Calhoun: The NPS Institutional Archive Faculty and Researcher Publications Faculty and Researcher Publications Collection 1998 A Computational Study on the Dynamic Stall of a Flapping Airfoil Tuncer, Ismail American Institute of Aeronautics and Astronautics, Inc. Tuncer, Ismail H., Ralf Walz, and Max F. Platzer. "A computational study on the dynamic stall of a flapping airfoil." AIAA paper 2519 (1998): 1998. http://hdl.handle.net/10945/50285
Transcript
Calhoun: The NPS Institutional Archive
Faculty and Researcher Publications Faculty and Researcher Publications Collection
1998
A Computational Study on the Dynamic Stall
of a Flapping Airfoil
Tuncer, Ismail
American Institute of Aeronautics and Astronautics, Inc.
Tuncer, Ismail H., Ralf Walz, and Max F. Platzer. "A computational study on the
dynamic stall of a flapping airfoil." AIAA paper 2519 (1998): 1998.
A COMPUTATIONAL STUDY ON THE DYNAMIC STALL OF AFLAPPING AIRFOIL
Ismail H.Tuncer *Middle East Technical University
06531 Ankara, Turkey
Ralf Walz f
Technical University of KarlsruheD-76128 Karlsruhe, Germany
Max F. Platzer *Naval Postgraduate SchoolMonterey, California 93943
Abstract
The dynamic stall boundaries of a NACA 0012 airfoiloscillating in either the pure plunge mode or in thecombined pitch and plunge mode is computed using athin-layer Navier-Stokes solver. Unsteady flowfields arecomputed at the free-stream Mach number of 0.3, theReynolds number of 1 • 106, and the Baldwin-Lomax tur-bulence model is employed. It is found that the pureplunge oscillation leads to dynamic stall as soon as thenon-dimensional plunge velocity exceeds the approxi-mate value of 0.35. In addition, the power extractioncapability of the airfoil operating in the wingmill modeis studied by computing the dynamic stall boundary fora combined pitch and plunge motion at the reduced fre-quency values of 0.1, 0.25 and 0.5.
Nomenclature
c Airfoil chord length (reference length)h Plunge amplitude normalized with ck Reduced frequency (wc/Voo)V<x, Free-stream speed (reference speed)Ofo Pitch amplitude01 Circular frequency of oscillation(j) Phase shiftT Non-dimensional time
Introduction
The problem of dynamic stall on helicopter, propellerand wind turbine blades has received considerable at-tention for quite some time because of the impact ofdynamic stall on the blade performance and on the (pos-sibly destructive) loads caused by the dynamic stall phe-nomenon. The blade is assumed to execute a pitching
'Assistant Professor, Department of Aeronautical Engineeringt Graduate Student, Institut fur Stromungslehret Professor, Department of Aero/AstronauticsThis paper is declared a work of the U.S. Government and is
not subject to copyright in the United States.
oscillation about some pitch axis located on the bladechordline. In recent years, a significant amount of newexperimental information has been obtained by Chan-drasekhara and Carr and by Lorber and Carta. For acomprehensive review of this experimental data we re-fer to the review paper by Carr and Chandrasekhara[1]. Also, the rapid advances in computational fluid dy-namics have made it possible to apply numerical solutiontechniques of the Reynolds averaged Navier-Stokes equa-tions to this problem. For a review of the current statusof dynamic stall computations refer to Ekaterinaris andPlatzer [2].The case of sinusoidal plunge oscillation has receivedmuch less attention in past years because a pure plungeoscillation was thought to have much less importancein practical applications. However, it has been knownfor many years that a flapping wing generates a thrustforce. This effect can be predicted using inviscid, in-compressible flow theory. For example, Garrick [3] usedTheodorson's oscillatory thin-airfoil theory and Platzeret al [4] applied an unsteady panel code to this problem.Very recently, it has been recognized that flapping wingpropulsion may be more efficient than conventional pro-pellers if applied to very small scale vehicles, so-calledmicro-air vehicles, because of the very small Reynoldsnumber encountered on such vehicles. For this reason,an experimental and computational research program isin progress by the authors to investigate the propulsivecharacteristics of flapping airfoils. Of special interest isthe determination of the dependence of the thrust forceon the amplitude and frequency of oscillation and onthe flow Reynolds number, especially the combinationof these parameters which leads to dynamic stall andtherefore loss of thrust and propulsive efficiency.Another problem of potential practical interest is the ex-traction of power from an air or water stream by an air-foil which has the plunge and pitch degrees of freedom.As is well known, this combined motion may easily leadto explosive bending-torsion wing flutter. However, asdemonstrated by McKinney and DeLaurier [5], the flut-tering airfoil can be used as an oscillating-wing windmill(wingmill) for power generation. Here again it will be
useful to identify the dynamic stall boundary which lim-its the generating capacity of the wingmill.For these reasons it is the objective of this investiga-tion to identify the dynamic stall boundary of a NACA0012 airfoil which has either the pure plunge or the com-bined pitch/plunge degrees of freedom. Recent watertunnel flow visualization experiments by Jones et al [6]and Lai et al [7] have provided a considerable amount ofinformation about the flow characteristics of sinusoidallyplunging airfoils, but these experiments were largely lim-ited to the visualization and measurement of the wakecharacteristics. Also, Tuncer and Platzer [8] exploredthe effect of plunge amplitude on the thrust of a sinu-soidally plunging airfoil using a compressible thin-layerNavier-Stokes solver, but they did not consider flows un-dergoing dynamic stall. In the present paper the sameNavier-Stokes solver is applied to the determination ofthe dynamic stall boundary of the NACA 0012 airfoil atlow subsonic Mach numbers. Inviscid panel code solu-tions are also compared with the Navier-Stokes solutionsfor attached flows.
Numerical Method
A compressible, thin-layer Navier-Stokes solver is em-ployed for computing the flow over a plunging or pitch-ing and plunging airfoil. The flowfields are analyzed interms of instantaneous velocity fields and the aerody-namic loads based on the surface pressure distribution.A panel code with wake vortices is also employed.
Navier-Stokes solver
The strong conservation-law form of the 2-D, thin-layer,Reynolds averaged Navier-Stokes equations is solved us-ing an approximately factored, implicit algorithm. Theconvective terms are evaluated using the third order ac-curate Osher's upwind biased flux difference splittingscheme. The governing equations in a curvilinear co-ordinate system, (£, £), are given as follows:
ftQ + flfcF + dcG = Re-ldcS (1)
where Q is the vector of conservative variables,(p,pu,pw,e), F and G are the inviscid flux vectors,and S is the thin layer approximation of the viscousfluxes in the £ direction normal to the airfoil sur-face. The pressure is related to density and total en-ergy through the equation of state for an ideal gas,P=(>y-l)[e-p(u2+w2)/2\.A fully turbulent flow is assumed to exist which is mod-eled by the Baldwin-Lomax turbulence model.
Computational DomainThe computational domain around the airfoil is dis-cretized with a single C-grid. The plunging or pitchingmotion of the airfoil is implemented by moving the air-foil and the computational grid as specified by the pitchand the plunge motions:
a = —ao cos(kt + <ypi = -hcos(kt) (2)
where ao denotes the pitch amplitude, h the plunge am-plitude (normalized with the airfoil chord), and <j> thephase angle between the pitch and plunge motion. Aphase angle of <t> = 90° therefore means, that the pitchmotion leads the plunge motion by 90 degrees, k is thereduced frequency, defined by k = wc/Voo- Here w isthe circular frequency, c the chord length and V^ thefree-stream velocity.Boundary ConditionsBoundary conditions are applied on the airfoil surfaceand at the farfield boundaries. On the airfoil boundarythe no-slip boundary condition is applied, and the den-sity and pressure gradients are set to zero. The surfacefluid velocity is set equal to the prescribed local airfoilvelocity. At the farfield inflow and outflow boundariesthe flow variables are evaluated using the zero order Rie-mann invariant extrapolation. Further details are de-scribed by Tuncer and Platzer [8].
Panel code
In the potential flow solution, UPOT, the flowfield isassumed to be inviscid, irrotational and incompress-ible. The unsteady flowfield is represented by distributedsource and vortex sheets on the airfoil surface and con-centrated vortices in the wake. As the unsteady flow so-lution marches in time, a vortex is shed from the trailingedge of the airfoil and converted downstream with thelocal velocity. The velocity field is expressed in termsof a disturbance potential. Laplace's equation is thensolved for the disturbance potential by superimposingthe source/sink and vorticity singularity solutions to sat-isfy the boundary condition on the airfoil surface. Amore detailed description is given by Platzer et al [4].
Results
We first computed flowfields as a NACA0012 airfoil un-dergoes a pure plunge oscillation at various amplitudesand reduced frequencies, and then computed the flow-fields for combined pitch and plunge motions. The flow-fields were mostly computed at the free-stream Mach
Fig. 4 Propulsive efficiency for attached and separatedflows.
number of M = 0.3 and the Reynolds number of Re =1 • 106, which is based on the airfoil chord. Additionalcomputations were also performed for a Reynolds num-ber of 5 • 106. However, no significant differences in theflowfields were observed. The Navier-Stokes solutionswere obtained on a C-type grid, which is of 121x62 size.A grid study with 241x61, 241x91 and 311x71 size gridsshowed that the computed results were not sensitive tothe grid size. In the panel code solutions 75 panels wereemployed on the airfoil surface.
Pure Plunge Oscillation
In Figures 1 and 2, the results of thrust computations forthe harmonically plunging NACA 0012 airfoil are shown.The reduced frequency, based on the airfoil chord, was
varied between 0.25 and 3.0 and the non-dimensionalplunge amplitude, based on the airfoil chord, rangedbetween 0.1 and 1.4. For a given reduced frequency,the amplitude was gradually increased until the combi-nation of frequency and amplitude which produced themaximum thrust could be identified. In the lower re-duced frequency range, shown in Figure 1, the thrustis observed to decrease quite rapidly as soon as a suffi-cient amount of dynamic stall is encountered. It can alsobe seen, that the Navier-Stokes predictions are in goodagreement with the incompressible potential flow predic-tion up to the dynamic stall onset point, using the panelcode. At higher reduced frequencies, shown in Figure 2,the onset of dynamic stall has a much more benign ef-fect on the achievable maximum thrust. Indeed, it is seenthat the thrust still increases after encountering dynamic
Fig. 5 Attached Flow, k = 0.8, h = 0.4Fig. 8 Fully separated flow, k = 0.8, h = 0.7
Fig. 6 Onset of flow separation, k = 0.8, h = 0.5
Fig. 7 Light flow separation, k = 0.8, h = 0.6
stall and then remains fairly constant with increasingamplitude. Again, the Navier-Stokes and the inviscidflow predictions agree at lower plunge amplitudes wherethe flow remains attached over the complete oscillationcycle.If one plots the dynamic stall onset points one obtainsthe stall boundary shown in Figure 3. Evidently, themaximum achievable thrust is a function of the productof reduced frequency and amplitude hk. This productmerely represents the maximum non-dimensional plungevelocity. One can either choose to select a large ampli-tude and a small frequency or vice versa, but as soonas the product exceeds a critical value, dynamic stallis encountered which limits the achievable thrust. Onthe other hand, if one wants to optimize the propul-sive efficiency it is advantageous to operate in the lowfrequency/large amplitude range as shown in Figure 4.Here the panel code prediction is shown as the solid line.The open circles and the starred symbols indicate theNavier-Stokes predicted efficiencies for cases just beforeand after the occurrence of the dynamic stall, corre-sponding to the cases shown in Figure 3. It is seen thatthe efficiency drops rapidly, in particular in the low fre-quency range. The dynamic stall mostly occurs whenthe airfoil passes through the zero amplitude positionbecause it then experiences the maximum incidence an-gle.Figures 5-8 show the velocity field around the leadingedge when the airfoil passes the mean position duringthe upstroke, as the plunge amplitude changes from 0.4to 0.7 at a constant reduced frequency of k — 0.8. It isseen that at h = 0.4 the flow is still fully attached, butincreasing amounts of flow separation are observed asthe plunge amplitude increases. Additional details aregiven by Walz in Reference 12.
If the airfoil is set into a combined pitch and plungemotion, one has to pay attention to the effective angle-of attack the airfoil experiences. As discussed by Jonesand Platzer [9], for small pitch amplitudes, correspond-ing to Figure 9a, thrust is produced whereas at higherpitch amplitudes, corresponding to Figure 9b, drag isproduced and power is extracted from the flow.
The thrust coefficient and the propulsive efficiency ofa NACA 0012 airfoil whose combined pitch oscillationabout the mid-chord leads the plunge oscillation by aphase angle <p (which varies from 30 to 150 degrees) isgiven in Figures 10 and 11. This case was recently in-vestigated by Isogai et al [10] for a Reynolds number of1 • 105 using a Navier-Stokes solver in combination with aBaldwin-Lomax turbulence model. As can be seen fromFigure 10, the non-dimensional plunge amplitude is 1and the pitch amplitude is 10°. This corresponds to athrust producing case, Figure 9a. To facilitate a directcomparison with Isogai et al [10] the plunge amplitudeand the reduced frequency are based on the half-chordand the thrust coefficient is denned as
Thrust
and the computations were performed at the Reynoldsnumber of 105.
The two Navier-Stokes computations are in qualitativeagreement, but the large differences in the predicted val-ues at k = 0.15 require further investigation. Similarqualitative trends are observed for the propulsive effi-ciency shown in Figure 11, but significant quantitativedifferences are again found for A; = 0.15.
b).
Fig. 9 Combined pitch/plunge oscillation with a) a smalland b) a large pitch amplitude
ig8o«
0.5
20 40 60 80 100 120 140Phase Angle
— Present.... Isogai et al.
Fig. 10 Thrust coefficient versus phase angle ath= 1.0,a0 = 10°, Re = 1 • 105
An increase of the pitch amplitude eventually leads to asign change of the effective angle of attack. The airfoilmotion now occurs as shown in Figure 9b. As pointedout for example by Duncan [11], the airfoil now is able toextract energy out of the airstream which may cause ex-plosive airfoil bending-torsion flutter. Therefore, an air-foil which is forced to oscillate in such a pitch and plungemode will run under its own power, i.e., as a flutter en-gine, when the phase difference between pitch and plunge
— UPOT,o Experiment at V^ = 6.2m/sec,* Experiment at V&, = 8.Qm/sec
12 Comparison of computed power of experiment ofMcKinney & DeLaurier, Plunge amplitude = 0.3,pitch amplitude = 25°
is close to 90 degrees or a smaller angle down to about15 degrees, but it will stop when the phase difference isreduced to zero. McKinney and DeLaurier [5] exploredthe feasibility of using such an oscillating-wing windmill(wing-mill) for power generation. Using an airfoil whichoscillated with a pitch amplitude of 25 degrees and anon-dimensional plunge amplitude of 0.3 they measuredthe power values shown in Figure 12. These experimen-tal data are affected by the occurrence of dynamic stall,especially at the higher wind speed of 8 m/sec. Neverthe-less, the inviscid panel code predictions agree reasonablywell with the measured power values.
As in the case of thrust production, it is of interest toexplore the conditions for maximum power extraction.Figure 13 shows the dependence of power coefficient onreduced frequency, pitch amplitude and phase angle be-tween pitch and plunge for a NACA 0012 airfoil whichis oscillating in plunge with a non-dimensional plungeamplitude of 0.2. These results are based on the invis-cid panel code. To determine the stall boundary at aphase angle of 100 degrees the computations were re-peated with the Navier-Stokes code. For the three re-duced frequencies shown on Figure 13, the Navier-Stokescalculations predicted no flow separation, but an increaseof the pitch amplitude by 2 degrees produced the onset ofdynamic stall in each case. Therefore, the curves shownin Figure 13 can be regarded as the wingmill operatinglines close to stall. It should be noted that the maximumeffective angle of attack is approximately the same for
0.07
0.06
0.05
: 0.04
65 70 75 80 85 90 95 100 105 110 115Phase Angle
x a0 = 16°* a0 = 20°o a0 = 24°
Fig. 13 Computed power coefficient (UPOT) versus phaseangle; plunge amplitude h = 0.2.
2.35
m 2.2c.0T3SJJ2.15
2.1
2.05
k=0.5
/ k=0.25
/
-O^.-X' -*''~ae •'•o....0..0....0
..*>'
.0
k=0.1n-0"'
65 70 75 80 85 90 95 100 105 110 115Phase Angle
x a0 = 16°* a0 = 20°o a0 = 24°
Fig. 14 Propulsive efficiency (UPOT) versus phase angle;plunge amplitude h = 0.2
each combination of reduced frequency and pitch ampli-tude, because the angle of attack induced by the plungemotion increases with increased reduced frequency. Ifthe induced angle of attack due to the plunging motion,on, is considered as
on = arctan(/ifc)
one obtains the following effective angles of attack, ae:
Hence, the effective angles of attack are in a range ofvalues where one expects the onset of flow separation.This consideration provides a plausible explanation forthe occurrence of stall predicted by the Navier-Stokescode. It can also be seen that the maximum power ex-traction occurs at phase angles between 80 and 110 de-grees. This is consistent with the experimental findingsof McKinney and DeLaurier. Finally, in Figure 14 thepanel code computed power extraction efficiencies areplotted for the same parameter combinations shown inFigure 13. For simplicity, the efficiency is denned hereas the inverse value of the propulsive efficiency. This isin contrast to the efficiency definition used by McKinneyand DeLaurier. Therefore, efficiency values greater thanone are obtained, where a "low value" corresponds to ahigh efficiency. It is seen that a wingmill running at areduced frequency of 0.1 has a slightly better efficiencythan one running at a higher frequency. Again, the high-est efficiencies occur at phase angles between 80 to 110degrees.
Concluding Remarks
Thin-layer Navier-Stokes computations were performedfor low subsonic flow over a N AC A 0012 airfoil oscillatingin either the pure plunge or the combined pitch/plungemode. Parametric variation of the frequency and ampli-tude of the pure plunge oscillation showed that dynamicstall is encountered as soon as the non-dimensionalplunge velocity hk exceeds values close to 0.35. Addi-tional calculations were performed for three reduced fre-quency values 0.1, 0.25 and 0.5 to determine the maxi-mum power of a NACA 0012 airfoil which operates asa wingmill. Further studies are necessary to explorethe more precise nature of the dynamic stall behaviorof plunging and pitching/plunging airfoils over a widerrange of Mach and Reynolds numbers. To this end, thecomputations need to be repeated with higher order tur-bulence models and a proper transition model.
References
1. Carr, L.W. and Chandrasekhara, M.S., "Compress-ibility Effects on Dynamic Stall", Progress in AerospaceSciences , 32, 523-573, 19962. Ekaterinaris, J.A. and Platzer, M.F., "Computa-tional Prediction of Airfoil Dynamic Stall", Progress inAerospace Sciences, 33, 1998, (to be published)3. Garrick, I.E., "Propulsion of a Flapping and Oscillat-ing Airfoil", NACA TR-567, 19374. Platzer, M.F., Neace, K.S., Pang, C.K., "Aerody-namic Analysis of Flapping Wing Propulsion", AIAApaper No. 93-0 484, January 19935. McKinney, W. and DeLaurier, J., "The Wingmill: AnOscillating-Wing Windmill", Journal of Energy, Vol. 5,No. 2, 109-115, March-April 19816. Jones, K.D., Dohring, C.M., Platzer, M.F., "WakeStructures Behind Plunging Airfoils: A Comparison ofNumerical and Experimental Results", AIAA paper No.96-0078, January 19967. Lai, J.C.S., Yue J., Platzer, M.F., "Control ofBackward Facing Step Flow Using a Flapping Airfoil",ASME Fluids Engineering Division Summer Meeting,FEDSM97-3307, June 19978. Tuncer, I.H. and Platzer, M.F., "Thrust Generationdue to Airfoil Flapping", AIAA Journal, Vol. 34, No. 2,324- 331, February 19969. Jones, K.D. and Platzer, M.F., "Numerical Compu-tation of Flapping Wing Propulsion and Power Extrac-tion", AIAA Paper No. 97-0826, January 199710. Isogai, K., Shinmoto, Y., Watanabe, Y., "Effects ofDynamic Stall Phenomena on Propulsive Efficiency andThrust of a Flapping Airfoil", AIAA Paper No. 97-1926,June 199711. Duncan, W.J.,"Introductory Survey", AGARDManual on Aeroelasticity, Vol. I12. Walz R., "A Computational Investigation of theDynamic Stall Boundaries of the NACA 0012 Air-foil Oscillating in Pure Plunge or in the CombinationPitch/Plunge Mode", TU Karlsruhe, June 1998
Acknowledgments
This investigation was supported by the Naval ResearchLaboratory, project monitor Kevin Ailinger. Also, theauthors gratefully acknowledge the assistance of Dr.Kevin Jones.
