _ __i_ _ _ __i_ _ _ ...J 0 .2 .4 .6 .8 1.0 x/c (b) r/R

=

0.88: azimuth

=

30, 90, 150 degrees. Fig. 24. Continued. 74-42

1.8 r/R

=

0.97 · - · 1 s t ITERATION- FPR 1.4 ---2nd ITERATION- FPR e---e DATA 1.0 .6

"'=

30° -C _p .2 -.2

"\

•.../ -.6 -1.0 1.8 1/1 =goo 1.4 1.0 -CP .6 .2 _"'-· -.2

'\:!

-.6 1.8

"'=

150° 1.4 1.0 -CP .6 .2 -.2 -.6 0 .2 .4 .6 .8 1.0 x/c (c) r/R = 0.97: azimuth - 30, 90, 150 degrees. Fig.

24.

Concluded.

1.5 1.0 -C _{p .} 5 r/R = 0.753 - - 1 s t ITERATION- FDR ---2nd ITERATION- FDR .._...DATA -.5 ' f - - - ' - - - - ' - - - ' - - - ' - - - - ' 1.5 1.0 -.5 L _ _ _ L _ _ L _ _ J . _ _ - 1 - _ _ J 1.5 1.0 -.5 _ _ _ _ _ ; L _ _ L _ _ . L _ _ . l . - - - - . . J 0 .2 .4 .6 .8 1.0 x/c

(a} r/R = 0.753: azimuth= 30, 90, 150 degrees.

Fig. 25. FDR surface pressure coefficient predictions - Condition 2.

1.5 _{- - 1 s t} r/R _{ITERATION- FDR} = 0.878 ---2nd ITERATION- FDR ...,DATA 1.0 -C p . 5 0 -.5 l____Jc...____l _ _ j _ _ _J_ _ _J 1.5 1/1 = 90° 0 -.5 L _ _ . L . . _ _ _L_ _ _ L _ _ . . L _ _ _j 1.5 1/1 = 150° 1.0 0 --..,..

:o.---.5 L.____l _ __i. _ _ L _ __j__..J 0 .2 .4 .6 .8 1.0 x/c (b) r/R

=

0.878: azimuth

=

30, 90, 150 degrees. Fig. 25. Continued.

1.5 r/R = 0.97 - - 1 s t ITERATION- FOR ---2nd ITERATION- FOR 1.0 .,.._.DATA -C _{p .} 5 0 -.5 L___j~____i _ __j_ _ _L_ _ _ j 1.5 1.0 0 -.5

.___J__ _

_ j _ _ __j_ _ _ j _ _ __J 1.5 1.0 -C _{p .} 5 0 -.5 c _ _ _ L _ _ _ _]__ _ _L_ _ _ j _ _ ___.J 0 .2 .4 .6 .8 1.0 x/c (c) r/R

=

0.97: azimuth

=

30, 90, 150 degrees. Fig. 25. Concluded. 74-46

2.50 2.00 1.50 CL 1.00 .50 0 2.0 1.6 1.2 CL .8 .4 0 1.50 1.20 .90 .60 .30 0

--STATIC STALL MODEL ---DYNAMIC STALL MODEL - - - UNAVERAGED DATA ·-·DATA- AVERAGED r/R = 0.75 r/R = 0.88 r/R = 0.97 (c) -~p·' 80

.

.

. _' ' ' ' ' 160 ' ' ' ' '

....

~ ..

.

.

' 240 AZIMUTH, deg ' . '

V\

320 400

Fig. 26. Effect of stall model on lift- Condition 3. (a) r/R = 0.75. (b) r/R

=

0.88. (c) r/R

=

0.97.

fig. 27. tion 3.

--STATIC STALL MODEL ---DYNAMIC STALL MODEL ---DATA 210 r/R = 0.20 (!) 70 2 - E Cl. 2 2 _-70 w c:l t-" w2

~ ~

-210 I

I

a.O <(:2: ...J LL -350

l,

-490 (a) 200 r/R = 0.54 (!) ₁₂₀ r 2

!\

- E Cl. 2 2 ₄₀ w c:l t-" _\'

..

_" w2

···-;

I CI)W

\\.

!J/ ·-·

-:;;: _-40 S:o ~:;;:

'

' ...J _I LL -120 ' _'·'-' ' -200 (b) 250 r/R = 0.80 (!) ₁₅₀

(\

2 - E Cl. 2 2 ₅₀ w o:l t-" w2 CI)W -:;;: _-50 S:o ~:;;: ...J -150 LL (c) -250 0 80 160 240 320 400 AZIMUTH, deg

Effect of stall model on flapwise bending moment -

Condi-(a) r/R

=

0.20. (b) r/R

=

0.54. (c) r/R

=

0.80.

Fig. 28. tion 3. 2400 c:J 1600 z o E z '

_wz

C!l t-'

wz

U)W -:;;: S:o ~:;;: 0 w 800 0 -800

--STATIC STALL MODEL ---DYNAMIC STALL MODEL ---DATA r/R = 0.20 (a) -1600~~~---2450 ~ 1750

o

E z ' w z 1050 C!l t-'

wz

UJW -:;;: 350 S:o ~:;;:

@

-350 r/R = 0.54 '--1050~~~~--~----~---~~ 1500 ~ 1000

o

E z '

~ ~-

500 wZ UJW -:;;: S:o

o

~:;;: 0 w -500 r/R = 0.80 ' _' ' _', -1000~---~~----~ 0 80 160 240 320 400 AZIMUTH, deg

Effect of stall model on edgewise bending moment - Condi-(a) r/R

=

0.20. (b) r/R

=

0.54. (c) r/R

=

0.80.

540 E 2 t-' 360 z w 2: ₁₈₀ 0 2:

_{_,}

<( ₀ z 0 C/) cr: -180 0 t--360 (a) 200 E 2 ₁₂₀ t-' z w 2: 40 0 2:

_{_,}

-40 <( z 0 ~ -120 0 t--200 (b) 120

\=

z 80 t-' z w 2: ₄₀ 0 2:

_{_,}

<( ₀ z 0 C/) -40 cr: 0 t-(c) -80 0

--STATIC STALL MODEL ---DYNAMIC STALL MODEL ---DATA \ 80

A

I I

I \

<

I ,J

r\ ,,

j:

' ~' ' ' <' \ 'I \ ,. ' ' I ' ' ' r/R = 0.20 ' ' 160 240 AZIMUTH, deg r/R = 0.54

I

' ' ' ' ' r/R = 0.87 320 400

Fig. 29. Effect of stall model on torsional moment - Condition 3.

(a) r/R

=

0.20. (b) r/R

=

0.54. (c) r/R

=

0.87.

6000 3000

z

c:i <( 0 ....J ₀ ::<:

z

....J J: u !::: -3000 a. -6000 ' ' 0

'

80 '

'

--STATIC STALL MODEL ---DYNAMIC STALL MODEL ---DATA- BLADE 1 ' ' ,

__

,' ' ,-' ' ' 160 240 AZIMUTH, deg ' ' '

'

' '

'

('

320

Fig. 30. Effect of stall model on pitch link loads - Condition 3. 400