24Th EUROPEAN ROTORCRAFT FORUM Marseilles, France- 15th-17th September 1998

REFERENCE : AE 08

TITLE : Experimental and Numerical Investigations of Dynamic Stall at IRPHE/ASI Laboratory

AUTHORS: E. Berton, D. Favier and C. Mllresca

lRPHE/ASI Laboratory, UMR 6594 of CNRS, Universitv of Aix-Marseille I & II 163 Avenue de Luminy, case 918, 13009 Ma;seille. France

This work concerns the experimental and numerical simulation of Dynamic Stall occuring on an airfoil in 2D/3D unsteady flow configuration. The flow unsteadiness is simulated by means of oscillating motions of the airfoil in translation, pitch and combined translation/pitch, which produce variations of velocity V and/or incidence a around the airfoil. The unsteadiness, characterized by overall and local analysis from experiments conducted on a 2D OA209 airfoil and a half-wing of the same airfoil, exhibits the influence of the finite span of the wing. The present results show that the main influence of the finite span is to delay the stalling vortex occurence and to modify the vortex chordwise propagation velocity along the upper surface. This involves a characteristic delay of the dynamic stall incidence and strongly affects the instantaneous behavior of lift, drag and moment. The dynamic stall calculation in the 3D flow configuration has been based on a semi-empirical approach (GBCN code), which consists to apply the 2D version of the GBCN code at the successive span wise airfoil sections zJh along the half-wing. Comparisons between calculation and experiment concerning the normal coefficient hysteresis loops Cn=Cn(a) are also presented to evaluate the prediction efficiency of this pseudo-3D numerical approach. The present paper also concerns an experimental investigation of the unsteady boundary-layer on a NACA0012 airfoil oscillating in a 2D flow configuration, that aims to bring up some basic data for future Navier-Stokes approach of Dynamic Stall. The study emphasizes on an Embedded Laser Doppler Velocimetry (ELDV) measurement method, suited for unsteady boundary-layer investigation on oscillating airfoils. Using this ELDV method, unsteady features on transition and separation/reattachment of the boundary-layer are investigated in both steady and unsteady flow configurations.

INTRODUCTION

The accurate prediction of unsteady aerodynamics associated with airfoil dynamic stall is of major interest in a wide range of aeronautical applications. For example, the dynamic stall occuring on the retreating blade of an helicopter rotor in forward flight produces significant changes in the airloads and moments spanwise distributions, and thus in the

overall rotor perfonnance 1-6 A proper simulation of the complex blade sections environment requires considering the influence of several parameters, including simultaneous variations in both angle-of­attack a=a(wt) and local flow velocity V=V(wt), compressibility, blade tip effects, airfoil geometry and sweep angle influence, crossflow and separation phenomena influences, ...

However, due to the complex nature of this 3D unsteady stall phenomenon, previous works in this domain have generally tackled the problem by means of simplified flow configurations, which are simulated to specifically dissociate the different

RH.

parameters, in order to analyze separately their respective influence. Relevant of such experimental and numerical works are the studies conducted on airfoils oscillating in 2D unsteady flows, and submitted to either pure incidence variations o:=o:(rot) by means of pitching and plunging motions or to pure velocity variations V=V(wt) by means of a fore­and-aft translation . To provide a better simulation of the dynamic stall conditions, previous works from the

present group 7-10 have concerned the study of dynamic stall generated by means of a combined translation/pitch motion in 2D flows. However, few

studies 11-15 have been devoted to investigate the dynamic stall process in 3D flow configurations.

Nowadays, the effort to improve the prediction of drag and moment coefficients in dynamic stall regime has to be focused on Navier-Stokes equations resolution. Modelisation will need more and more experimental flow physics features concerning boundary-layers and criteria on transition and separation. Thus, in order to gain a better

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understanding of the boundary-layer response to tlow unsteadiness, present works from ASI/IRPHE group are mamly focused on the development of 'm Embedded Laser Doppler Velocimetry (ELDV) method, suited for unsteady boundary-layer

as t ·11 . . f ·1 16-20 11 me uremen s on an osc1 aung mr 01 . 1e measurement principle has been based on an ELDV optical fibres option using an optical head embedded inside the oscillating model, so that the 2D velocity field is directly obtained in the reference frame linked with the moving wall. Such an ELDV method is moreover suited to characterize the unsteady transition, separation and reattachment of the boundmy-layer occuring on moving curved walls of oscillating airfoils.

The following sections give a detailed description of the experimental approach and data results, as well as some calculation/experiment comparisons, to exemplify the efficiency of a pseudo-3D numerical approach derived from a semi-empirical 2D code to model the lift hysteresis loops m 3D flow configurations.

EXPERIMENTAL SET-UP AND MEASUREMENT METHODS

As sketched in Figure 1, the experiments are conducted in the S2-Luminy subsonic wind-tunnel of the AS! Laboratory (rectangular test section : 0.5x I

m2 ; length = 3 m), where the free stream velocity

v~can be varied from 2.5 ms-1 to 25 ms-1 (natural

turbulence intensity less than 0.5 % ), providing a Reynolds number range based on the model chord

from 5.104 to 4.105

The generation of independent or simultaneous variations of velocity V and incidence a of the model is realized by means of an original combined translation/pitch motion (Figure 1). The motion in the two degrees-of-freedom is produced by an oscillating device designed to fit beneath the test section floor. The model is supported in a vertical position and attached to the oscillating device by a support shaft located at the quarter chord axis of the model. Different kinds of model motions can be

simulated7

fore-and-aft translation, plunging, pitching and translation coupled to pitching. Such a device produces variations of relative velocity and incidence as follows : V(wt) = V ~ (1 +A. coswt)

5

a(wt) =a 0 + L L1a, cos (nwt + <!> J n =I

Ref.

Moreover the (V,a) cycles are selected from 3D aerodynamics rotor code results, which provide the stalling conditions encountered by the retreating blade sections located at different span wise stations and for different tlight conditions (advancing parameter ).1.,

collective pitch 8, longitudinal and lateral cyclic tlap values ... ). Figure 2 gives the simulation domain of parameters (A =AwN=· k = cw/2V =) that can be covered by the capabilities of the present experimental facilities. The (A.k) cases numbered from 1 to 6, have been more specifically investigated in the present study.

In a first experimental approach, the simulation 1s conducted on a OA209 oscillating airfoil with values of A and k parameters located at the lower and upper limits of the tlight domain.

In the 2D flow configuration, the tested airfoil consists in a rectangular wing of OA209 profile (chord c = 0.2m; span h = 0.495 m) spanning the entire test section. In the 3D t1ow configuration the model consists in an half-wing of same OA209 profile and chord ( c = 0.2 m), with h = 0.40 m for span (see Figure 3). The same oscillating motions are given to either the complete wing (20) or the half-wing (3D)

and the results already obtained in the 2D case 8-12 are used as a reference basis to investigate both the finite span effect and the influence of unsteadiness on the half-wing behavior.

On both models (2D or 3D), overall measurements of instantaneous lift, drag and moment coefficients are canied out by means of a 3-components balance statically and dynamically calibrated, embedded with the oscillating device. Local measurements of pressure distributions along upper side and lower side of the model, are measured by means of miniature unsteady pressure transducers mounted flush with the airfoil surface. In the 2D flow case, the model is instrumented along the chordwise section with 18 transducers located at mid span of the wing. The 3D half-wing was built by stacking different elements as sketched in Figure 3. One of these elements was equipped with 18 pressure transducers. Local chord wise distributions can thus be measured at different section along the half-wing span by moving the instrumented section. Four spanwise sections were considered : numbered 1, 2, 3, 4 in Figure 3 and located at zlh = 0.50 ; 0.62 ; 0.74 and 0.86 along the span. More details concerning the measurement techniques and the data reduction procedures can be found in references 8-12.

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The second experimental approach concerns more specifically unsteady boundary-layer measurements on a NACA0012 airfoil model which oscillates according to the following motions :

- Pitching motion (instantaneous lncidence variation around a mean incidence) a.(t) = a.o + L\.acoswt,

- Translation motion (instantaneous velocity variation) : Urel(t) = U= + Atocoswt,

- Combined translation/pitch motion: a(t) = ao + L\.a(coswt + <jl), Ure\(t) = U= + Awcoswt.

Steady and unsteady measurements of the (u,v) velocity profiles have been performed at different distances from the leading edge along the upper-side of the airfoil, for 3 chordwise locations (s/C=0.3, 0.508, 0.67). The upstream Reynolds number is fixed

5 atRe=lO.

The NACA0012 airfoil is 30 em in chord, 49.5 em in span and 3.6 em in thickness (see Figure 4). The optical head is mounted on a supporting turntable which is attached to the oscillating frame as shown in Figure 4. The optical head is equipped with a beam­expander to increase the focal distance up to 400 mm, so that the laser beams are focusing at mid-span in the boundary-layer through a 45' mirror. Due to the fact that the supporting turntable is linked with the oscillating frame, the u and v velocity components are directly measured in the reference frame in relative motion.

Moreover, the optical head is also installed on an automatized 2D-displacement device mounted itself on the circular turntable. This teledriven system allows the adequate positioning of the measurement volume at any point of the airfoil surface (30 em in chordwise displacement). An angular sector (from 0' to 360° by

step of 0.1') provides 18

-20

the selection of the surveying normal direction, and the laser measurement volume can then be displaced along the local normal to the surface from y = 0.2 mm to y = 145 mm with a displacement accuracy of 0.1 mm.

Figure 5 presents the acquisition chain of the bidimensional EL V system operating in the back scatter mode. Data acquisition is made on a micro­computer from two Burst Spectrum Analysers delivering for each velocity component (u, v) the Doppler frequencies and the arrival validation time for each frequency measurement. The software (COMBSA) used for acquisition and data reduction

18-20 has been developed at AS! Laboratory under Apple-Lab VIEW system. The unsteady data reduction

Ret.

technique is made using an ensemble average procedure suited for periodic flows investigation.

Due to the periodicity of the flow, each period is considered as a specific sample of the same phenomenon, so that each velocity component, u(t) or v(t), can be obtained at each phase angle wt as the averaged value of the velocity samples recorded at the same given phase angle and over a large number (higher than \50) of cycles of oscillation. The simultaneousness of the 2D measurement is then obtained from a synchronisation procedure of the acquisition chain. providing the phase averaged \'alue of the mean velocity components and their associated

b I . . I S-20 C . h d' f tur u ent quant1t1es . oncernmg t e see tng o the flow, rates of data validation of about 500 Hz are obtained using a mixture of alcohol and glycerine producing particles of about 2 ~m in diameter. The freestream flow is seeded by means of a streamlined tube \ocated in the suction chamber of the wind­tunnel (see Figure I).

NUMERICAL APPROACH

When the model oscillates in !he 2D flow configuration, the dynamic stall calculation method of semi-empirical nature IS derived from the phenomenological model initially developped in Ref. 21 for an airfoil oscillating in pitch through stall. To take into account the simultaneous (V, a) variations generated by the combined translation/pitch motion of the model, the differential equations system has been expressed in terms of circulation and derivatives on

time 9-12 The calculation code obtained (so-called GBCN) also accounts for the quasi-steady lift behavior of the OA209 airfoil in steady flows conditions. Additionally, the derivation of a mathematical optimisation method for determining the set of constants to be introduced in the differential equations system has been also included in the GBCN

code 11-12 The present GBCN code is shown to provide an excellent description of the instantaneous lift hysteresis loops generated by the translation/pitch motion for stalling conditions in 2D flows.

When the model oscillates in combined translation/pitch motion in the 3D flow case, the present numerical approach consists to apply the 2D GBCN calculation model at the successive spanwise sections zJh = constant of the half-wing. All the quasi-steady lift behaviors of the 4 sections into consideration are then deduced from the experimental data base, and the optimization procedure for determining the set of constants is applied at each section z/h along the half-wing span.

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RESULTS AND DISCUSSION

OA209 AIRFOIL IN TRANSLATION/PITCH COMBINED MOTION

To exemplify the experimental results obtained on the airfoil oscillating in the 3D flow case, the fo1lowing data will concern the cycle variations (V.a) shown in Figure 2. For instance, Figure 6 gives the (V,a) variations of case I, for a mean value ao =

14.16° and quite low values of A and k. Consequently the unsteady effects generated on the model at such values of the oscillating parameters remain moderate but are shown to be much accentuated when increasing the values of .6..cxn, A and k.

The model response to the (V, a) variations of case I for 4 different values of the mean incidence ao = 6°; 9°; 12°; 14.16°, is given in Figure 7. The plots represent the evolution as a function of rot of the instantaneous overall coefficients (C], Cd. Cm)

obtained in the 2D/3D flow configuration. At each given incidence ao = constant, the results indicate

that the dynamic sta\1 incidence value UDD is higher

in the 3D flow case than in the 2D flow case. Additionally the phase wt of stall occurence in the 3D flow case, is delayed when compared to the 2D flow case. For instance at CX{) = 9°, the stalling incidence is

aDD= 14° and occurs at wt = 45° in 2D flow, while

in the 3D flow (Figure 7), aDD = !5° and occurs at (!)t = 600.

Moreover when compared to the 2D case, the results obtained on 3D stall also exhibit a strong attenuation of the amplitudes variations of the C]

coefticient. On the other hand the Cd amplitudes

variations are quite similar in both configurations. The nose-down effect on the Cm coefficient is also less intense in the 3D case.

The boundary-layer reattachment which corresponds to the occurence of positive value of Cm coefficient (nose-up) is shown to be generated at a phase Olt = 225° quite similar in both flow configurations. Consequently the half-wing is shown to stall along a part of the period which is shortened compared to the 2D case. Figure 8 illustrates the aerodynamic airloads vanatwns with the instantaneous incidence a, obtained in 2D and 3D flow configurations. As previously mentioned, the 3D effects are shown to significantly increase when the oscillating parameter values (A, k, Ll.an) increase (case 5 in Figure 8).

Ref.

Concerning the stalling vortex propagation along the upper surface of the OA209 model for case I. a comparison of results obtained in the 2D/3D flow configurations is shown in Figure 9. In this Figure the pressure waveforms Cp=Cp(wt) are plotted either in the 2D tlow case or at 3 different sections zJh = 0.62 ; 0.74 ; 0.86 in the 3D flow case. The phenomenology of the stall process is quite similar in both configurations (e.g. the occurrence and propagation of a strong upper side vortex along the chord of the model). Moreover the plots in Figure 9 reveal the imprints of the vortex by the successive pressure peaks on the Cp-waveforrns. The vortex emission generated in the 3D case is thus shown to be shifted between phases wt = ]5° and wt = 33' when the spanwise position increases towards the half-wing tip.

Figure 10 illustrates the unsteady mean Cp­distributions (averaged over a period) obtained in the 3D flow case as a function of the span wise position z/h of the airfoil section. The 3D effects are shown to be more accentued when z!h increases and to produce a decrease of the unsteady mean Cp-distributions both on the upper side and the lower side of the airfoil section, confirming the loss of unsteady mean lift as deduced from the overall measurements in Figure 8.

Figure II gives an example of comparisons between calculation and experiment concerning the normal force coefficient Cn at different sections of the span varying from zlh = 0.50 to zlh = 0.86. The Cn hysteresis loops calculated by the GBCN code previously discussed, are shown to be in good agreement with the experimental Cn (deduced by integration of instantaneous Cp-distributions measured at each z!h::::: constant). The main divergence between calculation and experiment is shown to occur in the wing tip region (zlh = 0.86) where the tip vortex path has a strong influence on the local loading distribution. For this wing span region, the results clearly show the limitations of the present pseudo-3D approach and indicate that the combined influences of the wing finite span, the tip vortex formation, and the flow unsteadiness have to be taken into account for an adequate modelling of the en­hysteresis loop behavior near the wing tip.

UNSTEADY BOUNDARY-LAYER CRITERIA

This section of the paper, focused on an experimental investigation of the unsteady boundary­layer on a NACA0012 airfoil oscillating in a 2D flow configuration, aims to point out useful data for future Navier-Stokes dynamic stall calculations. Unsteady flow features on transition and

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separation/reattachment of the boundary-layer are investigated in both steady ~md unsteady flow configurations.

Steadv flow conficruration

Considering first the steady NACA0012 airfoil, Figure 12 presents the evolution of the boundary­layer velocity components (u, v) measured as a function of y (normal distance to the model wall) at the reduced abscissa along the chord sic=0.67 and for different values of the mean incidence ao,

0°o£CX()o£l8°. The upstream Reynolds number is fixed 5

at Re= 10 and corresponds to a free stream velocity Uoo=5 m/s. Figure 12 shows an attached boundary­

layer behavior for 0°:S.::ao:S.::l2°, where the tangential

and nonnal velocities (u,v) remain both positive. From ao=l5° to 18°, the velocity profiles reveal a

separation of the boundary-layer (negative values of (u,v)) \Vhich strongly increases the values of the boundary-layer thickness o.

The development of the steady boundary-layer along the upper-surface of the airfoil is also presented in the Figure 13 for a fixed incidence ao= 12° at

5 Re= l 0 . For 3 values of sic (sic=0.3 ; 0.508 ; 0.67), Figure 13 presents the evolution of the (u,v) velocity profiles as a function of y and shows that for a fixed value ofy, the tangential and nonnal velocities (u,v) increase as s/c decreases.

Unsteadv flow configuration

The translation motion effect on the boundary­layer evolution is illustrated through the oscillating conditions which involves instantaneous velocity

variation with a 0=6°, Re=l05, A=0.25l, k=O.l88.

The evolutions of u=u(y) and v=v(y) along the period, are plotted in Figure 14 for 8 phase values wt (0°o£(J)to£360°), and 3 sic (sic=0.3 ; 0.508 ; 0.67).

As for the steady flow case, Figure 14 shows that the mean local external velocity Ue is more important

at the reduced abscissa located near the leading edge of the airfoil (sic=0.3) when compared with the Ue value

relative to sic=0.508 and 0.67. It can also be noted that all along the period, the decrease in Ue is linked

with the increase of the boundary-layer thickness o. This phenomenon is due to the decrease of the pressure gradient associated to the local airfoil curvature along the chord. Moreover, considering the entire oscillation cycle, it appears clearly that the velocity components (u, v) reach their minimal

Ref.

values at nearly the same phase of oscillation (wt=l80°).

For the same conditions of the fore-and-aft motion, Figure 15 presents the evolution of the u!Ue=u!Ue(Y)) profiles along the oscillation period at exo=6° and s/C=0.67. The velocity measurements

obtained in this case. are well matched by theoretical velocity profiles corresponding to transitional or turbulent boundary-layer (liN laws).

The characteristic evolution of the u=u(y,wt) velocity profile during a cyclic separation/reattachment process, is clearly exhibited in Figure 16 for the following parametric conditions

of the pitching motion : Cf{l=l2°, .6.cx=6°, Re=I05

,

k=0.188. At the 3 sic into consideration, the phases cot corresponding to an attached boundary-layer regime, range over more than the half of the period ( l35°:>Wt<360°).

As shown by the plot corresponding to wt=3l5° and Wt=0° (Figure 16), the separation process is initiated prior to the maximum incidence value (CX()~l8°) and is shown tO propagate from the leading

edge of the NACA0012 airfoil. At Wt=O', the intensity of the separated flow velocity region is more important at sic=0.3 and 0.508 when compared to the reduced abscissa sic=0.67.

During the incidence downstroke of the pitching motion (see also Figure 16), the separation of the boundary-layer concerns the whole upper-side region of the airfoil (Wt=45°, Wt=90°). The dynamic reattachment of the boundary-layer is then initiated from the leading edge and propagates all along the upper-side of the airfoil ( Wt= 135°).

The Sandborn & Kline separation criterion 22

previously checked to characterize the separation process occurring on the NACA0012 airfoil either in

steady flow or in pitching motion 7

-9

, has been also applied in Figure 17 to the present pitching oscillation conditions. This criterion, based on the instantaneous shape factor H which is expressed as a function of olio, is able to differentiate intermittent from fully developed separation regimes.

From the results of Figure 17, it is shown that the Sandborn & Kline criterion appears to be well suited to delimit the attached boundary-layer regime (black symbols) and the separated flow regimes (white symbols) in the case of pitching motion. However, within the separated zone, the criterion appears to be less efficient in differentiating the intermittent

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separation from the attached boundary-layer regime. The plots in Figure 17 indeed show that the phase Wt= 135', which corresponds to an anached boundary­layer, is identified by the criterion as an intem1ittent separation.

Concerning the influence of the superposition of incidence and velocity variations. the unsteady boundary-layer behavior is analyzed on Figures 18 and 19. Figure 18 presents the evolutions of u=u(y) for 8 successive phases wt along the oscillation period. at the 3 reduced abscissa s/c=0.3, 0.508, 0.67. The parametric conditions of the combined motion correspond to a velocity/incidence coupling in phase

($=0') at a 0=6', i\a=6', Re=l05

, A=0.25l, k=0.188.

As for the pitching case, the plots corresponding to wt=3l5°, 0°, 45°, show an increase of the boundary-layer thickness 0 when s/c is increasing on the upperside of the airfoil towards the trailing edge direction. It can also be noted, that this growth of 8 is linked with the decrease of the mean local external velocity Ue.

The validation of the unsteady transition criterion

established in previous 16-18 works on flat plate model and on a NACA0012 airfoil oscillating in pitching motion, has been extended here to the translation/pitch combined motion. This criterion is based on the integral energy thickness parameter 0' 3·

and is formulated as shown in Figure 19.

An example of such an extension which confirms the validity of the above criterion for the conditions of unsteadiness generated by the combined motion is shown in Figure 19, corresponding to the oscillating conditions previously mentioned. The boundary-layer survey is performed in this case at sic = 0.67.

In Figure 19, the instantaneous values of R0'3 are

plotted as a function of Res at different phases of the

period. The R8' 3 evolution is shown to be like an

hysteresis loop in the Res-Reo' 3 diagram which is

typical of the instantaneous transitional response of the boundary-layer as a function of the unsteadiness parameters (k)c) generated by the forced airfoil motion. The results clearly indicate the capability of the transition criterion in delimiting accurately the laminar regime (white symbols) from the transitional/turbulent regime (black symbols), as a function of phase wt.

CONCLUSIONS

Ref.

The present paper has presented an experimental and numerical investigation of the airfoil dynamic stall in a 2D/3D unsteady flow configuration. The aerodynamic response of a halt~wing (0A209 airfoil) submitted to stall generated by simultaneous variations of velocity V and incidence a, has been characterized from local and overall instantaneous measurements. From the overall measurements performed on the half-wing, an increase in the dynamic stall incidence value CXDD is obtained when

compared to the 2D stalling conditions. The local pressure measurements Cp=Cp(wt,x/c.z/h) have shown that the stalling vortex occurence is delayed along the period when the spanwise sectional position zlh increases towards the wing tip.

A numerical approach of the non11al coefficient loops Cn=Cn(a) generated through stall in the 3D flow, has been derived in the present study using the GBCN model at different span wise sections zlh of the half-wing. A good agreement between the GBCN code results and the measured Co-loops has been obtained all along the wing span excepted for the regions very close to the tip. An improvement in modelling the combined influences of the tip vortex formation and development, the finite span of the wing, and the flow unsteadiness are required for this region of the span.

ln a second part, the Embedded Laser Doppler Velocimetry (ELDV) method has been successfully applied to 2D velocity measurements (u, v) both in steady flow case and around a moving airfoil oscillating in pitch, translation, and translation/pitch combined motions. Using this ELDV method, the boundary-layer dynamic behavior and the specific local unsteady flow features relative to separation and transition, have been investigated over a large range of non-steady parametric conditions. The experimental results, so obtained, will constitute an useful data base for future Navier-Stokes dynamic stall calculations.

NOMENCLATURE

A oscillation amplitude of the model, (m). c, C chord of the model, (m).

Cd drag coefficient, (Cd=T/0,5pSV2).

Cl lift coefficient, (Cl=T/0,5pSV2).

Cm pitch moment coefficient,(Cm=M/0,5pSV2).

Cn normal force coefficient, (Cn=Fn10,5pSV2).

Cp pressure coefficient, (Cp=p-p=/0,5p v2). f frequency of oscillation, (Hz). H integral shape factor (H=81i82).

k reduced frequency of oscillation, (cwi2U=l·

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k reduced frequency of oscillation, (cw/2U=)· Reynolds number, (U=c/v). Rc

Res s

u

u

v

local Reynolds number, (Ue(s,t)slv).

curvilinear distance along the wall from the airfoil leading edge, (m). time, (sec). instantaneous tangent velocity (parallel to the wall), (ms· I).

mean velocity tangent to the wall, (ms-1 ).

mean local external velocity, (ms-1).

free stream velocity, (ms-1 ).

flow velocity due to the fore-and-aft motion,

(ms· I). instantaneous velocity normal to the wall, (ms· I).

V mean velocity normal to the wall, (ms· I). y normal distance to the model wall, (m). ex instantaneous incidence of the model, (deg). ao mean incidence of the model, ( deg).

aoo dynamic stall incidence of the model, (deg). aos static stall incidence of the model, (de g). o boundary-layer thickness, (m). 0] integral displacement thickness, (m).

02 integral momentum thickness, (m). 83 first integral energy thickness, (m). 8'3 second integral energy thickness, (m). 6. ex angular amplitude relative to the pitching

motion, (deg). <1> phase shift between velocity and incidence

oscillations, (deg).

11 reduced Blasius normal distance, (YYRe,ls) A. reduced amplitude relative to the fore-and-aft

motion, (Aw/U=).

v kinematic viscosity, (m2s· I).

w angular trequency, (21lt), (rads· I). wt phase of the period, (de g).

ACKNOWLEGMENTS

The authors wish to thank the support provided by the "Direction des Recherches Etudes et Techniques" under Grant 95/052.

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Ret,

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15-GALBRAITH, R.A., COTON, F.N., JIANG, D., GILMON, R., "Preliminary Results From 3D dynamic Stall experiments of a Finite Wing", Proceedings of the 21st European Rotorcraft Forum, Paper n' 2-3, Saint Petersbourg, September 1995.

16-FAVIER, D., MARESCA, C. and BELLEUDY, J., "Unsteady flows around an oscillating flat plate model using an embodied technique of fibre optics laser velocimeter.", Proceedings of the 17th Congress of Aeronautical Sciences, I.C.A.S.-A.l.A.A., Stockholm, September 1990.

17-FAVIER, D., MARESCA, C., RENON, P. and AUTRIC, J.M., "Boundary-layer measurements on oscillating models using an optical fibre LDA technique", Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, July 1992.

Ret.

18-PASCAZIO, M., STEINHOFF, J., BERTON, E., FA VIER, D., "Influence of coupling incidence and velocity variations on the airfoil dynamic stall, comparisons between Navier-Stokes calculations and experiments", A.I.A.A., Proceedings of the 33rd Aerospace Sciences Meeting, AIAA Paper N' 95-0310, Reno, January 1995.

19-FA VIER, D., MARESCA, C. and BERTON, E., 1996, ''Etude experimentale et numenque du dCvcloppement de la couche limite instationnaire sur modeles oscillants en ecoulement 2D/3D.", D.R.E.T. Contract n' 95/052, Synthesis Report.

20-BERTON, E., FAVIER, D., MARESCA, C., ''Embedded L. V. methodology for boundary-layer measurements on oscillating models", A.I.A.A., Proceedings of the 28th Fluid Dynamics Conf., A.I.A.A. paper n' 9711832, Snowmass, June 1997.

21-PETOT, D., "Modelisation du decrochage dynamique par equations differentielles", La Recherche Aerospatiale, Vol. n' 5, Join 1989.

22-SANBORN, V.A. and KLINE, S.J., "Flow Models in Boundary-Layer Stall Conception", J. Basic Eng., pp. 317-327, 1961.

AEDS Page 8

AIRFOIL

TRANSLATION CyCAM

PITCHING

;: SEEDING

TUBE

FORE-AND AFT

LASER SOURCE

TRANSMITTER

Frgure 1 : Schematrcs o the S2-Lummy wind -tunnel at the ASI-IRPHE La oratory

L~

0.8

0.6

0.4

0.2

0

CASE

2

5

6

- V moy

Actual rotor flight--~

domain

0.04 0.08

A(m) Vmoy(rnls)

0,34 12,56

0,40 5,20

0,24 5,20

0,32 5,16

0.12

f(Hz) ao(nom)

1,0 14,16°

1,2 15,50°

1,2 10,20"'

1,2 11,94°

Cas 2

Cas 6

Cas 5

k = ___£!Q_ 2V

0.16 0.2

). k

0,170 0,050

0,580 0,146

0,350 0,146

0,465 0,146

2D Flow configuration

c = 0.20rn h = 0.495m

3D Flow configuration

c=0.20m h = 0.40m

~

V(t) a(t)

c

tip salmon

(t) (t)

~

v a

z

~ 14.

3

1

u

h

h

Figure 2 : Simulation of dynamic stall conditions within the rotor flight domain.

Figure 3 : Schematics of 2D and 3D wings

Ref. AE08 Page 9

airfoil (NACA0012)

\

measuring volume

optical fibres expander 45° mirror

Figure 4: NACA0012 airfoil- Embedded measurements linked with the oscillating frame model.

Transmitting block

Colour separator

Computer

Laser source 5 W

Burst Spectrum Analysers

Figure 5 : ELDV data acquisition chain.

Ref. : AE08 Page 10

Position sensor

15 V(t)

" 1.1

" ll

10

a(t) ~~

" 16

" " 10

' 0

VELOCITY V t\RIATIONS

<)ll l~ll ~711

INCIDENCE VARIATIONS

90 ISO ~70

cot 360

360

Unsteady paramerers:

l. = 0.170 k = 0.050 f= 1.0 Hz

Voo"" 12.56 m/s

A= 0.34 m

a 0 =14.l6°

1\o: I = 6.454198 <1> 1 =-85 .964

11o:2 = 0.353701 <1> 2= 119.163

Llo:3 = 0.089478

11cx4

= 0.014106

1\o: 5 = 0.008015

<1>3=-104.59

<!> 4 = 104.825

<!> 5=-23.13

Figure 6 : Parametric conditions of variations (V ,a) for case 1.

2D Flow configuration 3D Flow conti o-uration e

0.6

V>Z:::s:·> ~ '/ "'\ ;c:::,_

---;_.__.--

·, ~ ,' 0.6

0.-1 ·· .... ,_ .-· · ... ·····

OA

0.2 .......

0 ~~-L~~~~~~~_L~~~~~ 0 0 60 120 !80 2-10 JOO (l)t 360 ISO 2-10 Joo rot 360

:: v;C.0~\ c······;············•·· ........ ,.. I

021//' .· -~ l 0 I :' ' • ' '', \\ ...

. . . ' '::;,~'-:7, .. ,,<,:: : Q

OA

0.)

0.2 ·--~

. , .. -· ~.-.-.-: ...... r. 0.1 .. _._. ....

o 60 no Jso 2-10 3oo rot 360

.()_05

~.I .------:--· ... ,. ---------··:-···

.().]5

Figure 7 : Instantaneous CI, Cd, Cm for case L

Ref. AEOS Page 11

C!l.6

1.4

1.2

0.8

0.6

0.4

0.2

0

0.5 Cd

0.4

0.3

0.2

0.1

0

0.05 Cm

0

-0.05

-0.1

-0.15

-0.2

-0.25

--

I •

/;, ··~

h~. :...· '

.. . ····-·-

/k!Y //~·

v a(t)"

0 4 8 12 16 20 24

0 4 8 12 16 20 24

..... ·······-···-

r \ ': \

\\ \ .........

\' ../I -~ ............ ) ......... ------~--

\ -· ·············-···· '-,.....- ··----~---

cx(t)r i i i 0 4 8 12 16 20 24

steady unsteady 2D flow configuration

- steady JD flow configuration unsteady

Figure 8 : Cl, Cd, Cm as a function of cx(t) for case 5 - Combined Translation/Pitch motion, 2D and 3D flow configurations.

Ref. : AE08 Page 12

c

0

2D

\toftd en)iss\on bt i · :wl=S:\8~ ·

270 (113~()

zlh=0,62

; 1 i : : : : .... ' ' . . .

wt=l5F • : ' i'

~· 181)

zlh=0,74 zlh=0,86

. . .

Vc"';ll\l-1 ! : : : ....

'1./c-=0 lwt=Zsl0

i ' ~· IW 0 ISO

Figure 9 Instantaneous Cp-distributions and stalling vortex propagation for case I.

-20 --o··JD zJh=D,5 -D-30 v'h=0,62 - -6-· 30 zfh=0,74 -.....4- 3D zlh,Q,86

·' ~"-'-'--'--'--'--'"-"===~~~ 0.2 OA

Figure 10: Unsteady mean Cp-distribution for case 1.

,;c '

z/h=05 z/h = 0.67 1.6 ,•. lo /. .. l.4 Cn

0,80

1.4

1.2 h /

1.0 ~ , .,/··v·•; ...... ,. , +r'

................... o.8o I • z~+"r".f, ...... fx (OJ o.6o r . P:L.J.., :: :: ·~ (b)

0 ·60s'--'--..lJO--IL5_-'-20----"25 ° ,4o 6'--'-8 -'I o---.JL2-'-14-'I-.-6 _IL8_2..l0:--:'22

z!h = 0 74 z/h = 0.86 1.4 Ch 1,2 Cn· 1,2 ·-! .... : .... _~:j./'

····!··---:-----;-- , .. ; .. ·: l :,.. ...

1,0 1,0

0,80 ..... : .. _.+······· 0,80

0,60 --. .,... 0,60

0,40 0,40 L_.::_j _ __, _ __, _ __,

6 8 10 12 14 16 18 20 22 5 10 15 20 25

Experiment in 3D flow GBCN Calculation

Figure 11 : Comparisons GBCN/experiment for easel.

Ref. AE08 Page 13

140,---------~----~----~--~ 140 ,---,---,---,---,---,---~----,

120

100

80

60

40

20

0

y (mm)

-·-------~~·

J'

'

...... .... ··~·t

'\ n 1L' I~

JL 1:\

v ... : . ....li ············----···'···

-2 0 2 4 6 8

120

100

80

60

40

20

0 -1

y (mm)

-0.5 0 0.5 1 1.5 2 -+--cxo=l8° _.,_ -uo=15''-·-·A-··-cxo=l2°--)(-- cx0=9°· ·+· -c.(o=6'--c.- -cxo=3°-·o--uo=(P

Figure 12: Tangential and normal velocities (u,v) in steady flow as a function of cxo,

Re = 105, s/c = 0.67

140 : :

[ i ··············--·:···· ... -- ______ : ................... : .............. .

I 120

······-··------------· ............. : ................... : ........ ~---·· ! 100

. . .

80 ·· l.................. ·······································r •

60 ................. ;... ······- __ : ___________________ ;··········t·····i~---

i ! : \ • • ... 40

20 .•....... .. L L ~ ~~J.t:;;

0 ~~~~~~~.c~~~=-~ .. ~-*~·~-~~···-~~-~~--~L·~•"~··~ .. ~-·~~--~~;(~Im~SL-~1 ) 0 1 2 3 4 5 6 7

140

120

100

80

60

40

20

0 0 0.2 0.4

-+--- s/c=0.67

0.6 0.8 1.2 1.4

•- · s/c=0.508 ----.to.---- s/c=0.30

Figure 13 :Tangential and normal velocity profiles (u,v) in steady flow

as a function of s/c, Re = 105, cx0 = 12°

Ref. AE08 Page 14

2.5

y(mm)

y(mm)

y(rnm)

120 ' ' ro~;:oo :

too iu>;;u ' , • 80 . .J~-~-----m.'J..~ ········--·-- ;

60 .. ; ... ' • o:

y(mm)l20 100

80

60

40

ffit=0°i ····i=u·-~-------~ -------'--·----•--rcl tit~~----- ..... ,. 4 ---~---

·········' ...... : ...... ,.: ······<··· . 0 _, ...... : ....... ; -----0 -------1

~~ :::: .. L :::::::·::::~~:. 0

'-·-· ·_L1' _ _,.,,_."''-'-'~'-;-~ '"'&,!___j u ( m/ s)

0246810

20 [ 0 ~ 0 "0

' ! 0 '---'-----~·..,iJ"~'-o-nLi _.L__.I v(m/s) -0.5-0.25 0 0.25 0.5 0.75

120 .-----~-~--~ w t~90°

~~~ o~~i-oi .. ·' 60 ····•.,-··-

•u ····...0----

•: 0

120 r-~-c---~~-, y(mm) Wt~90"'

too ·<u • < , 80 ref ~ ._. __ :--- _ L ...... !

60 ··:, .... ,. •···'··· :. 0

40 ...... ; ...... ;. -----;o­

;. b 40

20

0

···--•oo ········· 20 : ....... _: ______ .,0°ci0 ·-~

c__J___,_,..,,..,_jl~_"1'i:,,_c___j u(m/s) 0

L__j__.;_-'l.___l__!.i__j v(m/s)

0 2 4 6 8 10 -0.5-0.25 0 0.25 0.5 0.75 l 120 r----;:_. ---"--~-', 120 . .

o:t=180" ' y(mm) cot,;l801 tOO fv;~f\J;;;;~· 100 ju:su' •' 80 · · .... · ....... ,... 80 . .r.eL .. Jpin. ·•··· 60 ....... ,. ·······~· ..... ,... 60 ......... , .....• ;

:. 0 "' 40 ........ ;. ····---;.o--- _: 40 ;. 0

20 ·· ··>· ······<•ro·· · 20

0 '--""' '-""~,_r_,~oc_J__j__ju(m/s) 2 4 6 8 10 0

···0-·-'-

: : .. 0 :

'·····---i-----t:jO---···j····· .. i

L.il i ', v(m/s) 0

-0.5-0.25 0 0.25 0.5 0.75

PO · y(mm) - Wt=:i70"

too -u;~Fu: , ·• ············ 120 =2' 70" y(mm) cot-, ' 100 ru '=u!

rei ~

····---~--- __ :

80 ········>········j······•i· ·····-+··

60 ........ ; ·······+·····• .......... ; .. . •:o

40 . ; ...... :-o-- ---~---

20 r-- :::::r ::::::::;:: ..... ;i; ... ._.,~ ~

0 0 2 4 6 8

u(m/s)

10

80 ........ . ----·~

60 ~· ....... • .• :.

······-: .. :o 40 -------~0--

2~ ~------f ·····t;-~<t;o.o-~---

-0.5-0.25 0 0.25 0.5 0.75

v(m/s)

l

Figure 14: Tangential and normal velocities (u,v) in fore-and-aft motion as a

function of y and rot, Re = 105, a 0 = 6°, 'A= 0.251, k = 0.188 2 201r-r-~, ~, -,~---,~

1115 ' c.Ot=Oo, • ' 11 15 Olt=IBO<i

IC

5

•:

: : :.~~ u!U 0 ___ ,_ . .,,' -0.2 0 0.20.40.60.8 I 1.2 20r-r-.r-.----.~~~

1115 . .C':it---~00 •

10 l 5 ·······-·

• -1---. '. . : . ,

:. -----~

' i i, '• u!U : , ... ~:• . e 0 --·- ' -0.2 0 0.20.40.60.8 I 1.2

• experiments

10 ,.

·,e:··· ; I

' . ' s ···1· : -----:·----··;-~~~-r~-----~

0 · _ i _ __ -_._..i i : e1

-0.2 0 0.20.40.60.8 I 1.2 20

11 Olt=270~ 15 ..... ,. .. ... , ... '

·····-10 ----~---, . _,.: . , 5 . . -)· .

l i ·-~~ /•) t0l e 0 ---- ' -0.20 0.20.40.60.8 I 1.2

- - -- N theoretical transitional or turbulent boundary layer profiles (liN Law)

Figure 15 : u!Ue=u!Ue (T\) evolutions in fore-and-aft motion , s/c =

0.67, Re= 105, ao=6°, A=0.251, k=0.188

RH, AE08 Page 15

0

0

• s/c=0.3 s/c=0.508 s/c=0.67

15

12

9

6

3

0

PO y(mm\oo CO tto0°

a~~~~l . I _:0 120

y(mm) 100 mt;,180° ci=6L -----.··.·.:.·. ---o:---·

·'······· ~--o -.-:-··· .: . . '

80 60

- . -·0:----

·····<···· -- --------: --·-6----•cj:l

80 60 40 .. 0. :·······<··eO-·-:---- 40 ·•OO

•~o

,j~J: ~. i i u(m/s) 20 T L.Jll 0 L__L_--L___j__.~=.:J~

~ 0 2 4 6 8 4 ~ 0 2 4 6 8

: 0 :0 • :

20

0 -4 u(m/s)

120 ,--~~_,--~oo,--. (\) ,: 450 , y(mm) '·'t=.',,.-725·, ·or······· . '"'·· '1 : ..... C ..... <-. 100 W - ·········OQ ...

y(mm)l20 r-~~~-~-,.-, 100 80 60 40

o:'=l5? ' C\=9~ : ..... ' ....... : ..• ,.... 80 ................... .. .... .' .. ..,; .. j : :

---o -----..:--- 60 : ........ : ......• ~------ce : : o .-::a

0····-:-• -- ~-o--- : 0: • 40 ··-· ---·~---

•Po 20 -o o·:·~t,;~ ____ ,____ u(m/s) 20 ·-- --~--- · -- ····:-~~i)\ .. 0 -4 -2 ,_j0_2l___j_4__l_6__j8 ° -'4-~-2----'0-2'---""4'-"-'6-"--'8 u(m/s)

120 120 y(mm) 100 r-wt;o90~J. ·····~··· y(mm) 100 wt,;,noo ' : .. •o

80 I-Cfs'12J ..... :. •o 80 o:;=l~<Yt oo : : :

601- : •·+ 60 ........• ;, • : o p j : i eoo

40 r- ··T·---·--:- --~---~···O·-:---- ~-:o--- 40 -- , ________ ;... ______ : -- •?o---20 t-- ·+······\··--o-~--o . .':·-· 20 : ;: ....... 1 ..... ;~~---

L__JCi,,_~~-" __,_; __L__j___j u(m/s) ; ";..-J" "' 0

-4 -2 0 2 4 6 8 ° -4 -2 0 2 4 6 8

u(m/s)

120 120 ,---.,----~-,--,--~, y(mm\ 00 cotbl35Jo .L : ~i y(mm) 100 mtk3Jlio . ,¢

80 r- g :on . . ~· .. 8o cx:=ISfl : : ·"

H

60 1-40 1-

··eo:--- 60 ····•<>··· ! !•~ -4o ... : ........ ~-----~--- 40 ··-·-«1-···0··

• : 0 ci . . . . ·: 0

20 1-· ···' · ·--:-----··•···---o~------o~--- 20 ___ ; __ ·····y------j········i··t·o·f···cp· . ,; sl :o 0 ~ u(m/s) ' c..i.·~lc?' 0 u(m/s)

0 -4 -2 o 2 4 6 .-:8'--___

0 ......... -4 -2 o 2 4 6 8

o s/c=0.3 0 s/c=0.508 • slc=0.67

Figure 16: Tangential velocitiy u=u(y,mt) in pitching motion, Re =

105, o:o = 12°, C.o: = 6°, k = 0.188

CUt=454 • H (experimental values) ·······················

...................... : ··--··················:···.

!cot=l3SO mt=Iso4

... _:: .... ::·-i· ;;i~.___~!3.[co=t=<~li~~c; . 81/8

L__ ___ wt=225° -C0t=270°-·'-----'

Sandborn & Kline criterion :

H ~ Hdec = A[ ~ ] (1--1)

8 - - • fully separation (A = 1. 70) ---intermittent separation (A = 1)

• attached flow

0 2.125 10-1 4.25 10-1 6.375 101 8.5 10-l Cl intermittent separated flow o fully separated flow

Figure 17 : Sandborn & Kline separation criterion in pitching motion,

sic= 0.67, Re = 105,0:0 = 12°, C.o: = 6°, k = 0.188

Ref. : AEOS Page 16

40

PO v(mm) -- 100

80 60 40

• o! o 20 ~ . ·' ·' •oD u(n"'S) 20 I : : • o: 0 jj_

Q ',.--,•~J'tooo~O Q

- .... ~---·

- .................. . ;., '-:;---

..... :., .. ·~ ~~ I

0 4 6 8 u(nl!s)

10 PO 0 2 4 6 8 10 PO

y(mm)- Ft~ \(mm)-J 00 {J)t=45° •o ' J 00 80 0:=9° ~ 80

. . .

·················~·M=235°··· ................... ~ 0:=3?

60 L •o 60 40 :~~ 40 20 :~~ 20 ........ · .... ---:·-«<J···=·····

•" o I u(nl!s) ,,.ill , u(nl!s) Q I t•J t,o~ 'boo tq I Q

. . . : : : :_ ....... :--.a--- ;

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

120 o 2 4 6 8 10 120 o,---,2-~4 -oc6-,8 ___,10

y(mm) 100 .COt=90.? ., y(mm) 100 r-C0t=27do ···~··· 80 0:=60• .. .,..... 80 0:=60 .... ., ...

60 I-···· ' •O 60 I .,

~ ci 40 ···'······-~--- 40 ··'·····m

.io ~0

2g i. }.~~J 0 2 4 6 8

( )120 . . .

Y mm 100 cotdn§P., • 80 o:=3 ' ~ .

- .: ... 0···: : «! !

.... : .. .u---:

y(mm)l20 100 80 60 40

0

60 40 20 0

\ill u(nl!s) 20 0~02·~~4~6~~8~10 °

o s/c=0.3 o s/c=0.508 • s/c=0.67

........ : ......... -f-·--·---~~---i no ~\\

2 4 6 8

.. : .......... :··•0··· :

. : ...•..•..• : .. *<)

: •oo: .. : .......... : .. •o-o:·-·

: 1 .0 ~ .. : ....... ~[;:!~~-----

2 4 6 8

u(nl!s)

10

u(nl!s)

10

Figure 18 : Tangential velocitiy u=u(y ,cot) in translation/pitch combined

motion, Re = 105, o:0 = 6°, 1'10: = 6°, A= 0.251, k = 0.188, ~ = 0°

800 Reo'3 : . ' 4"0 : . · · ··o Transition criterion

700

600'

500 I-

400

300

············-·---~ ..................•. - -----············ .. -.:)--- -;..-•----···;! ...... .

..................•. -----------------:----

·········---------:- .................• -----············· --.-------.

(Reo·3)t = 0.0135 (1+1.5e-Re/35000).Res0.8

Res< 2.105

... 0 100 !so; ;;:: · 2.25~· ... -. 270o ' Res Transition criterion

0 5 104 6 104 7 104 8 104 9 104 1 105 o laminar profiles

• transitional or turbulent profiles

''------------------' Figure 19 : Transition criterion in translation/pitch combined motion,

sic = 0.67, Re = 105, o:0 = 6°, 6.o: = 6°, A= 0.251, k = 0.188, ~ = oo

Ref. : AEOS Page 17