Wake structure and similar behavior of wake profiles downstream of a plunging airfoil

Ali R.DAVARI

Department of Mechanical and Aerospace Engineering,Science and Research Branch,Islamic Azad University,Tehran 147789-3855,Iran

Wake structure and similar behavior of wake profiles downstream of a plunging airfoil

Ali R.DAVARI

Department of Mechanical and Aerospace Engineering,Science and Research Branch,Islamic Azad University,Tehran 147789-3855,Iran

Very limited attention has already been paid to the velocity behavior in the wake region in unsteady aerodynamic problems.A series of tests has been performed on a flapping airfoil in a subsonic wind tunnel to study the wake structure for different sets of mean angle of attack,plunging amplitude and reduced frequency.In this study,the velocity profiles in the wake for various oscillation parameters have been measured using a wide shoulder rake,especially designed for the present experiments.The airfoil under consideration was a critical section of a 660 kW wind turbine.The results show that for a flapping airfoil the wake structure can be of drag producing type,thrust producing or neutral,depending on the mean angle of attack,oscillation amplitude and reduced frequency.In a thrust producing wake,a high-momentum high-velocity jet flow is formed in the core region of the wake instead of the conventional low-momentum flow.As a result,the drag force normally experienced by the body due to the momentum deficit would be replaced by a thrust force.According to the results,the momentum loss in the wake decreases as the reduced frequency increases.The thrust producing wake pattern for the flapping airfoil has been observed for sufficiently low angles of attack in the absence of the viscous effects.This phenomenon has also been observed for either high oscillation amplitudes or high reduced frequencies.According to the results,for different reduced frequencies and plunging amplitudes,such that the product of them be a constant,the velocity profiles exhibit similar behavior and coalesce on each other.This similarity parameter works excellently at small angles of attack.However,at near stall boundaries,the similarity is not as evident as before.

©2017 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1.Introduction

During the past two decades,the problem of an oscillating airfoil or wing from aerodynamic perspective grabbed much more attention because ofits wide applicability in various practical problems.An airfoil oscillating in pitch or plunge or a combination of them has many applications in biology and biomechanics1,2,flutter analysis and other aeroelastic surveys,3aeronautical applications4and more recently in wind turbines.5–9Among the different aspects of wind turbine aerodynamics,the unsteady wake behavior of a blade undergoing an oscillatory motion is in the forefront.10–13

Also,in the recent years with the advent of micro air vehicles(MAVs),more attention has been paid to this issue.MAVs are small-size flying vehicles and the next generation of them,exploiting the modern technologies,would even be as small as common insects.Today,there is a continuing and increasing demand to explore and understand the physics of a flapping wing in biology to adopt or modify the concept for design of modern MAVs.The aerodynamic knowledge and the associated prediction and modeling tools to handle the problems encompassing the flapping motion are thus the basic requirement for implementing the idea in human-made insects.14

Generally speaking,the most important and dominant nondimensional parameter to characterize the unsteady flows is the Strouhal number or reduced frequency.Of equal importance is the Reynolds number,which affects the aerodynamic behavior of the flapping airfoil or wing.Usually,the birds fly at rather high Reynolds numbers,while most insects operate within low Reynolds number range,in which the flow separates extensively from the leading edge.15

Cebeci et al.16were the first ones to resolve the normal force vector into either thrust or drag and lift.They explained that a flapping airfoil is exposed to an effective rather than geometric angle of attack.This is due to the induced angle of attack resulting from downstroke or upstroke motion of the flapping body.This phenomenon,known as Knoller-Betz effect,has been verified experimentally by Katzmayr17in 1922.He inserted a fixed airfoil in an oscillatory free stream and reported an average thrust on the airfoil.

An airfoil flying with the constant velocityU∞is considered.If the airfoil starts to descend with the velocityw,it experiences an angle of attack α=arctan(w/U∞)which can be assumed to be α =w/U∞for small values.The lift generated by this airfoil has a small component parallel to and in the opposite direction ofU∞,which can be thought of as thrust force.Likewise,the upstroke motion of the airfoil develops a drag force instead of thrust.Sinusoidal up and down motion(plunge or flapping motion)then generates a sinusoidally varying small thrust force(Fig.1)16,provided that the viscous effects are sufficiently small.In this figure,L,NandTdenote lift,drag and thrust,respectively.Furthermore,hAis the plunging amplitude andz(t)is the vertical distance from a reference position.

According to Kelvin’s theory,the circulation about a closed path remains constant with time.Thus,if the vorticity of a certain segment on an airfoil changes,a counter-reacting vortex with the same strength would shed from the trailing edge.For an airfoil in harmonic pitching or plunging motions,the total circulation around the airfoil is a strong function of time and a periodic vortex shedding into the wake region is also likely to occur.

Von Ka´rma´n and Burgers.18have modeled the wake structure at low Reynolds numbers by two streamwise rows of vortices of different signs.This system of streamwise vortices to model the wake structure is known as Ka´rma´n vortices.Fig.2 shows this arrangement schematically.

If the vortices on the upper and lower rows change their positions,such that the upper vortices are counter clockwise and the lower are clockwise,the arrangement would be the one illustrated in Fig.3,which is known as reverse Ka´rma´n vortex street.In this case,the time averaged velocity indicates an extra momentum or jet flow which develops thrust.

As the distance between the clockwise and counter clockwise vortices increases,the associated drag or thrust developed by the wake structure also increases.However,when the two rows of vortices are coalesced,the wake can no longer produce drag or thrust.The wake structure in this case is known as neutral wake and is shown in Fig.4.

Jones et al.19arranged extensive water tunnel flow visualization surveys on the wake of a plunging airfoil.Fig.519shows the drag and thrust developing wake structures.As can be observed,for the drag producing wake,the clockwise vortices are at the upper rows and the counter clockwise ones are at the lower rows.For the thrust producing wake,the directions of the vortices are reversed.

Taylor et al.20investigated the flapping frequencies and amplitudes of several species of birds,bats and insects,and discovered that they mostly fly within a Strouhal number range between 0.2 and 0.4.The Strouhal number is defined asSr=fA/U∞,wherefis the flapping frequency andAthe wake width.The importance of this parameter in unsteady aerodynamic was also underlined by Ref.20who extended the linearized potential flow theory to study the incompressible flow past oscillating airfoils.He named this parameter the reduced frequency.

Once the role of the reduced frequency has been highlighted,it has been realized that an important feature of a flapping airfoil,namely the starting vortices shedding from the airfoil trailing edge,has been taken into account in the Knoller–Betz model.15He showed that the ratio of two characteristic speeds is a dominant parameter describing the flapping motion.This similarity parameter,usually designated byk,is the reduced frequency,and an airfoil of chordc,exposed to a free stream velocityU∞and undergoing a flapping frequencyf,is defined ask=πfc/U∞.This parameter can be thought of as a measure of the flapping velocity to the flight speed.

Define a dimensionless parameter,h=hA/c,wherehAis the plunging amplitude,and the relationship between the productkhand the Strouhal number can be expressed askh=πhA/(ASr).The productkhand consequently the Strouhal number illustrate the induced angle of attack,developed by upstroke and downstroke motions of the flapping airfoil,i.e.,αeff=arctan(kh).

In a recent work,Khalid et al.21proposed a criterion based on the Strouhal number to establish equivalence between a pitching motion and the corresponding plunging motion using the distance traveled by the trailing edge in each case.They claimed that under this criterion,the aerodynamic coefficients for the two motions match well.

Several attempts have already been made to treat the inviscid plunging flat plate or airfoil problem and predict the drag or thrust produced by this motion.22–24Over the past two decades,with the advent of digital computers,the viscosity effect has been taken into account using the Navier–Stokes equations.

Lai and Platzer in 199925described the thrust generation mechanism for a NACA0012 airfoil in a water flow of 0.2 m/s at a Reynolds number of about 17000,oscillating in pure plunge at various combinations of the reduced frequency and amplitude.Fig.625shows their findings.They observed the classic Ka´rma´n vortex street shed from the stationary airfoil.As the airfoil starts to oscillate in plunge with increasingkhin Fig.6(b)and(c),the vortex wake structure changes until a reverse Ka´rma´n vortex street is achieved(Fig.6(d)).Note that unlike the notation adopted in the present paper,the reduced frequency in Ref.25has been defined ask=2πfc/U∞.

They reasoned that the upper row of vortices in the reverse Ka´rma´n vortex street has counter clockwise vortices,whereas the lower row has clockwise ones.The flow then would be entrained between the vortex rows in such a manner that the averaged velocity distribution during an oscillation cycle in planes perpendicular to the airfoil chord is that of a jet profile,and consequently a thrust force is developed on the airfoil.They observed that this thrust increases as frequency and amplitude of oscillation increase.

Fig.6 illustrates that the reverse Ka´rma´n vortex pattern or the thrust producing phenomenon occurs for certain values ofkhbecause the transition from the drag-producing Ka´rma´n street shed from the stationary airfoil shown in Fig.6(a)to the thrust-producing reverse Ka´rma´n street occurs via the shedding of the vortex pairs in Fig.6(b)and(c).Young and Lai26pointed out that the vortex-pair shedding observed by Lai and Platzer25is caused by the interaction between bluffbody type natural shedding from the trailing edge and the motion of the airfoil.

Jones et al.19were the first ones to discover the relationship between the productkhand the wake pattern.They proposed that for the values ofkhlarger than about 1.5,the vortex shedding is asymmetric and the angle of attack induced by the plunging motion could be high enough to encounter the dynamic stall issue.They have shown that in such circumstances,the thrust generating pattern would be deteriorated and can be changed to the conventional drag producing pattern.

In the recent years,it has been well understood that near the dynamic stall boundary and for sufficiently large Strouhal numbers,the thrust generated by a plunging airfoil would be maximized.Young and Lai27for the NACA0012 have shown that for a givenkh,and hence the Strouhal number,a flapping motion at a higher reduced frequency and a lower amplitude generates more thrust than the corresponding case when operating at a lower frequency and a higher amplitude.

Up to now,valuable information is achieved,which sheds a lot of light to the problem of a plunging airfoil and its wake structure.However,the surveys undertaken so far on this issue have mostly been restricted to qualitative and comparative flow field study on NACA airfoils and their thrust generation mechanism.In this paper, an experimental survey was performed on a wind turbine blade section oscillating in pure plunge to investigate the wake velocity pro files for several combinations of the reduced frequency and plunging amplitude.

The role of the parameterkhon wake structure has been studied and observed that the wake velocity pro files with different values of reduced frequency and plunging amplitude while their product is the same coalesce on each other and resemble a similar shape and behavior.This analysis can be useful in the circumstances when the turbine blade undergoes flapping motion.

2.Experimental apparatus and setup

The experiments were performed in a subsonic wind tunnel of closed circuit. The test section dimensions are 800 mm×800 mm×2000 mm.The static pressure inside the test section could be varied by the valves provided around it.In this tunnel,the airspeed is controlled by setting its variable-pitch fan rotational velocity and pitch angle.A maximum velocity of 100 m/s can be attained in the test section.

In these experiments,the velocity profile downstream of an airfoil was measured,while the airfoil was oscillating in plunge mode in a reduced frequency range of 0.01 to 0.1 for three mean angles of attack of 0°,5°and 10°.The plunging amplitude to the chord ratio was 0.14,0.2 and 0.32.The free stream velocity was constantly set to 30 m/s corresponding to a Reynolds number of 4.2×106.

The model considered in the present experiments is the airfoil section at 68%of the span of a 660 kW wind turbine blade.The aerodynamic loading at this section of the blade has been found to be more critical.The model has been manufactured by composite materials having a smooth surface.A steel shaft was provided for this model as the oscillation axis in pitching motion.For the present experiments,to study the plunging behavior of this model,the aforementioned shaft acts as the point to transfer the heaving motion of the oscillation mechanism to the model.This shaft was located at 25%of the chord from the leading edge.The airfoil shape and the model installed in the test section are shown in Fig.7.The model chord length was 250 mm.

An oscillation mechanism was designed and manufactured for these experiments to convert the rotational motion of an electric motor into the reciprocating motion by means of crank shaft,rods and joints.The maximum oscillation amplitude in this system is 8 cm with a frequency range from 1 to 4 Hz.The oscillations were measured by a potentiometer.Fig.8 shows this system.

A rake was used to measure the transverse total pressure distribution downstream of the model.It consisted of tiny steel pitot tubes of 2.5 mm external diameter.The tubes’spacing was 3 mm at the center and 20 mm at the ends.The rake has been located at a constant distance of 1.5 chord length downstream of the model.Each pitot tube was connected to a pressure transducer via a plastic tube.Different tube lengths and materials were examined to find the best combination to impart as minimum time lag as possible to the transducer.Fig.9 shows the rake installed behind the model in the test section.A schematic view of rake arrangement and the associated nomenclature is shown in Fig.10.

The output signals of the potentiometer together with those from each transducer were read by a 64 bit A/D board of NIDAQ-64E-3 and a terminal board of SCB-100 placed into the computer.The data acquisition in the present experiments was performed during several plunging oscillation cycles and 300 output samples have been recorded during the oscillations.

3.Results and discussion

The results presented in this paper can be divided into two sections.The effects of the reduced frequency,plunging amplitude and mean angle of attack on wake structure and the onset of the thrust producing wake pattern are discussed in the first section followed by the result discussing the similar behavior of the wake velocity profiles.

3.1.Wake survey results

Fig.11 shows the hysteresis loops of velocityu/U∞behind the model at a longitudinal distance 1.5 chord downstream for three points located above the stationary location of the trailing edge(TE),and three points below it for a plunging amplitude ofhA/c=0.32.For the upper measuring positions,the velocity hysteresis loops are clockwise,while the lower ones are counter clockwise.For the mid points in either halves,both clockwise and counter clockwise loops are observed which indicates that both time lead and lag exist in this region forming an 8-figure shape in the hysteresis loop.Furthermore,in the mid region where is directly exposed to the plunging wake,the width of the loops is more than those in the upper and lower positions due to the unsteady effects.

For sinusoidal plunging oscillations of the model,to satisfy the trailing edge boundary condition,i.e.the Kutta condition,the vortices shed into the wake region are clockwise during the down stroke motion where the induced angle of attack increases,and change sign to counter clockwise during upstroke.These vortices are periodically shed into the wake in each oscillation cycle.

According to Fig.11,forhA/c=0.32 at a reduced frequency ofk=0.059,the uppermost measuring points are exposed to counter clockwise vortices reducing the velocity at these positions and make a clockwise hysteresis loop of velocity during an oscillation cycle.Accordingly,the lowermost positions under consideration are faced with clockwise vortices and exhibit a counter clockwise loop.As stated in the previous section,this is the reverse Ka´rma´n vortices pattern(Fig.3),which is the thrust producing wake.In this pattern,the clockwise vortices are in the lower halves and counterclockwise ones are in the upper halves of the wake profile as is the case in Fig.11.

The hysteresis loops of velocity for the same conditions as those in Fig.11 with a smaller plunging amplitude,namelyhA/c=0.14,are shown in Fig.12.Evidently,for this lower amplitude,the hysteresis loop at the uppermost position is counterclockwise and changes sign to clockwise for the lowermost point,while the loops for the mid points in the upper and lower halves still have the 8-figure shape,containing both clockwise and counterclockwise vortices.

For the combinations of the plunging amplitude and reduced frequency in Fig.12,from the signs of the hysteresis loops in the uppermost and lowermost measuring points,it can be inferred that the vortices at the upper half of the origin are clockwise and those at the lower half are counterclockwise.In this arrangement,the velocities at the upper and lower regions in the wake are higher than those at the points near the origin where the TE at its static condition locates.

According to Fig.2,this is the conventional drag producing wake pattern,in which the upper rows of the vortices are clockwise and the lower rows are counter clockwise.In this case,the momentum deficit downstream in the wake region exerts drag on the body.

Thus,the wake pattern in an oscillatory plunging motion of an airfoil can either be drag producing,i.e.the conventional case,or thrust producing,depending on the oscillation frequency and amplitude as well as the static angle of attack.

Impact of the reduced frequency on behavior of the velocity hysteresis loop at a point near the origin,which is directly exposed to the wake,is shown in Fig.13.As the reduced frequency increases,the vertical speed of the model and consequently the induced angle of attack seen by the model increase as well.

The signs of the loops are the same for both frequencies,indicating that the total amount of vorticity shed into the wake during each oscillation cycle at the position under consideration does not change sign for both reduced frequencies.As the oscillation frequency changes,even for a constant amplitude,the motion time history obviously changes and as a result,the magnitudes of time lead and lag differ.For this reason,the width of the loop at the higher reduced frequency is more than that for the lower frequency.

Fig.14 shows the instantaneous wake profiles at a reduced frequency ofk=0.047 and plunging amplitude ofhA/c=0.32 for two static angles of attack α0of 0°and 10°.The profiles are shown for the phase angles,ωt=90°and 270°corresponding to downstroke and upstroke motions respectively.

At 0°static angle of attack,shown in Fig.14(a),the thrust producing wake is observed,which is the result of the reverse Ka´rma´n vortices discussed earlier.This is due to the structure and signs of the vortices shed into the different transverse regions of the wake.As the angle of attack increases,these vortices change sign and the reverse phenomenon,i.e.the conventional wake structure,occurs,which results in a drag force,instead of thrust,on the airfoil.

Further,note that the wake profiles for both upstroke and downstroke motions at zero angle of attack in the absence of flow separation,where the potential flow dominates,are nearly the same.However as the angle of attack increases,during the upstroke and downstroke motions different flowfields are formed on the airfoil and the separation point location changes periodically.As a result,the wake profile differs in upstroke and downstroke while both exhibit a drag producing pattern at nonzero angles of attack.

At a smaller amplitude ofhA/c=0.14 and a reduced frequency ofk=0.059,the experiments show that the wake structure is always of drag producing type.Fig.15 shows these profiles for two angles of attack of 5°and 10°.In contrast to the previous case ofk=0.047 andhA/c=0.32,where the momentum loss and consequently the associated drag force were less than the static case,forhA/c=0.14 andk=0.059,the momentum deficits in static and plunging motion are nearly of the same order with an exception in the upstroke motion at α0=10°.

When the airfoil is moving upward,the induced angle of attack seen by the model decreases and the separation point moves downstream.This reduces the momentum loss in the wake region.Further,for these oscillation parameters,the path for vorticity convection to the wake,brought the minimum velocity point to a lower position than that in static case.

As observed from the results,the plunging motion with an amplitude ofhA/c=0.32 can produce either thrust or drag depending on the reduced frequency and angle of attack,while forhA/c=0.14 no thrust producing wake pattern was found for any combination offrequency and angle of attack.Effects of reduced frequency on the instantaneous wake profiles forhA/c=0.32 are shown in Figs.16 and 17 for static angles of attack of 0°and 10°for both upstroke and downstroke motions individually.

At 0°angle of attack,where the thrust producing wake is observed,the momentum enhancement due to the jet effect increases as the reduced frequency increases.This may be attributed to an increase in the strength of the vortices shed into the wake region.However,fork=0.082,this momentum increasing trend suppresses.It seems that the time lag between the motion and the instantaneous flowfield has been changed to a lead.

The overall amount of vorticity is deemed to be reduced in this case as a result of the smaller convection time scale.This leads to a decrease in the jet velocity downstream of the model in the wake compared to the smaller reduced frequency cases.This phenomenon is less pronounced during upstroke motion(Fig.16(b)).It seems that the negative angle of attack seen by the model in this case has justified the aforementioned phenomenon and the maximum wake velocities fork=0.059 and 0.082 have a smaller difference.Note that the velocity increase in upstroke is a little lower than that during downstroke at this angle of attack.

At 10°angle of attack(Fig.17),a drag producing pattern is observed.At this angle of attack,the flow separation is dominated and the reduced frequency has less to do with the wake structure,though a little more favorable behavior of the wake profile is observed at the higher reduced frequency during both upstroke and downstroke motions.At this angle of attack during upstroke motion,the associated decrease in effective angle of attack seems to effectively change the shedding pattern of the vortices from the airfoil and brought the minimum velocity point considerably lower than both the static and the associated downstroke cases.

Similar results were shown in Figs.18 and 19 forhA/c=0.14,where only a drag producing wake was observed for all cases.For both angles of attack examined,as the plunging frequency increases,a more favorable behavior can be observed in the wake profile and the momentum loss decreases,which in turn less drag would be produced.This is more evident at 5°angle of attack during upstroke motion,where the higher frequency oscillations brought the effective angle of attack well below the value at which the viscous effects come into play.

Fig.20 shows the averaged velocity profiles in the wake over one oscillation cycle forhA/c=0.32 at two angles of attack of 0°and 10°.Similar to the instantaneous profiles,for a reduced frequency ofk=0.082,the increasing trend of the jet velocity with frequency stops.Another noteworthy problem in Fig.20(a)is the position of the maximum velocity in the wake profile.This point during a plunging motion moves downward.However,it again moves up as the reduced frequency increases and remains nearly unchanged from the value corresponding to maximum jet velocity.This highlights the role of plunging oscillation frequency in determining the path for shedding of the vortices into the wake.

At an angle of attack of 10°(Fig.20(b)),increasing the reduced frequency is accompanied by a continuous decrease in flow momentum,in contrast to zero angle of attack case.Furthermore,as the reduced frequency increases,the wake width also increases.For a smaller convection time scale,a wider area downstream is affected by the strong vortices shed from the oscillating model.However,the drag of the plunging airfoil is still less than that of the static case.

ForhA/c=0.14,Fig.21 shows the averaged velocity profiles in the wake over one oscillation cycle at two static angles of attack of 5°and 10°.For such drag producing profiles at α0=5°,increasing the reduced frequency is observed to have a favorable effect on the momentum loss and decreases the associated drag.For both angles of attack,the value of the minimum velocity first decreases as the reduced frequency increases from 0.047 to 0.059,and then increases atk=0.082.

The velocity profile in the wake region has been integrated using the momentum theory to determine the axial force developed on the airfoil.Fig.22 shows the variations of this axial force coefficientCAwith the reduced frequency for two amplitudes ofhA/c=0.32 and 0.20.ForhA/c=0.32,at α0=5°,the negative values of the axial force indicate thrust as discussed earlier,while at 0°static angle of attack,the wake is in its conventional form and produces drag force.This value slightly decreases as the reduced frequency increases.

ForhA/c=0.20,the wake structure still produces drag,though the drag developed on the plunging airfoil is less than its static value and decreases as the oscillation frequency increases.At 0°static angle of attack,where the viscous effects are negligible,the wake structure is of thrust producing type at the reduced frequencies higher than about 0.6.It seems that for this amplitude setting,the vortices shed into the wake change sign fromk=0.600 on,to increase the flow momentum and generate thrust instead of drag.

3.2.Similar behavior in wake profiles

To investigate the role of the similarity parameter,kh,on wake profiles,further experiments were performed in different combinations of the reduced frequencies and oscillation amplitudes to make the productkha constant.The associated time averaged velocity profiles are shown in Figs.23–26.For low angles of attack shown in Figs.23 and 24,the wake profiles have been shown for five reduced frequencies and plunging amplitudes such that the productkhis the same for all profiles.

Despite the different time histories for each profile,the overall behavior can be seen to be nearly the same for all.As stated earlier,the reduced frequency and the plunging amplitude justify the longer and shorter time histories along with the amount of lead and lag in motion.As a result,the profiles with the same values ofkhcoalesced on each other regardless of their reduced frequency and amplitude individually.

Note that both the thrust producing pattern at 0°static angle of attack(Fig.23)and the conventional drag producing wake at 5°static angle of attack(Fig.24)exhibit this similar behavior in the sense that the maximum or minimum velocities due to the momentum increase at 0°angle of attack and momentum deficit at α0=5°for all profiles are nearly the same.

For α0=10°,however,the issue of the airfoil stall appears and the separated flows generating the Ka´rma´n street play an important role in the wake structure and behavior.According to previous studies,the static angle of attack for this airfoil has been measured to be about 11°.28The mean angle of attack of 10°is thus in the region of the dynamic stall of the airfoil during both the upstroke and downstroke motion.Note that during the upstroke,the effective angle of attack seen by the airfoil reduces and the stall is postponed to higher angles,and in downstroke motion,the effective angle of attack increases and the stall onset is hastened.

For these conditions,Figs.25 and 26 show that the similar behavior in the profiles is not as evident as that observed at lower angles of attack well below the stall range.The intensive separated flows shed into the wake region,generate additional clockwise upper row and counter clockwise lower row vortices,and deteriorate the similar behavior.In near stall range,the magnitude and direction of the vortices in the wake region depend strongly on both the reduced frequency and the plunging amplitude.For this reason,the profiles failed to resemble a similar behavior for different reduced frequencies and amplitudes despite the product of them was the same.

Note that the reduced frequency determines the amount of lead and lag in the hysteresis loops and the plunging amplitude determines the time history of motion.However some evidences of the similar behavior can still be observed in the wake profiles.This is especially the case in Fig.26 for the upstroke motion in which the effective angle of attack decreases.As a result,less Ka´rma´n vortices are shed into the wake region.

Furthermore,from Figs.25 and 26 at α0=10°,note that the difference in the plunging amplitudes for the samekhis evident at the beginning of the velocity deficit part of the profile.For higher amplitude oscillations,the velocity deficit region extends laterally along the profile,while the magnitude of the minimum velocity would more or less be preserved for all profiles.

4.Conclusions

An extensive test program has been arranged and undertaken to study the wake structure for a plunging airfoil.The airfoil is a critical section of a 660 kW wind turbine blade.The experiments were performed in several combinations of static angle of attack,oscillation amplitude and reduced frequency.

The wake structure downstream of the plunging airfoil shows hysteresis behavior and makes the wake velocities to be different during the airfoil upstroke and downstroke motions.The reduced frequency has been found to be a major contributor in the wake profile shape for the cases where the static angle of attack is well beyond the stall.The time averaged velocity profiles in the wake show that the plunging amplitude,which affects the oscillation time history,is a dominant factor in the wake structure.This parameter along with mean angle of attack determines the direction of the vortices shed into the wake and consequently the direction of the axial force developed on the airfoil.

A clockwise vortex arrangement in the lower halves and counter clockwise in the upper halves of the flowfield downstream designate a reverse Ka´rma´n vortex pattern.In this pattern,a jet flow issues at the core of the wake profile and the fluid momentum increases.An axial force in the opposite direction of the free stream would then be created on the model,which can be thought of as a thrust force.This pattern has been observed for the cases sufficiently below the stall angle where attached flow dominates.

In this case,the thrust generation phenomenon was observed either at high reduced frequency with a fixed amplitude or high oscillation amplitudes at a fixed reduced frequency.With the later case,there would be sufficient time for the vortices to shed widely into the wake and impart their induced effects to the flowfield,while in the former,stronger vortices would be generated and shed into the wake.

The product of the reduced frequency and plunging amplitude has been found to be a similarity parameter in the wake profiles.The wake velocity profiles for different plunging amplitudes and reduced frequencies,such that the product of them was the same,exhibit similar behavior and coalesced on each other.This behavior was more highlighted at the angles of attack well beyond the stall.The degree of similarity decreased at higher angles of attack near the stall region,due to the separated vortices shed into the wake region,which are strong functions of the reduced frequency and amplitude individually.

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16 June 2016;revised 21 August 2016;accepted 5 September 2016

Available online 7 June 2017

E-mail address:ardavari@srbiau.ac.ir

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Hysteresis;

Plunging;

Reduced frequency;

Von Ka´rma´n street;

Wake