Evaluation of Dynamic Stall Models with UH-60A Airloads Flight Test Data

Khanh NguyenNASA Ames Research Center

Moffett Field, California

Wayne JohnsonJohnson AeronauticsPalo Alto, California

Abstract.

This paper presents an evaluation study of the fivedynamic stall models in the rotorcraft comprehen-sive analysis CAMRAD II. The five models arethe Johnson, Boeing, Leishman-Beddoes, ONERAEdlin, and ONERA BH models. Oscillating airfoilresults show that all five models can compute thelift stall reasonably well, while the Johnson,Leishman-Beddoes, and ONERA BH models cancompute the stall peaks in the pitching momentfairly accurately. In the rotor environment, all stallmodels predict the stall locations fairly well, but allare unable to compute the right magnitudes of thepitching moment peaks. Proper wake modeling canbe crucial in the calculation of the stall events.Small changes in collective pitch and in blade twistdistribution do not significantly affect the stallcalculation.

IntroductionAccurate prediction of blade stall is crucial in thedesign of helicopters and the sizing of the rotorstructural components. This problem has remainedone of the major challenges of the rotorcraft aero-mechanics community. Stall limits the rotor struc-tural envelope, in particular, the helicopter maxi-mum speed and the rotor loading capabilities. Atthe stall boundary, the large blade pitching momentinduced by stall can cause stall flutter and exces-sive loading, leading to fatigue of structural com-ponents. In addition, stall increases the rotor shafttorque, causes excessive vibration, and adverselyaffects the aircraft handling qualities. Efficientrotor design technology requires improved under-standing and a reliable prediction of rotor stall.

Classical treatments of rotor stall indicate that stalltypically occurs near the retreating blade tip. Inforward flight, a blade encounters a time-varyingdynamic pressure due to the combination of theblade rotation and the rotor translational speed.Thus, the dynamic pressure is greater on the ad-

Presented at the American Helicopter Society54th Annual forum, Washington, DC, May 20-22,1998. Copyright © by the American HelicopterSociety, Inc. All rights reserved.

vancing side than the retreating side. For rollmoment balance, the blade operates at angles ofattack that are low on the advancing side and highon the retreating side. At high blade loading , thelocal blade section angle of attack can becomelarge enough to initiate stall.

Operating in an unsteady environment, the mostsevere type of stall encountered by a rotor blade isdynamic stall. In forward flight, the blade experi-ences time-varying dynamic pressure and angle ofattack arising from blade pitch inputs, elasticresponses, and non-uniform rotor inflow. If super-critical flow develops under dynamic conditions,then dynamic stall is initiated by leading edge orshock-induced separation. Even though under-standings about the development of supercriticalflow in the rotor environment are quite limited,flow visualization results of oscillating airfoil testsat low Mach number suggest that supercritical flowis associated with the bursting of the separationbubble as the bubble encounters the large adversepressure gradient near the blade leading edge [1].Dynamic stall is characterized by the shedding ofstrong vortices from the leading edge region. Theleading edge vortex produces a large pressure wavemoving aft on the airfoil upper surface and creatingabrupt changes in the flow field. The pressurewave also contributes to large lift and momentovershoots in excess of static values and prolongsflow separation, both causing significant nonlinearhysteresis in the airfoil behavior.

The other type of stall typically observed in two-dimensional wind tunnel tests involves trailing edgeseparation. The phenomenon of trailing edgeseparation is associated with either static or dy-namic conditions. Separation starts from the airfoiltrailing edge, and with increasing angle of attack,the separation point progresses towards the leadingedge region. Trailing edge separation contributesto nonlinear behavior, such as hysteresis, in lift,drag and pitching moment due to the loss in circu-lation. In contrast to dynamic stall that is charac-terized by abrupt changes in airfoil behavior,trailing edge stall progresses at a moderate rate.

A recent investigation of blade pressure data fromthe UH-60A Airloads Program [2] has helpedimprove understanding about rotor stall behavior.Test results reveal that stall is not confined solely tothe retreating side but rather spreads to the firstquadrant of the rotor disk. Since stall is stronglycoupled with the blade dynamics, especially thetorsion mode, this coupling manifests in a stallcycle that begins in the fourth quadrant of the rotordisk and continues up to the first quadrant in twocycles (three stall peaks). The stall cycle has afrequency closely matched with the blade torsionfrequency. Note that this stall event is distinct fromanother stall pattern, identified from flight test data,that occurs in the inboard region of the third quad-rant and is attributed to fuselage upwash. Flighttest data also indicate that rotor stall exhibits be-haviors similar to that observed in airfoil oscillatingtests where the shedding of the strong leading edgevortex dominates the flow pattern. After shedding,the leading edge vortex traverses over the bladeupper surface, causes a sharp nose down pitchingmoment (moment stall) and a lift build up, whichare followed by an abrupt loss in lift (lift stall) anda subsequent trailing edge flow separation. Theflow over the airfoil may or may not fully reattachbefore the next stall cycle.

Stall data from the UH-60A Airloads Program isused in this paper to evaluate the different dynamicstall models. Most of the dynamic stall modelscurrently used in rotorcraft analyses are semi-empirical, synthesized from oscillating airfoil testdata. As suggested by the flight test results, thestrong correlation between the development of thestall cycles and the blade torsion dynamics suggestsany meaningful analyses of rotor stall must includeaeroelastic effects. Accurate computation of thevehicle trim and rotor inflow must also be included.The availability of five dynamic stall models in anew version of CAMRAD II, a comprehensiverotorcraft analysis, facilitates the evaluation study.These five dynamic stall models are from Boeing[3], Johnson [4], Leishman-Beddoes [5], andONERA Edlin (for Linear Differential Equations)[6], and ONERA BH (for Hopf Bifurcation) [7].

First, CAMRAD II results using all five models arecompared with the oscillating airfoil data from boththe NACA 0012 and the SC-1095 airfoils to verifythe proper modeling of the isolated stall models.Then, the rotorcraft analyses with the five stallmodels are compared with the UH-60A airload datafor a steady-level flight condition with significant

rotor stall. The study aims to determine whetherthe current stall models are adequate for rotorcraftanalyses and which models better capture the rotorstall. The effects of the rotor operating conditions,rotor wake modeling, and blade twist on the stallbehavior are also investigated.

CAMRAD II AnalysisThis section aims to provide a brief overview of theCAMRAD II analysis and of the stall models usedin the paper. Reference 8 provides further detailson the analysis, and Ref. 9 on the dynamic stallmodels as implemented in CAMRAD II.

CAMRAD II is an analysis of rotorcraft aerome-chanics that includes multi-body dynamics, nonlin-ear finite elements, and rotorcraft aerodynamics.Multibody mechanics allows modeling of largerigid body motion with exact kinematics. Thefinite element model provides an elastic blademodel that includes beam bendings, torsion, andextension. The blade elastic model is based onbeam theory with small strain and moderate de-flections. The analysis computes the blade airloadswith lifting-line theory, using two-dimensionalairfoil characteristics and vortex wake for rotorinflow. The aerodynamic model has corrections foryawed and swept flows. The options for inflowmodels are uniform inflow, prescribed wake, andfree wake with either one or two tip vortices (dualpeak model).

The five dynamic stall models available inCAMRAD II are the Johnson model, the Boeingmodel, the Leishman-Beddoes model, the ONERAEdlin model, and the ONERA Hopf Bifurcation(BH) model. As implemented, all the stall modelscompute components of the stalled loads from thevalues within the static airfoil tables based on astall delayed angle of attack. The stall delayedangle of attack can include unsteady attached floweffects.

Compared to the other three stall models, both theJohnson and the Boeing models are relativelysimple models with the delayed angle of attackdriven by the pitch rate. The Johnson model uses adelayed angle of attack proportional to the pitchrate and three delay parameters, one each for lift,drag, and pitching moment. The leading edgevortex is modeled with two distinct lift and momentincrements, initiated after the delayed angle ofattack reaches a prescribed dynamic stall angle.

The Boeing model uses a delayed angle of attackmodel that is proportional to the square root of thepitch rate and three delay parameters, one each forlift, drag, and pitching moment. The Boeing modeldoes not include separate lift and pitching momentincrements due to the leading edge vortex.

In the Leishman-Beddoes dynamic stall model, thedelayed angle of attack is governed by two distinctprocesses, each of which is modeled with a firstorder linear dynamic model. The first process isassociated with the airfoil pressure response and isdriven by the attached flow lift. The second dealswith the boundary layer response and is driven bythe trailing edge separation distance (measuredfrom the trailing edge), obtained from theKirchhoff model. As implemented in CAMRADII, the delayed angle of attack allows the computa-tion of the nonlinear lift, drag, and pitching momentwithout the leading edge vortex effects, directlyfrom the static airfoil tables. Also, the criterion forinitiating the shedding of the leading edge vortex isthe delayed trailing edge separation distance ex-ceeds 30 percent of the airfoil chord. Once shed,the leading edge vortex is modeled by another firstorder linear dynamic model. The Leishman-Beddoes dynamic stall model requires eight pa-rameters, four of which depend on the airfoilcharacteristics.

The ONERA Edlin model employs three second-order linear dynamic systems for the leading vortexload increments, driven by the differences betweenthe linear and nonlinear lift, drag, and pitchingmoment. The delayed angle of attack is computedbased on a first-order linear dynamic model, andthe model requires 22 parameters.

The three second-order dynamic systems for theleading vortex load increments in the ONERA BHmodel are nonlinear and are driven by the timederivatives of the angle of attack. The coefficientsused in the equations require 18 parameters andhave values that depend on whether the flow isseparating or reattaching, resulting in two distinctdynamic processes. The separating flow process isgoverned by a Van-der-Pol-Duffing type equationthat yields a chaotic response (non-periodic), whilea damped oscillator is used for the reattaching flow.As implemented in CAMRAD II, the switchingcondition (or Hopf condition) occurs when thetrailing edge separation distance crosses a pre-scribed critical value. For the delayed angle ofattack calculation, the model employs a scheme

adapted from the Leishman-Beddoes model. TheONERA BH model requires 18 parameters.

Validation of Stall Models with Airfoil DataThe oscillating airfoil data obtained by McAlisteret. al [10] is used to evaluate the dynamic stallmodels in CAMRAD II under the prescribed angleof attack conditions. The test program, performedin the U.S. Army 7- by 10-Foot Wind Tunnel,includes eight test models, each with a two-footchord and different airfoil sections. Test resultsinclude both static and oscillatory airfoil data atfree stream Mach number up to 0.3. The integratedlift and pitching moment are obtained from the 26pressure transducers distributed over the upper andlower surface of the models.

Figure 1 shows the comparison of the computed liftwith test data for the oscillating NACA-0012 airfoil(Frame 10022 of Ref. 10). The test conditions are0.301 Mach number, 0.098 reduced frequency; themean and oscillatory pitch are 11.84 and 9.87 deg,respectively. CAMRAD II results are obtained bydirect numerical integration of the dynamic stallgoverning equations. Figure 1(a) shows the John-son and Boeing results, and Fig. 1(b) the Leishman-Beddoes, ONERA Edlin, and ONERA BH results.The Boeing model captures the lift hysteresis wellin both the upstroke and the downstroke. TheJohnson model performs equally well in the up-stroke, slightly overpredicts the lift overshoot in the17–20 deg angle of attack range. In the down-stroke, the Johnson model overpredicts the lift byan almost uniform amount over the complete rangeof angle of attack. Referring to Fig. 1(b), theLeishman-Beddoes and both ONERA modelscapture the lift behavior quite well in the upstroke.The ONERA Edlin model prolongs the stall delay,yielding a larger lift overshoot than test data. In thedownstroke, the Leishman-Beddoes model over-predicts the lift, the ONERA Edlin underpredicts it,while the ONERA BH model has a lift behaviorthat oscillates about the test data.

The pitching moment comparisons of the NACA0012 are shown in Fig. 2. The Johnson modelcaptures the moment overshoot magnitude butmisses its phase by 2.5 deg; the Boeing modelseems to capture the right phase but underpredictsthe magnitude by roughly two-third. Both modelspoorly predict the moment reattachment process.In Fig. 2(b), the ONERA BH model captures both

magnitude and phase of the moment overshootquite well, while Leishman-Beddoes model has theright phase and a magnitude 25 percent higher thantest data. In the downstroke, the Leishman-Beddoes model performs reasonably well, showinga reattachment rate slower than test data. Theoscillatory behavior of the ONERA BH resultsuggests a peculiar second moment overshoot,absent in the test data. The ONERA Edlin modelseverely underpredicts the moment overshoot.

Before proceeding to the oscillating SC-1095results, it is worth noting that all five stall modelsare semi-empirical, and thus the computed resultsare highly dependent on the parameters used ineach models. Since the parameters available inCAMRAD II at the time of this study are limited tothose developed for the NACA 0012 airfoil, goodcorrelation results are expected for most of thesemodels as shown earlier. However, good correla-tion results when the same parameters are used toanalyze the stall behavior of airfoils other than theNACA 0012 are be expected.

The results for the oscillating SC-1095 airfoil areshown in Figs. 3 and 4. The test data are obtainedfrom Frame 37305 of Ref. 10, corresponding the0.3 Mach number, 0.10 reduced frequency; 11.86deg mean pitch with oscillatory component of 7.9deg. In the upstroke, the Boeing model capturesthe lift behavior well but underpredicts the lift inthe downstroke (Fig. 3a). The Johnson modeloverpredicts the lift overshoot but captures thedownstroke behavior well. Both the Leishman-Beddoes and the ONERA BH models slightlyunderpredict the lift overshoot magnitude butperform reasonably well in the downstroke (Fig.3b). The ONERA Edlin model captures lift be-havior in the upstroke well, but underpredicts thedownstroke values as in the NACA 0012 results.

Figure 4 shows the pitching moment results for theSC-1095. As in the NACA 0012 results, the Boe-ing model underpredicts the moment overshoot,while the Johnson model is again capable of cap-turing the right magnitude but misses the phase.The Leishman-Beddoes model captures well boththe magnitude and phase of the moment overshootas well as the reattachment behavior. The ONERABH results also shows good correlation with testdata but slightly underpredicts the overshoot value.As in the NACA 0012 results, the ONERA Edlinmodel underpredicts the moment overshoot by asignificant amount.

Note that the good correlation results of the Leish-man-Beddoes and ONERA BH shown in Figs. 3and 4 are due in part to the fact that the CLMAX value,critical to these models, are obtained from the staticdata of the same test program at 0.3 Mach number(Frame 35021 of Ref. 10). The CLMAX value iscritical because it is used to dictate the conditionfor initiating dynamic stall process in both models.An attempt to use the value from the airfoil tablecommonly used in the UH-60A analyses [11] leadto poor correlation results for these two stall mod-els.

Validation of Stall Models with Flight TestDataThe flight test data from the UH-60A AirloadsProgram [12] are used to evaluate the capability ofCAMRAD II analysis with these dynamic stallmodels to compute blade airloads under stallconditions. The aircraft has a four-bladed fully-articulated rotor with 20 deg swept tip blades. Oneof the blades was fully instrumented with 221pressure transducers for airloads measurements atnine radial stations. The integrated pressure datayield the blade section normal force (normal to thechord line) and aerodynamic pitching moment. Toobtain high rotor loading, the UH-60A Airloadsaircraft was flown at normal gross weight but athigh altitude for reduced density.

The CAMRAD II model of the UH-60A rotor is anadaptation of a CAMRAD/JA model [13] andsubsequently updated as described in Ref. 14. Theupdates include a reduced blade flapwise andchordwise stiffnesses that reflect the absence of thenickel abrasion strip in the outboard region of thepressure-instrumented blade. Another updateinclude the effects of the chordwise c.g. shift due toinstrumentation wiring. The blade pre-pitch overthe SC-1095R8 segment is reduced by 1 deg,consistent with description of the airfoil chord line.The airfoil tables of the SC-1095 and the SC-1095R8 are adapted from those reported in Ref. 11.Finally, the updated value of the pitch-link stiff-ness, based on the recently completed controlstiffness measurement at NASA Ames [14], isincluded. In particular, a single spring is used tomodel both the pitch-link stiffness and the flexibil-ity of the control system in the non-rotating frame,yielding a blade torsion frequency of 4.1 per rev atthe nominal rpm of 258.

In order to simplify the analysis, a wind tunnel trimsimulation is used. The prescribed variables are therotor shaft tilt, cyclic flapping angle, and either theaircraft weight coefficient-solidity ratio (CW/σ) orthe collective pitch. Trimming to CW/σ is desirablebut is sometimes unachievable due to the numericalconvergent difficulties associated with the impul-sive loading of dynamic stall.

The evaluation study uses test data from a steady-level flight, corresponding to a CW/σ of 0.13 anddesignated as Counter 9017 in the UH-60A Air-loads Program. For this flight condition, the ad-vance ratio is 0.236, the forward shaft tilt is 3 deg,and the lateral and longitudinal cyclic flapping,measured at the blade flapping hinge, are 9 and –7deg, respectively.

Effects of Stall Models. The evaluation of thedifferent dynamic stall models is carried out with aprescribed collective pitch setting of 15 deg for theCounter 9017 flight. The rotor inflow is calculatedwith the dual-peak free wake model, and theLeishman-Beddoes attached flow model is used tocalculate the attached flow unsteady airloads.Figure 5 shows the lift over the rotor disk for theflight test data and for the CAMRAD II resultsobtained with the static stall, Johnson, Boeing,Leishman-Beddoes, and ONERA Edlin models.The numerical solutions with the ONERA BHmodel are divergent, and hence no results arepresented. In Fig. 5, the lift is represented by CNM

2

where CN is the normal force coefficient and M isthe Mach number.

In Fig. 5(a), the flight test data shows two stallevents in the outboard blade region in the fourthquadrant of the rotor disk. The overall comparisonsof the rotor lift distribution between the test dataand CAMRAD II results are fair in general. Thestatic stall model produces a single small stall eventat the blade tip in the fourth quadrant. The twostall events produced by the Johnson model occurprematurely, as in the two-dimensional cases, andhave smaller magnitudes compared to the test data.The Boeing model produces several stall regions,all distributed along the blade span in the 300–360azimuth range. The Leishman-Beddoes results arevirtually identical to the static stall results, both failto predict any significant stall events. The ONERAEdlin model produces two stall events in the fourthquadrant, the first one appears to occur prematurelycompared to test data.

Figure 6 shows the pitching moment distribution.The most prominent feature of the moment data arethe two stall peaks in the outboard blade region inthe fourth quadrant. The subsequent moderatelylarge pitching moment near the outboard regionsuggests that the passage of the leading edge vortexhas delayed flow reattachment up to the first quad-rant. The stall region produced by the static stallmodel exhibits a phenomena associated with trail-ing edge stall. As expected, this stall model doesnot produced the two stall peaks, prominent in thetest data and attributed to the leading edge vortexshedding. For this case, the Johnson model per-forms better in predicting pitching moment thanlift. The model produces two stall events at thelocations that match with test data but have lowermagnitudes. The Boeing model produces severalstall events, all of which have lower magnitudesthan the two prominent peaks in the test data. As inthe lift results, the Leishman-Beddoes results forpitching moment is similar to that of the static stallmodel. Since this model has been shown in thetwo-dimensional cases to be particularly sensitiveto the airfoil CLMAX, the inability of the Leishman-Beddoes model to produce any significant stallevents suggests the airfoil tables need to be as-sessed. The ONERA Edlin model produces twostall events at the locations matching that with testdata but having lower magnitudes.

Effects of Rotor Inflow Models and CollectivePitch. Figure 7 and 8 shows the computed lift andpitching moment distributions using the uniforminflow and dual-peak free wake models. Thenumerical results are conducted at 16.5 deg collec-tive pitch, using the Leishman-Beddoes dynamicstall model. The prescribed wake results arevirtually identical to that for the free wake and arenot shown. The comparison clearly indicates thesensitivity of the computed airloads to the wakemodels for this flight condition. Note that the shaftangle for this flight condition is only 3 deg forward,and thus the wake effects are quite prominent in therotor inflow. The pitching moment plots shown inFig. 8 further reinforce the fact that proper wakemodeling is important for pitching moment com-putation.

Comparing the results of Figs. 7(b) and 8(b) at 16.5deg collective with that of Figs. 5(e) and 6(e) at 15deg collective shows the effects of increasingcollective pitch on the stall computation of the

Leishman-Beddoes model in a rotor environment.The comparisons indicate that the increase incollective pitch does not help improve the calcu-lated results.

Effects of Blade Pre-Twist. One unique feature ofthe UH-60A rotor is the use of positive twist in theoutboard 94 percent of the blade. The effects ofeliminating the positive twist region are evaluatedanalytically using two linear twists: a high twist of–15.7 deg and a low twist of –12.7 deg. Figure 9shows the twist distributions for these cases. In theanalysis, the Leishman-Beddoes dynamic stallmodel and the dual-peak free wake model are used;the rotor is trimmed to a CW/σ of 0.13. The resultsfor the high twist are shown in Fig. 10. The lowtwist rate results are virtually identical to that of thehigh twist and are not presented. Since the resultsof Fig. 10 are similar to that of Figs. 7(b) and 8(b),it is concluded that small changes in the blade twist,as considered in this study and within the modelingcapabilities of CAMRAD II, do not significantlyaffect the stall behavior of rotors.

Concluding RemarksAn analytical investigation was conducted toevaluate the capabilities of the five dynamic stallmodels in the comprehensive analysis CAMRAD IIto compute the stall behavior in both the two-dimensional and the highly three-dimensional rotorenvironment. The five stall models are the John-son, Boeing, Leishman-Beddoes, ONERA Edlin,and ONERA BH models.

For the two-dimensional cases, all five modelscompute the stalled lift reasonably well. Both theBoeing and the ONERA Edlin models underpredictthe magnitude of the pitching moment peaks duringdynamic stall. The Leishman-Beddoes modelseems to produce the most reliable results com-pared to test data but is found to be quite sensitiveto the CLMAX values from the airfoil tables.

In the rotor environment, all stall models predictthe stall locations fairly well, but all are unable tocompute the correct magnitudes of the pitchingmoment peaks. The ONERA BH model can causethe numerical solutions to diverge. Proper wakemodeling can be crucial in the calculation of air-loads, in general, and of stall events, in particular.Small changes in collective pitch and in blade twistdistribution do not affect the stall calculationsignificantly as considered in this study.

AcknowledgmentsThe authors would like to thank Mr. Robert Kufeldfor the help in setting up the CAMRAD II struc-tural model and in extracting test data from theUH-60A Airloads Program.

References1. McCroskey, W. J., Carr, L. W., and McAlister, K. W.,

“Dynamic Stall Experiments on Oscillating Airfoils,”AIAA Journal, Vol. 14, No. 1, 1976, pp. 57-63.

2. Bousman, W. G., “A Qualitative Examination ofDynamics Stall from Flight Test Data,” Proceedingsof the American Helicopter Society 53rd Annual Fo-rum. Virginia Beach, VA , May 1997.

3. Gormont, R. E., “A Mathematical Model of UnsteadyAerodynamics and Radial Flow for Application toHelicopter Rotors,” USAAVLABS TR 72-67, May1973.

4. Johnson, W., “The Response and Airloading ofHelicopter Rotor Blades Due to Dynamic Stall,” Mas-sachusetts Institute of Technology, ASRL TR 130-1,May 1970.

5. Leishman, J. G. and Beddoes, T. S., “A Semi-Empirical Model for Dynamic Stall,” Journal of theAmerican Helicopter Society, Vol. 24 (3), Jul 1989.

6. Petot, D., “Differential Equation Modeling of Dy-namic Stall,” La Recherche Aerospatiale, No. 1989-5.

7. Truong, V. K., “A 2-D Dynamic Stall Model Based ona Hopf Bifurcation,” Proceedings of the 19th Euro-pean Rotorcraft Forum, Cernobbio, Italy, Sep 1993.

8. Johnson, W. “CAMRAD II, Comprehensive Analyti-cal Model of Rotorcraft Aerodynamics and Dynam-ics.” Johnson Aeronautics, Palo Alto, CA, 1992-1997.

9. Johnson, W., “Rotorcraft Aerodynamics Models for aComprehensive Analysis,” ,” Proceedings of theAmerican Helicopter Society 54th Annual Forum,Washington D. C., May 1998.

10. McAlister, K. W., Pucci, W. J., McCroskey, W. J.and Carr, L. W., “An Experimental Study of DynamicStall on Advanced Airfoil Sections; Volume 2: Pres-sure and Force Data,” NASA TM-84245, Sep 1982.

11. Shanley, J. P., “Validation of UH-60A CAMRAD/JAInput Model,” SER-701716, Nov 1991.

12. Kufeld, R. M., Balough, D. L., Cross, J. L., Stude-baker, K. F., and Jennison, C. D., “Flight Testing ofthe UH-60A Airloads Aircraft,” ,” Proceedings of theAmerican Helicopter Society 50th Annual Forum,Washington D. C., May 1994.

13. Bousman, W. G. and Maier, T. H., “An Investigationof Helicopter Rotor Blade Flap Vibratory Loads,” ,”Proceedings of the American Helicopter Society 48thAnnual Forum, Washington D. C., Jun 1992.

14. Kufeld, R. M. and Johnson, W., “The Effects ofControl System Stiffness Models on the Dynamic StallBehavior of A Helicopter,” Proceedings of the Ameri-

can Helicopter Society 54th Annual Forum, Washing- ton D. C., May 1998.

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0.6

0.8

1

0

90

180

270

360

-0.02

0

0.02

0.04

0.06

0.08

r/RAzimuth, deg

e)

-Cm

*M2

0.2

0.4

0.6

0.8

1

0

90

180

270

360

-0.02

0

0.02

0.04

0.06

0.08

r/RAzimuth, deg

f)

-Cm

*M2

Fig. 6 Comparison of UH-60A pitching moment distribution with computed results using five dynamic stallmodels, (a) flight test data (Counter 9017, CW/σ = 0.13, µ = 0.236.), and analytical results (15 deg collective) (b)static stall model, (c) Johnson model, (d) Boeing model, (e) Leishman-Beddoes model, (f) ONERA Edlin model.

0.2

0.4

0.6

0.8

1

0

90

180

270

360

-0.1

0

0.1

0.2

0.3

0.4

0.5

r/RAzimuth, deg

0.2

0.4

0.6

0.8

1

0

90

180

270

360

-0.1

0

0.1

0.2

0.3

0.4

0.5

r/RAzimuth, deg

Fig. 7 Effects of inflow modeling on the computedlift on the UH-60A rotor, (a) uniform inflow, (b)dual-peak free wake (θ75 = 16.5 deg, µ = 0.236).

0.2

0.4

0.6

0.8

1

0

90

180

270

360

-0.02

0

0.02

0.04

0.06

0.08

r/RAzimuth, deg

a)

-Cm

*M2

0.2

0.4

0.6

0.8

1

0

90

180

270

360

-0.02

0

0.02

0.04

0.06

0.08

r/RAzimuth, deg

b)

-Cm

*M2

Fig. 8 Effects of inflow modeling on the computedpitching moment on the UH-60A rotor, (a) uniforminflow, (b) dual-peak free wake (θ75 = 16.5 deg, µ =0.236).

-4

-2

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1

Bla

de

Pit

ch, d

eg

r/R

-12.7 deg Twist

UH-60A Twist

-15.7 deg Twist

Fig. 9 Twist distributions of UH-60A blade compared to the two linear twist used in the analysis.

0.2

0.4

0.6

0.8

1

0

90

180

270

360

-0.1

0

0.1

0.2

0.3

0.4

0.5

r/RAzimuth, deg

0.2

0.4

0.6

0.8

1

0

90

180

270

360

-0.02

0

0.02

0.04

0.06

0.08

r/RAzimuth, deg

b)

-Cm

*M2

Fig. 10 Computed airloads on the UH-60A with a linear twist of –15.7 deg, (a) lift distribution, (b) pitchingmoment distribution (θ75 = 16.5 deg, µ = 0.236).