136 J. AIRCRAFT VOL. 17, NO. 3

ARTICLE NO. 79-0211R

Dynamic Stall at High Frequency and Large Amplitude

Lars E. Ericsson* and J. Peter Reding!Lockheed Missiles & Space Company, Inc., Sunny vale, Calif.

A previously developed quasisteady analytic method has been shown to give predictions that are in goodagreement with experimental stall results as long as the oscillation amplitude and frequency are of moderatemagnitudes. In the present paper, this quasisteady method is extended to include the transient effect of the"spilled" leading-edge vortex, thereby providing simple analytic means for prediction of dynamic stallcharacteristics at high frequency and large amplitudes. The veracity of the method is demonstrated by criticalcomparisons with the extensive experiments performed by Carr et al.

cKa/m

Uxza.CLOFA6

Nomenclature= two-dimensional chord length= dynamic overshoot coefficient, Eq. (2)= section lift, coefficient c, = // (p^ U2

00/2)c= section pitching moment, coefficient cm = mp/

(pQOU200/2)c2

= section normal force, coefficient cn=n/

timevelocitychordwise distance from the leading edgevertical translationangle of attacktrim angle of attackcirculationincrementangle-of-attack perturbationdimensionless x coordinate, £ = x/ccenter of oscillationair densitywake lagstall-induced additional phase lagoscillation frequency, co =

CGp<pw<psw,o>

Subscriptsc — convectionCG = center of gravityD YN = dynamicef f = effectiveLE = leading edgeIg = linear growthmax = maximumQS = quasisteady5 = stallsp = separation point movementTE = trailing edgetot = totalv = vortexvg = vortex growthvs = vortex spillage

Presented as Paper 79-0211 at the AIAA 17th Aerospace SciencesMeeting, New Orleans, La., Jan. 15-17, 1979; submitted Feb. 13,1979; revision received Aug. 13, 1979. Copyright © 1979 by LarsEricsson. Published by the American Institute of Aeronautics andAstronautics with permission. Reprints of this article may be orderedfrom AIAA Special Publications, 1290 Avenue of the Americas, NewYork, N.Y. 10019. Order by Article No. at top of page. Member price$2.00 each, nonmember, $3.00 each. Remittance must accompanyorder.

Index categories: Nonsteady Aerodynamics; Aerodynamics.*Consulting Engineer. Associate Fellow AIAA.tResearch Specialist. Member AIAA.

w = wake and walloo = undisturbed flow

Superscriptsi ^induced and inducing, e.g., a' = separation in-

ducing angle of attack( — ) = mean value

Introduction

SINCE the classical investigation by Halfman et al.,1 thedynamic stall problem has been studied intensively.

Although our understanding of the basic flow phenomena hasimproved greatly as a result, no substantial advancement ofour capability to predict dynamic stall characteristics hasresulted. On the one hand, it is difficult to use subscale testdata because of the problem of dynamic simulation,2

especially in the presence of three-dimensional flow effects inso-called "two-dimensional" dynamic stall tests.3'4 On theother hand, no pure theory exists that can predict the dynamicovershoot of static stall5'6 or the dynamic overshoot of staticreattachment. It will be quite some time before pure theorycan predict all the details in the oscillatory dynamic stall cycleleading to negative aerodynamic damping and associated stallflutter. It will also be a while before simulation of full-scaledynamics in subscale tests becomes routine.7

An earlier developed analytic method8'9 has been shown topredict numerical and experiment results as long as thereduced frequencies and oscillation amplitudes are of modestmagnitudes.10 In order to provide an analytic method thatcan predict the dynamic stall characteristics also when theoscillation amplitude is large and the reduced frequency ishigh, the transient effect of the "spilled" leading edge vortexhas to be considered.11'12 The extensive, systematic ex-periments performed by Carr et al.13 indicated that othermodifications of the quasisteady theory also were needed. Thepresent paper describes these modifications. To make theanalysis easier to follow, the salient parts of the quasisteadymethod8'10 will be recapitulated.

AnalysisThe present method is semiempirical in nature. It uses static

experimental data as an input. In addition, certain criticalproportionality constants for the effects of pitch amplitudeand frequency on the unsteady separation process have beendetermined by use of dynamic experimental data.

Quasisteady AnalysisIn the analysis it is postulated that the quasisteady over-

shoot of static c/max is caused by the following dynamic effectson the boundary layer: 1) boundary-layer improvement due topitch-rate-induced upstream pressure gradient relief; and 2)

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MARCH 1980 DYNAMIC STALL 137

boundary-layer improvement caused by the leading edgeplunging, the so-called "leading edge jet" effect. It ispostulated further that the upper boundary for this dynamicimprovement of the boundary layer is the static infiniteReynolds number limit. Thus, the quasisteady overshoot ofstatic c /max, expressed in the form of an increase of the stallangle, is cla • A«5, where Aa5 has the following components:

(1)

moves toward the leading edge and a leading-edge vortex is"spilled." If the airfoil is describing oscillations in pitch, 6 ( t )= A0sin(w/)» around a0, the phase angle (cot)vs for the vortexspillage can be obtained as follows by use of Eq. (2).

Ao:c =

a0 + A0sin [ ( w t ) v s - < p w - < f > s ] = a s

Ka A0wcos ( w t ) v s : oj A0cos ( a t ) < 0.02

( Aa5 ) max = 0. 02Ka : coA0cos ( otf ) > 0. 02

For an airfoil pitching around £C G , one has

^(xs=Kaca/U<x < (Aa5)m a

(2)

For the analysis to date, which has been concerned largelywith the NACA-0012 airfoil, Kal =2 and Ka2=4; that is,Ka =3 for £CG =0.254 It is also assumed that (Ac*5)max =0.02Ka based upon dynamic experimental data.14

In addition to this dynamic overshoot, cln Aa5, of static liftmaximum, there is an overshoot Aa due to pure time lageffects which causes no corresponding overshoot of static liftmaximum. One contribution to this lag is the Karman-Searscirculation lag.15 It was shown in Ref. 8 that this wake lageffect could be approximated as follows for an airfoiloscillating in pitch.

(3)

(4)

0.245: u>0.16

That is, Aavv- = A0sin<£w.For a rampwise a change, the lag effect is:

&aw=L5c6t/UQO

In the engineering analysis to date,8"10 it has been assumedthat Eq. (3) could be applied also when oscillating into thestall region. The experimental data by Carr et al.13 show thatthis is a bad assumption. Figure 1 illustrates why. Whenoscillating through stall, the vortex wake does not have thecontinuously changing sinusoidal shape typical for attachedflow (Fig. la), but rather resembles that of an airfoildescribing a series of a ramps (Fig. Ib). Thus, in the presentanalysis, <pw is described by Eq. (3) only for completely at-tached flow. For oscillations into the separated flow region,the constant time lag approximation is applied also forco>0.16.

<pw = 1.5w (5)

Another contribution to the lag term (Aa), the boundarylayer convection lag (Aac), which is important for trailingedge stall, e.g., due to shock-induced boundary-layerseparation,16 is of little importance when dealing with leadingedge stall, which is the stall type dealt with in this paper,except when expressly stated otherwise.

Transient EffectsWhen the static stall angle as has been exceeded by Aas +

Aa, separation occurs on the oscillating airfoil and thefollowing transient events take place. The separation point

0.75: turbulent separation

3.0: laminar separation

Ka = 2(7+2£C G)

Solving for (ut)vs in Eq. (6) gives:For o>A0 cos (ar t)«*< 0.02,

(a>/)u s=2tan

(6)

(a0-as)/AO

(7a)For co A0 cos (co/) vs > 0.02,

*•,„-> (0'02K-+a>-ao\ (7b)

JNote that for a sharp leading edge, Ka — 0.

According to measurements,17'18 the "spilled" leading-edgevortex travels down the chord with an average velocityUv -0.55C/00. The phase lag, (AwOyTE» corresponding to thetime needed for the vortex to travel from the leading edge tothe trailing edge is:

Equation (6) shows that it makes a big difference whetherthe leading-edge separation is laminar or turbulent. In thestatic case, the separation is definitely laminar. It was longassumed that the dynamic leading edge stall also was laminar.It has been suggested earlier19 that the dynamic leading-edgejet effect9'19 could be very similar to the effect observed byHurley and Ward,20 of airjets in the leading-edge region.Hurley showed that by applying minute blowing rates in theregion between stagnation and separation points, the laminarleading-edge bubble could be eliminated completely. Mc-Croskey et al.21 recently published dynamic experimentalresults that demonstrated that the laminar separation bubbledid indeed disappear and that dynamic leading-edge stall isturbulent in nature, at least for the NACA-0012 airfoil.

Figure 2 shows how this change from ^ =3.0 to £5 =0.75,together with the change of <pw discussed earlier, dramaticallychanges the prediction of dynamic stall at high frequencies. Itshould be noted that the predicted upper branch will be liftedin Fig. 2b when the "spilled" vortex effect is included, as willbe demonstrated shortly. Figure 2a shows that the lowerbranch will also be lifted if a modified phase lag is used, inwhich the moving separation point does not reach its meanvelocity instantaneously, but requires a certain time to ac-celerate to this speed.22

Figure 3 shows the results obtained for NACA-0012 by useof Eqs. (6-8). A value of as = 14.5 deg was obtained from thedata in Ref. 13. It can be seen that the agreement betweenpredicted vortex spillage and measured begin moment stall isgood. Also, the measured phase lag for moment maximum,

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138 L.E. ERICSSON AND J.P. REDING J. AIRCRAFT

Fig. 1 Unsteady vortex wakes forattached and stalled flow over anairfoil. 2) attached flow; b) dynamicstall.

b)

2.0Cl

1.5

1.0

a)-55

-.——— EXPERIMENTALRESULTS (REF 14)

-—— ANALYTICESTIMATES

-— MODIFIEDPHASE LAG (REF 22)

2.Or

10 15 20

Fig. 2 Predictions of dynamic lift stall loops, a) old method; b) newmethod.

NACA-0012 : CG = 0.25a(t) = 15° + 10° sin (art)

yt Present Prediction Experiment (Ref. 13)

140

80^

60°-

40°-

20°-

0

_————Wv o Begin Moment Stall°"CmMAX

/

>xx

0.1 0.2 0.3 0.4 O . S c o

Fig. 3 Predicted and measured dynamic stall phase angles.

cm , is in good agreement with the predicted phase lag forpassage of the spilled vortex over the trailing edge. Themoment should, of course, peak just before the vortex leavesthe airfoil, and cnmax should occur somewhat earlier.9 The testdata in Fig. 3 indicate that the phase lag that should be addedto (otf)t;s to predict the occurrence of cnmax is approximately10% of (AcoOyTE • This estimate is shown by the dashed line inFig. 3.

Figure 4a shows similar results for a cambered airfoil § forwhich the static stall angle is as = 16 deg (see Ref. 13). Theresults shown in Fig. 4b for an airfoil with a sharp leadingedge are, however, quite different. For the sharp leading edge,Ka=0 and v?5 = 0, as the separation is fixed at the leadingedge. For this airfoil, the data in Ref. 13 show a5 = 12 deg.The agreement between (co/)y5 and begin moment stall is

§This airfoil has trailing-edge type stall. However, at c /max stalloccurs near the leading edge and it is assumed that also for this airfoilAac » 0 and <p5 = 0.75 o).

PREDICTION EXPERIMENTPRESENT (REF. 13)

o BEGIN MOMENTSTALL

————— (ut)vs+(Acot)v,f?E-cm MAX

20°! //a(t) = 15° + 10° SIN (cot)

^CAMBERED AIRFOIL r /c = 0.0117

a) 0 0.1 0.2 "dTs" OT4 0̂ .5 co

80'

60°

20c

PRESENT EXPERIMENTPREDICTION (REF. 13)

————— (wt) o BEGIN MOMENT

~20° " a(t) = 15° + 10° SIN (cot)SHARP LEADING-EDGE

r /c = 0.004ux-40b) o 0.1 0.2 0.3 0.4 0.5 co

Fig. 4 Effect of profile shape on dynamic stall phase angles, a)cambered airfoil; b) sharp leading-edge airfoil.

good, but it appears that the vortex may travel slower than inthe case of the other two airfoils. UV/U(X>»OA is indicatedrather than UV/U(X —0.55, the vortex velocity measured onNACA-0012.17'18 This would be in agreement with the ob-servation made at the test13 "that the vortex is much morehighly coiled and is further forward on the airfoil than thatassociated with trailing-edge stall" (on the cambered airfoil).

When the amplitude and frequency of the oscillation are ofappreciable magnitudes, the "spilled" leading-edge vortexcan be seen to have a marked effect on the unsteady stallcharacteristics13 (Fig. 5). As the oscillation frequency is in-creased, the Sj ed vortex effect moves from the upstroke tothe downstroke portion of the cycle with associated largeeffects on the dynamic stall loops. For example, at o> = 0.3, theeffect on the pitch damping is negligible but becomes highlyundamping at w = 0.5. Thus, it is very important to be able topredict the phase angle for the spilled vortex event, acapability demonstrated in Figs. 3 and 4. In addition, oneneeds to be able to predict the vortex-induced force andmoment amplitudes. Previously, the space-time equivalencebetween the unsteady "spilled" vortex and the stationaryvortex on a delta wing has been used to develop the followingexpression for the vortex-induced normal force. n'12

=7.57rsin2o:tl (9)

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MARCH 1980 DYNAMIC STALL 139

where, for the oscillating airfoil,

(10)

That this formulation may be an oversimplification wasalways understood. Both Carta's fluctuating pressuremeasurement23 and the flow visualization results obtained bySilcox and Szwarc24 indicate that the vortex is not "spilled"from the leading edge directly, but first spends some time nearthe leading edge growing in size. Carta's data23 suggest thatthe vortex moves from the leading edge to 25% chord withhalf the mean vortex velocity; i.e., Uv] =0.5 Uv. The phaseangle corresponding to this vortex growth period is 0.9 a). Itis, therefore, proposed that Eqs. (9) and (10) be changed asfollows:

(11)(12)

The expressions for (c^max)DYN are:

( C*max ) DYN = ( C*max ) QS + ( Ac J QS

~ (Cm (0-25 —

(13)

(14)

(Ac,,) QS and (Acw) QS are the contributions caused by pitch-rate-induced camber and apparent mass effects.10J9 They areusually negligibly small compared to the other contributions.

For the common case that £C G=0.25, Eq. (14) becomessimply

~ (Cm max) ^ - (Acw ) QS (15)

Figure 6 shows that the peak dynamic normal force andmoment predicted by Eqs. (13) and (15), respectively, are inreasonable agreement with those measured on a NACA-0012airfoil at different frequencies.13 The data uncertainty in-dicated in Fig. 6 was obtained from Ref. 25. It should benoted that these quantitative results are very different fromthose given in Ref. 6 for the same test conditions. This datauncertainty is reflected in the fact that no quantitative scalesare given in Ref. 13 for cn or cm. One source of data un-certainty is the nonrepetivity of the dynamic stall loops.9-26

Another is the sidewall three-dimensional flow interfer-ence,2"4 which is present in Ref. 13 until w<0.3 according tothe authors.

When considering the cambered and sharp leading-edgeairfoils, Figs. 7a and 7b, respectively, the comparison is not asgood. In addition to the experimental data uncertainty, onehas to consider that the parameter values Ka and <ps ofNACA-0012 were used also for the cambered airfoil, and thatKa = 0 is a rather crude approximation for the sharp leading-edge airfoil.

Rampwise a-ChangeIn the case of rampwise a-change, Eq. (6), as amended by

Eq. (12), is substituted by Eq. (16) following the procedureoutlined in Ref. 10.

= Kaca/UQO

- 0.2

co - 0.5

15a, deg

25

Fig. 5 Dynamic stall loop for the NACA-0012 airfoil oscillating athigh frequencies and large amplitude (10 deg) around £«, =0.25 anda0 = 15 deg (Ref. 13).

(16)

Due to the pitch-rate-induced camber and apparent masseffects, the attached flow lift curve will lag the instantaneousangle of attack by only half the Karman-Sears wake lag. 10

Thus, the linear lift growth will stop at the angle

(17)

———— PREDICTION

0 EXPERIMENT (REF. 13)

.5 co

Fig. 6 Maximum dynamic force and moment for the NACA-0012airfoil.

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140 L.E. ERICSSON AND J.P. REDING J. AIRCRAFT

QX

———— PREDICTIONo EXPERIMENT (REF. 13)

oo

———— PREDICTIONo EXPERIMENT

(REF. 13)

.1 .5 co.2 .3 .4

Fig. 7 Effect of airfoil shape on the maximum dynamic force andmoment, a) cambered airfoil; b) sharp leading-edge airfoil.

Combining Eqs. (11-17) gives the prediction shown in Fig. 8of the experimental results obtained by Ham and Garelick.27

The excellent agreement resulted after the predictions hadbeen zero-shifted - 2.5 deg to agree with the attached flow liftat low angles of attack. How the attached flow characteristicsare obtained is described in detail in Refs. 10-12 and also inRef. 28. Comparing the present prediction with that in Ref. 12shows that the introduction of Aavg greatly improves theagreement with experimental results.

The experimental a-ramp data in Fig. 8 exhibit anoscillatory behavior. There is a great similarity between theincompressible stall data obtained by Ham and Garelick27

and the compressible, shock-induced stall data published byLambourne.29 It was shown in Ref. 16 how the unsteadycharacteristics of the shQck-induced separation can bepredicted. An equivalent to Etj. (16) determines the magnitudeof the first oscillatory overshoot of the static separation point.Thexcorrelation between separation point movement and deepstall'lift characteristics for NACA-0012 and NPL 9619 (Ref. 3and Fig. 9) indicates that the analysis of Ref. 16 could

-0.2

-0.4

-0.8

Fig. 8 Comparison of ex-perimental a-ramp results withpresent predictions.

uoo

EXPERIMENT(REF. 26)

———O——— -

1.0

12 14 16 18 a° 20

Fig. 9 Static deep stall characteristics (Ref. 3).

probably be extended to predict the incompressible oscillatorya-ramp characteristics shown in Fig. 8. The large amplitudeoscillatory tests performed by Carr et al.13 also producedsuperimposed oscillations similar to those for the a-ramp, butonly for the NACA-0012 and cambered airfoils, not for thesharp leading-edge airfoil (Fig. 10). This is all in agreementwith the role played by the moving separation point in thesesuperimposed oscillations. As the sharp leading-edge airfoilhas the separation fixed at the leading edge, £5/7=0 asdiscussed earlier, the large effects of the moving separationpoint on phase lag and superimposed oscillations are absent(Fig. 10).

With the introduction of the constant time-lag ap-proximation for the deep stall characteristics, Eq. (5), and thevortex growth period Aaug in Eq. (16), the interesting dynamicstall inhibition phenomenon observed by McCroskey andPhilippe30 can be explained. The top part in Fig. 11 showstheir data, with the NACA-0012 airfoil oscillating into thestall region without ever realizing lift stall. The bottom partshows the graphic representation of the corresponding phaselag characteristics, presented in Ref. 31. With the oldmethod,10 the required phase lag, <ptot = I . ITT, for inhibitionof stall could not be predicted. The present modified methodgives <ptot = 6.15co = 1.337T, thus predicting the stallinhibition. This high-frequency bonus, the stall inhibition,

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MARCH 1980 DYNAMIC STALL 141

- 0.035c-0.025c

- Q . O l c "/[' BASIC NACA 0012^ V r /c =0.0158

CAMBERED AIRFOIL SHARP LEADING-EDGEr /c = 0.0117 r /c = 0.004

— NACA0012 AIRFOILCAMBERED AIRFOIL

— NACA 0012AIRFOILSHARP LEADING-EDGE AIRFOIL

15a°

25 5 15 25a°

Fig. 10 Stall loops at co = 0.10 for various airfoil shapes (Ref. 13).

test

Fig. 11 Dynamic inhibition of the stall (Ref. 31).

has important practical implications for the rotor design ofhelicopters, windmills, and axial compressors.

The preliminary results obtained so far indicate that thepresent analytical method, with the improvements madepossible by the detailed experiments performed by Carr etal.,!3 can predict existing experimental dynamic stall results.Thus, if the computerized method outlined in Ref. 22 is ex-tended to include all the changes that have occurred sincethen, described and summarized in the present paper, itshould provide a valuable preliminary design tool for thehelicopter and compressor industries.

As noted by McCroskey in his most recent review of theexisting capability in predicting unsteady separated flows onoscillating airfoils,32 the present method is the most com-prehensive one. It utilizes all available experimental andtheoretical information and is, for example, the only onedistinguishing between plunging and pitching oscillations.Although the present method in no way obviates basicresearch into the complex flow phenomena composingdynamic stall, semiempirical methods of this type are the onlyones that can provide the engineer with any help forpreliminary design, a conclusion also reached by Mc-Croskey.32 Bore, in his review of our work,33 goes one stepfurther, pointing out how the simple, explicit flowmechanisms on which our method is based, in addition to

helping the vehicle designer to understand dynamic stall, alsoilluminate the vital flow processes in stall flutter, rapid pull-ups, wing rocking, and buffet.

ConclusionsA renewed look at earlier developed engineering analysis

methods for dynamic stall, inspired by the extensive,systematic dynamic experiments performed by Carr et al. hasproduced the following conclusions.

1) The constant time-lag approximation of the Karman-Sears wake lag applies to all dynamic stall occurrences, in-cluding stall during oscillations in pitch.

2) Adding the moving separation point effect to thequasisteady separation value correctly predicts the "spilling"of the leading-edge vortex.

3) Adding further the time required for the spilled vortex toreach the trailing edge correctly predicts when the peak pitch-ing moment occurs. Whereas the average speed with which thespilled vortex travels from the leading edge to the trailing edgeis 55% of freestream velocity for the NACA-0012 andcambered airfoils, as expected, the measurements by Carr etal. indicate that it is only 40% for the sharp leading-edgeairfoil.

4) Adding to the previously developed unsteady timeequivalent to Polhamus5 leading-edge suction analogy theinitial growth period for the "spilled55 leading-edge vortex, asdescribed by Carta's detailed unsteady pressuremeasurements, provides analytical means for prediction ofthe normal force and moment peaks generated by the"spilled55 leading-edge vortex.

ReferencesI Halfman, R.L., Johnson, H.C., and Haley, S.M., "Evaluation of

High-Angle-of-Attack Aerodynamic-Derivative Data and Stall-Flutter Prediction Techniques," TN 2533, 1951, NACA.

2Ericsson, L.E. and Reding, J.P., "Dynamic Stall SimulationProblems," Journal of Aircraft, Vol. 8, July 1971, pp. 579-583.

3Moss, G.F. and Murdin, P.M., "Two-Dimensional Low-SpeedTunnel Tests on the NACA 0012 Section Including MeasurementsMade During Pitch Oscillation at the Stall," CP No. 1145,Aeronautical Research Council, Great Britain, 1971.

4Gregory, N., Quincey, V.G., O'Reilly, C.L., and Hall, D.J.,"Progress Report on Observations of Three-Dimensional FlowPatterns Obtained During Stall Development on Airfoils, and theProblem of Measuring Two-Dimensional Characteristics," CP No.1146, Aeronautical Research Council, Great Britain, 1971; also, NPLAero Report 1309, 1969.

5McCroskey, W.J., "The Inviscid Flowfield of an UnsteadyAirfoil," AIAA Journal, Vol. 11, Aug. 1973, pp. 1130-1137.

6McCroskey, W.J., "Recent Developments in Dynamic Stall,"Proceedings of Symposium on Unsteady Aerodynamics, University ofArizona, Tucson, Ariz., Vol. 1, March 1975, pp. 1-33.

7Ericsson, L.E. and Reding, J.P., "Scaling Problems in DynamicTests of Aircraft-Like Configurations," AGARD Symposium onUnsteady Aerodynamics, Ottawa, Canada, AGARD CP-227, Paper25, Sept. 1977.

8Ericsson, L.E. and Reding, J.P., "Unsteady Airfoil Stall, Reviewand Extension," Journal of Aircraft, Vol. 8, Aug. 1971, pp. 609-616.

9Ericsson, L.E. and Reding, J.P., "Dynamic Stall of HelicopterBlades," American Helicopter Society Journal, Vol. 17, Jan. 1972,pp. 10-19.

10Ericsson, L.E. and Reding, J.P., "Dynamic Stall Analysis inLight of Recent Numerical and Experimental Results," Journal ofAircraft, Vol. 13, April 1976; see also AIAA Paper 75-26, Jan. 1975.

I I Ericsson, L.E. and Reding, J.P., "'Spilled' Leading Edge VortexEffects on Dynamic Stall Characteristics," Journal of Aircraft, Vol.13, April 1976, pp. 313-315.

12Ericsson, L.E. and Reding, J.P., "Further Consideration of'Spilled' Leading Edge Vortex Effects on Dynamic Stall," Journal ofAircraft, Vol. 14, June 1977, pp. 601-603; errata, Journal of Aircraft,Vol. 15, Jan. 1978, p. 64.

13Carr, L.W., McAlister, K.W., and McCroskey, W.J., "Analysisof the Development of Dynamic Stall Based on Oscillating AirfoilExperiments," NASA TN D-8382, Jan. 1977.

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14Liiva, J., Davenport, F.J., Gray, L., and Walton, I.C., "Two-Dimensional Tests of Airfoils Oscillating Near Stall," Vols. I and II,USAAVLABS TR 68-13 A&B, April 1968.

15Von Karman, Th. and Sears, W.R., "Airfoil Theory for Non-Uniform Motion," Journal of Aeronautical Sciences, Vol. 5, No. 10,Aug. 1938, pp. 370-390.

16Ericsson, L.E., "Dynamic Effects of Shock-Induced FlowSeparation," Journal of Aircraft, Vol. 12, Feb. 1975, pp. 86-92.

17Philippe, J.J., "Le Decrochage Instationnaire d'un Profil," TPNo. 936, ONERA, 1938.

18Werle, H. and Armand, C., "Measures des Visualisations In-stationnaires sur les Rotors," TP No. 777, ONERA, 1969.

19Ericsson, L.E. and Reding, J.P., "Analytic Prediction ofDynamic Stall Characteristics," AIAA Paper 72-682, June 1972.

20Hurley, D.G. and Ward, G.F., "Experiments on the Effects ofAirjets and Surface Roughness on the Boundary Layer Near the Noseof a NACA 64-006 Airfoil," ARL Aero Note 128, Sept. 1963, Aer.Research Labs, Australia.

21McCroskey, W.J., Carr, L.W., and McAlister, K.W., "DynamicStall Experiments on Oscillating Airfoils," AIAA Journal, Vol. 14,Jan. 1976, pp. 57-63.

22Ericsson, L.E. and Reding, J.P., "Unsteady Airfoil Stall andStall Flutter," NASA CR-111906, June 1971.

23Carta, F.O., "Analysis of Oscillatory Pressure Data IncludingDynamic Stall Effects," NASA CR-2394, May 1974.

24Silcox, R.J. and Szwarc, W.J., "Wind Tunnel Dynamic Analysisof an Oscillating Airfoil," AIAA Paper No. 74-259, January 1974.

25Philippe, J.J., "Le Decrochage Dynamique: Un Exampled'lnteraction Forte Entre Ecoulements Visqueaux et NohVisqueaux,"

AGARD Symposium on Unsteady Aerodynamics, Ottawa, Canada,AGARDCP-227, Paper 21, Sept. 1977.

26Liiva, J. and Davenport, F.J., "Dynamic Stall of Airfoil Sectionsfor High-Speed Rotors," Proceedings 24th Annual Forum of theAmerican Helicopter Society, Washington, D.C., May 1968, PaperNo. 206.

27Ham, N.D. and Garelick, M.S., "Dynamic Stall Considerationsin Helicopter Rotors," American Helicopter Society Journal, Vol. 13,April 1968, pp. 44-55.

28Ericsson, L.E. and Reding, J.P., "Quasi-Steady and TransientDynamic Stall Characteristics," Paper 24, AGARD CP-204, AGARDSymp. on Pred. of Aero. Loading, Moffet Field, Calif., Sept. 1976.

29Lambourne, N.C., "Some Instabilities Arising from the In-teraction Between Shock Waves and Boundary Layers," CP 473,Aeronautical Research Council, Great Britain, Feb. 1958.

30McCroskey, W.J. and Philippe, J.J., "Unsteady Viscous Flowon Oscillating Airfoils," AIAA Paper 74-182, Jan. 1974.

31 Ericsson, L.E. and Reding, J.P., "Dynamic Stall Analysis inLight of Recent Numerical and Experimental Results," AIAA Paper75-26, Jan.1975.

32McCroskey, W.J., "Prediction of Unsteady Separated Flows onOscillating Airfoils," AGARD Lecture Series on Three-Dimensionaland Unsteady Separated Flow at High Reynolds Numbers, VKI,Belgium, AGARD LS-94, Paper 12, Feb. 1978.

33 Bore, C.L., "Unsteady Airloads in Separated and TransonicFlow," AGARD SMP Specialists' Meeting on Unsteady Airloads inSeparated and Transonic Flow, Lisbon, Portugal, AGARD-CP-226,Paper 1, April 1977.

From the AIAA Progress in Astronautics and Aeronautics Series..

EXPERIMENTAL DIAGNOSTICSIN COMBUSTION OF SOLIDS—v. 63

Edited by Thomas L. Boggs, Naval Weapons Center, and Ben T. Zinn, Georgia Institute of Technology

The present volume was prepared as a sequel to Volume 53, Experimental Diagnostics in Gas Phase Combustion Systems,published in 1977. Its objective is similar to that of the gas phase combustion volume, namely, to assemble in one place a setof advanced expository treatments of the newest diagnostic methods that have emerged in recent years in experementalcombustion research in heterogenous systems and to analyze both the potentials and the shortcomings in ways that wouldsuggest directions for futu-re development. The emphasis in the first volume was on homogenous gas phase systems, usuallythe subject of idealized laboratory researches; the emphasis in the present volume is on heterogenous two- or more-phasesystems typical of those encountered in practical combustors.

As remarked in the 1977 volume, the particular diagnostic methods selected for presentation were largely undeveloped adecade ago. However, these more powerful methods now make possible a deeper and much more detailed understanding ofthe complex processes in combustion than we had thought feasible at that time.

Like the previous one, this volume was planned as a means to disseminate the techniques hitherto known only tospecialists to the much broader community of reesearch scientists and development engineers in the combustion field. Webelieve that the articles and the selected references to the current l i terature contained in the articles will prove useful andstimulating.

339 pp., 6x9 illus., including one four-color plate, $20.00 Mem., $35.00 List

TO ORDER WRITE: Publications Dept., AIAA, 1290 Avenue of the Americas, New York, N.Y. 10019

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