effects of wing locations on wing rock induced by forebody vortices

Ma Baofeng,Deng Xueying,Wang Bing

Ministry-of-Education Key Laboratory of Fluid Mechanics,Beihang University,Beijing 100083,China

effects of wing locations on wing rock induced by forebody vortices

Ma Baofeng*,Deng Xueying,Wang Bing

Ministry-of-Education Key Laboratory of Fluid Mechanics,Beihang University,Beijing 100083,China

Previous studies have shown that asymmetric vortex wakes over slender bodies exhibit a multi-vortex structure with an alternate arrangement along a body axis at high angle of attack.In this investigation,the effects of wing locations along a body axis on wing rock induced by forebody vortices was studied experimentally at a subcritical Reynolds number based on a body diameter.An artificial perturbation was added onto the nose tip to fix the orientations of forebody vortices.Particle image velocimetry was used to identify flow patterns of forebody vortices in static situations,and time histories of wing rock were obtained using a free-to-roll rig.The results show that the wing locations can affect significantly the motion patterns of wing rock owing to the variation of multivortex patterns of forebody vortices.As the wing locations make the forebody vortices a two-vortex pattern,the wing body exhibits regularly divergence and fixed-point motion with azimuthal variations of the tip perturbation.If a three-vortex pattern exists over the wing,however,the wing-rock patterns depend on the impact of the highest vortex and newborn vortex.As the three vortices together influence the wing flow,wing-rock patterns exhibit regularly fixed-points and limitcycled oscillations.With the wing moving backwards,the newborn vortex becomes stronger,and wing-rock patterns become fixed-points,chaotic oscillations,and limit-cycled oscillations.With further backward movement of wings,the vortices are far away from the upper surface of wings,and the motions exhibit divergence,limit-cycled oscillations and fixed-points.For the rearmost location of the wing,the wing body exhibits stochastic oscillations and fixed-points.

1.Introduction

Vortex flow over a slender body of revolution has long been recognized being able to produce symmetry breaking at high angle of attack (AOA),even without sideslip.Previous research1–7revealed that development of asymmetric vortices was significantly influenced by tip irregularities.Tip irregularities,probably arising from manufacturing tolerance,will cause the orientations of asymmetric vortices to change alternatively with the rotation of an axisymmetric slender body around the body axis.The asymmetric vortex wakes exhibit a time-averaged multi-vortex structure with an alternate arrangement along a body axis at high AOAs,3,8but the vortical flow may become unsteady at extremely high AOAs.8,9As a higher vortex breaks away from the body,a newborn vortex will be yielded under it.The asymmetric vortices can induce a wing body to produce self-excited oscillations,called''wing rockquot;,where the forebody vortices can induce driving moments on the wings.

The wing rock was first observed in an HP-115 research aircraft with high sweep wings.Therefore,slender delta wings10–17are usually used as simplified models to study self-excited oscillation.Since the n,researchers have believed that the self-excited oscillations are produced primarily by wing vortices over slender wings with sharp leading edges.Nguyen et al.10were among the first to perform a free-to-roll experiment using a slender delta wing with sweep angle of 80°in a laboratory.They successfully simulated the typical limitcycled oscillation experienced by airplanes in flight.Arena and Nelson11discovered,by experiments,that the dynamic hysteresis of vortex positions normal to the wing causes negative damping moments that induce destabilization of the wing in roll and drive rolling oscillations.Levin and Katz12conducted freely rolling experiments using delta wings with sweep angles from 70°to 80°.They found that oscillatory motion occurs only when the sweep angle is more than 75°and that the starting AOA for oscillation is inversely proportional to the sweep angle.Neverthe less,recent experiments13,14showed that some non-slender wings exhibit rolling oscillations,as well.Numerical simulations were also carried out to successfully recover the wing-rock phenomena for slender wings.15–17

Neverthe less,the wing body can also produce wing rock by forebody vortices regardless whether the wings alone are able to oscillate.Brandon and Nguyen18originally found,by experiments,that even with very low sweep wings(26°),a generic wing body with slender forebody could produce periodic oscillatory motions at high AOAs.They found that the shape of the cross section of forebodies has an important effect on rolling oscillations.They also found that oscillatory motion starts at high AOAs and reaches a steady periodic oscillation in considerably shorter time relative to that of a slender wing.However,the amplitudes are still large.Ericsson19postulated,by analyzing the existing data,that the oscillation on a wing body may arise from forebody asymmetric vortices,rather than wing vortices,because the latter is weak and prone to breakdown at high AOAs for low sweep wings.Forebody vortices produce unstable moments on wings,whereas wings are merely taken as a surface on which aerodynamic loads act.However,the motion patterns obtained by various researchers were different,and the experimental results showed some uncertainty,as well.In the experiments by Brandon and Nguyen,18the wing body exhibited periodic oscillations around the zero roll angle and the maximum amplitude approached 45°.However,in the experiments performed by Pamadi et al.20who used another model,the wing body showed no apparent oscillatory motion but barely fluctuated around non-zero roll angles with the amplitude of approximately 7°.Quast et al.21also observed this type of one-sided oscillation,using a wing body model.Ericsson and Beyers22attributed the discrepancy in the experimental results to the Reynolds number effect.Ng et al.23ever attempted to control the wing rock by using micro-blowing on a nose-tip,but not studying the effects of tip perturbations on motion patterns.In recent studies24,25however,it was shown that geometric micro-irregularities on a forebody nose-tip can significantly influence the behavior of the self-exited oscillations of a wing body,resulting in uncertainty in experimental results,although the Reynolds numbers are the same.These self-excited oscillations are attributed to the sensitivity of asymmetric vortex flow to the imperfections of the nose-tip of a slender forebody.The study24also showed that the wing locations can have an effect on wing rock and the wing rock can be weakened with backward movement of wings.Never the less,the study on the effects of wing locations in Ref.24was incomplete,only focusing on limit-cycled oscillations that are just one of wing-rock patterns.

In this paper,a further investigation on the effects of wing locations along a body axis is presented,with emphasis on the combined effects of tip perturbations,wing locations,and angles of attack on the wing-rock patterns.It is anticipated that the tip-perturbation can influence the orientations of asymmetric vortices,and the wing locations and angles of attack can influence the multi-vortex structure in front of wings and vortex strength.As a result,the wing-rock patterns will be altered due to the variation of forebody vortices.

2.Experimental setup

All experiments were carried out in the wind tunnel of Institute of Fluid Mechanics of Beihang University.The wind tunnel is a low speed and closed-return tunnel that can be run with either an open or closed test section.The test sections are 1.5 m wide,1.5 m high and 2.5 m long,with a turbulence level of less than 0.1%.The open test section was used in the present experiments,and the model layout in the wind tunnel is illustrated in Fig.1(a).

The free-to-roll model is shown in Fig.1(b).The model consists of a slender body and a wing with 30°sweep angle and sharp leading edges.The present investigation focuses on wing rock induced by forebody vortices.Thus,a cropped delta wing with sweep angle of 30°was chosen,and the isolated wing cannot produce self-excited oscillations.26The pointed-ogive forebody was tangent to the cylindrical afterbody (diameter D=90 mm).The model was made of aluminum,with a moment ofinertial I=0.007 kg.m2around the body axis and the corresponding non-dimensional moment of inertial I*=0.63 (I*=I/ρL5; airflow density,ρ=1.225 kg/m3;span length of wing,L=390 mm).The moment of inertia was estimated using CAD software and validated through a freely falling method.The model has a 27.5 mm long rotatable nose driven by a small step motor to change the azimuthal angle of the tip perturbation.Previous studies have revealed that circumferential locations of tip perturbations are more important to the patterns of asymmetric vortex flow over a slender body than axial locations that merely influence the level of vortex asymmetry;therefore,in our experiments,only the circumferential locations of a perturbation varied.An micro-particle was placed on the nose-tip as an artificial perturbation,and its location was denoted by the azimuthal angle γ.The zero point of γ was set on the symmetry plane on the windward side,and the direction of γ was defined by the right-hand rule at the body frame OXYZ.OXYZ is an active frame that moves with the model,as shown at the bot-tom right corner of Fig.1(b).The diameter d of the tip perturbation is 0.2 mm.The roll angle φ of the model was identified at the fixed frame xyz,and the zero roll angle corresponds to the level state of the model.The rolling direction was determined by the right-hand rule.The wing varied in experiments for four positions of-X/D=3,4,5 and 6,and the wing locations are denoted by the locations of the wing apex.U sinα is the normal component of the freestream velocity U,and α is angle of attack.

Fig.1 Experimental layout and model.

A free-to-roll rig based on mechanical bearings with high precision was used for the freely rolling experiments.The schematic diagram of the rig was given in the previous study.26Inside the rig,a 12 bit digital optical encoder was installed to record instantaneous roll angles.Roll angular rates were obtained using a fifth order centered difference scheme in terms of the time histories of the roll angles.Before the difference calculation,a filtering procedure was used to eliminate high-frequency noises.On the basis of the obtained roll angular rates,the same difference scheme was applied to calculate the roll angular acceleration.Finally,the rolling moment can be determined from the angular acceleration and the moment of inertia of the model.To demonstrate the reproducibility of the motion patterns,the standard deviation of various types of motion patterns was estimated.The standard deviations of the maximum amplitude for a typical limit-cycled oscillation is 1.2°,3.2°for fixed-points with slight fluctuation,and 4.2°for a chaotic oscillation.

The particle image velocimetry (PIV) system was utilized to identify the orientations and patterns of forebody vortices in static situations of the model.The AOAs of the model varied through sideslip angles for performing PIV more conveniently.The laser sheet for PIV illuminates the leeward side of the forebody normal to the body's axis from one side.The PIV snapshots were taken from a front view,but presented in their mirror images in the following Section 3,and equivalently seen from a rear view.The PIV that we used was a Dantec PIV with dual 350 mJ Nd:Yag lasers.Airflow was seeded with microsized oil particles generated by an atomizer and vegetable oil.The oil particles were illuminated by a sheet of 3 mm thick laser light.Images were taken using a Hisense 4M digital camera(12 bit,2048X2048 pixels)at the maximum 7 frames per second.Image pairs were correlated to determine particle displacement and the n,velocity fields.The 32X32 pixel interrogation windows and 25%window overlap were used.The PIV results for the total deviation of all the velocity vectors σ are taken from the section-X/D=2.5 of a forebody.Typical velocity fields consist of 85X85 velocity vectors in one PIV snapshot;the components u and v of a velocity vector are considered individually.Relative deviation is the ratio of σ to the maximum value among all calculated quantities.The final results show that the relative deviation for u-component is 2.1%,and 3.0%for v-component.

3.Results and discussion

The static PIV results and free-to-roll results are presented in the following.The measurement sections of PIV are always located at the wing apex for each wing location to determine the patterns of the forebody vortices over the wings,so PIV snapshots were taken at four sections of-X/D=3,4,5 and 6 corresponding to four wing locations.The incoming wind speed in free-to-roll experiments is 25 m/s,and the associated Reynolds number Re based on cylinder diameter is 1.61X105;the incoming velocity for PIV is 15 m/s and Re is 0.95X105.The Reynolds numbers can guarantee that boundary layers over the forebody are laminar separation.1,27The angles of attack were selected in a range of 40°–55°where the asymmetric vortices are developed sufficiently and take a multi-vortex pattern.

3.1.A pair of vortices over wings

Fig.2 Static time-averaged PIV results with tip perturbation of γ=30°and level state of wings(φ =0°),rear view.

A pair of forebody vortices exists over the wings as the locations of wings are-X/D=4 at α =40°,as well as-X/D=3 and α =45°(Fig.2,S is the magnitude of X component vorticity).The PIV results were taken in a stationary situation of the model with the level state of the wings(φ =0°).The tip perturbation is located at γ=30°to trigger asymmetric vortices so that the right vortex is higher than the left one.Fig.3(a)shows the variation in the amplitude of wing rock Amaxwith the azimuth angle γ of tip perturbation changing.The maximum roll angle in a time history was chosen as the nominal amplitude of oscillation.Fig.3(b)shows the variation in time-averaged values of time histories with γ.The timeaveraged values demonstrate the equilibrium locations of oscillatory motions.It can be seen that the wing rock was influenced greatly by the azimuth angle γ of perturbation.The wing body exhibits regularly two types of motion patterns with variation of γ.One is a fixed-point with slight fluctuation at γ=45°–145°and 215°–300°,and another is a divergent motion at γ=0°–45°,145°–215°,and 300°–360°.The fixedpoints own various equilibrium locations for various γ(Fig.3(b)).The divergent motion has infinite amplitude theoretically,and Fig.3 displays maximally only up to 180°.Fig.4 presents time histories and phase diagrams of these motions,divergent motion in Figs.4(a)and 4(c)and fixedpoints in Figs.4(b)and 4(d).

For fixed-point motions,the rolling moments acted on the wings consist of statically stabilizing restoring moments and positive damping moments,which is similar to those of the isolated wing.At certain azimuthal angles of tip perturbation where the wing body produces fixed-point motions,the forebody vortices are asymmetric and produce rolling moments even at zero roll angle.Therefore,the equilibrium locations of the wing body are necessarily non-zero roll angles where the rolling moments from both the forebody vortices and the wing flow are balanced.Due to the special locations of the tip perturbations,when the wing body is slightly displaced away from the equilibrium roll angles,the tip perturbations cannot trigger the forebody asymmetric vortices to change their orientations.As a result,the forebody vortices cannot produce any dynamic hysteresis because of the unchanged vortex positions.Hence,for the fixed-point motions,the rolling moments dominating the convergent motion mainly come from the wing flow as the wing body is displaced,especially the damping moments.

For divergent motions,the forebody asymmetric vortices can produce the statically destabilizing moments at low roll angles due to the two-vortex pattern of asymmetric vortices.The destabilizing moments result in exponential divergence of the wing body.

3.2.Three-vortex pattern over wings

With the backward movement of the wings,the forebody becomes longer,thus three vortices being able to exist over the wings.The effects of forebody vortices with a threevortex pattern are more complicated,depending on whether the highest vortex in the vortex system has a significant influence on the wing flow.If the highest vortex is relatively close to the upper surface of the wing and the newborn third vortex is weaker,the wing flow will be dominated by the three vortices together.If the highest vortex is far away from the wing owing to a further backward movement of the wing,the two lower vortices close to the wing will dominate the wing flow and the associated aerodynamic moments.

Fig.4 Time histories and phase diagrams of wing rock at α =40°,-X/D=3.

(1)Wing flow dominated by three vortices together

Three forebody vortices exist over the wings as the locations of wings are at α =45°,-X/D=5,and at α =50°,-X/D=3,as well as at α =52.5°,-X/D=3(Fig.5).Fig.6(a)shows the variation in the maximum amplitude of wing rock and time-averaged values of time histories with the azimuth angle γ of tip perturbation.It can be seen that the wing body regularly exhibits two types of motion patterns with variation of γ.One is a fixed-point with slight fluctuation roughly at γ=45°–145°and 215°–330°,and another is a limitcycled oscillation at γ=0°–45°,145°–215°,and 330°–360°.The fixed-points own various equilibrium locations for various γ,but can change regularly with variation of γ(Fig.6(b)).Fig.7 presents time histories and a phase diagram of these motions.The phase diagram in Fig.7(d)reveals that the selfexcited oscillation in Fig.7(a)is a limit-cycled motion in which the asymptotic behavior of the phase trajectories forms a closed orbit,independent of initial values,and the maximum angular rate are not at zero roll angle.

Fig.5 Static time-averaged PIV results with tip perturbation γ=30°and level state of wings(φ =0°),rear view.

Fig.6 Variation of maximum amplitude and time-averaged values of time histories with azimuthal angle of tip perturbations at α=45–52.5°,-X/D=3,5.

Fig.7 Time histories and phase diagrams of wing rock at α =50°,-X/D=3.

Comparing Fig.3 with Fig.6,we can see that the γ regions for fixed-points in both cases are almost the same,but the motion patterns become limit-cycled oscillations in a range of γ where the original patterns are divergent motions.These results reveal that the highest vortex still has an impact on the formation of fixed-points,but the newborn vortex starts to influence the divergent motion,suppressing the magnitude of divergence.The time history in Fig.4(a)also shows that the divergent motion is an oscillatory motion,but has infinite amplitude.Therefore,the motion can transition to limit-cycled oscillations as the amplitude attenuates.

Fig.8 Roll moments coefficient against roll angle at α =50°,γ=0°.

The rolling moment coefficient Clagainst the roll angle for a limit-cycled oscillation is shown in Fig.8.The rolling moments formed typical''double eightquot;patterns through the dynamic hysteresis effect of the flow fields,which have been found extensively in wing-rock experiments of slender wings.10–12,15–17For limit-cycled oscillations,the rolling moments during the oscillation consist of statically stabilizing restoring moments at whole roll angles,and negative damping moments at low roll angles,but positive damping moments at high roll angles.The statically stabilizing restoring moments are caused by the switching of the wing flow and the forebody vortices with the roll angle.The role of wing flow has been analyzed above.The vortex switching comes from the response of forebody vortices to the tip perturbation.The dynamic hysteresis of the forebody vortices uniquely contributed to the negative damping moments triggering the destabilization of the wing body at low roll angles,because wing flow produces positive damping moments only.The positive damping moments at high roll angles are caused by the dynamic hysteresis of both the wing flow and the forebody vortices.Although the wing flow makes a contribution to the total rolling moment,it is not necessary for triggering and sustaining a limit-cycled oscillation.Hence,the wing flow influences the amplitude and frequency of oscillation only,but it is unable to determine whether the oscillation occurs.

Fig.9 Static time-averaged PIV results with tip perturbation γ=30°and level state of wings(φ =0°),rear view,α=52.5°,-X/D=4.

As the wing moves rearwards,the motion patterns become different,although there are still three vortices over the wing(Fig.9).Fig.10 shows the variation in amplitude and the equilibrium locations of wing rock with γ at certain AOAs and wing locations.The wing body regularly exhibits three types of motion patterns with variation of γ:limitcycled oscillation,apparently chaotic oscillation,and fixedpoint.By comparison with Fig.6,one more type of motion occurs at around γ=90°and 270°which are critical azimuthal angles for switching of orientations of the forebody vortices.

The associated time histories and phase diagrams are presented in Fig.11.The limit-cycled oscillation and fixedpoints are similar to the ones above.The chaotic oscillation in Fig.11(c)seems to switch randomly between two limit cycles,which can be seen more clearly in the phase diagram in Fig.11(d).This type of oscillation is extremely sensitive to the initial condition of the model and the time histories cannot be duplicated,even when the model is released from the same initial roll angle.However,the motion types can be repeated in different runs,and the phase diagrams are the ''eightquot;structures.In addition,the apparently chaotic motion only exists in a relatively narrow range of γ(Fig.6).Specifically,it occurs in the transitional state from one type of fixed-point to another type when the perturbation locations change.The reason for forming apparently chaotic motion is complicated;the three forebody vortices together induce the special oscillations,as revealed in previous study.25

(2)Wing flow dominated by two vortices near wings

As the AOAs are sufficiently high and wing locations are beyond-X/D=5,the highest vortex in the three-vortex system will be far away from the wing and reduce the impact of forebody vortices on the wing flow(Fig.12(a)).Consequently,the wing flow is dominated only by the two vortices near the wing.Fig.13 shows the variation in the amplitude of wing rock and time-averaged values with γ at α =50°, –X/D=6 and α =52.5°, –X/D=5.The motion patterns change significantly by comparison with the ones above.The wing body regularly exhibits three types of motion patterns:fixed-points,limit-cycled oscillations,and divergent motion.The fixedpoints have various equilibrium locations for various γ(Fig.13(b)).Fig.14 presents time histories and phase diagrams of these motions.

Fig.10 Variation of maximum amplitude and time-averaged values of time histories with azimuthal angle of tip perturbations γ at α =47.5°–52.5°,-X/D=4,5.

Fig.11 Time histories and phase diagrams of wing rock at α =50°,-X/D=4.

Although the fixed-points,limit-cycled oscillations,and divergent motions have been mentioned in the cases above,the corresponding γ values are different from the present ones.The present limit-cycled oscillation and divergence occur around γ=90°and 270°,but the divergence in Fig.3 and limit-cycled oscillation in Figs.6 and 10 take place around γ=0°and 180°.The difference comes from the changing of the forebody vortex system dominating the wing flow.In addition,the phase diagrams in Fig.14(b)reveal that the limitcycled oscillation comprises stochastic components,because the orbit trajectories are scattered and unable to completely converge to a limit cycle.The stochastic components most likely arise from intrinsic unsteadiness of the asymmetric vortex wakes downstream.8,9

Fig.12(b)presents the PIV results at the rearmost location of the wing in experiments,and in this case,the highest vortex is further away from the model Fig.12(b)has a larger flow field compared with Fig.12(a).The corresponding motion patterns are shown in Figs.15 and 16.Since the impact of the forebody vortices on the wing is further reduced,the divergent motions around γ=90°and 270°disappear,and only the limit-cycled oscillations remain.Never the less,the limit cycle consists of more stochastic components(Fig.16).

Fig.12 Static PIV results with γ=30°and level state of wings(φ =0°),rear view,α =52.5°.

Fig.13 Variation of maximum amplitude and time-averaged values of time histories with γ at α =50°,52.5°,-X/D=5,6.

Fig.14 Time history and phase diagram of wing rock at α =52.5°,–X/D=5,γ=75°.

Fig.15 Variation of maximum amplitude and time-averaged value of time histories with γ at α =52.5°,-X/D=6.

Fig.16 Time history and phase diagram of wing rock at α =52.5°,–X/D=6,γ=300°.

4.Conclusions

The effect of wing locations along a body axis on wing rock induced by forebody vortices was studied experimentally at a subcritical Reynolds number based on a body diameter.Some conclusions can be drawn as follows:

The wing locations can influence the multi-vortex structure of forebody vortices before the wing,thus significantly affecting the motion patterns of wing rock.As the wing location makes the forebody vortices a two-vortex pattern,the wing body regularly exhibits divergence and fixed-point motion with azimuthal variation of a tip perturbation.For the case with a three-vortex pattern over the forebody,however,the patterns of wing rock become different,and specific motion patterns depend on the impact of the highest vortex and newborn vortex.As the three vortices together influence the wing flow,the wing-rock patterns arefixed-points and limit-cycled oscillations with variation of a tip perturbation.With the wing moving backwards,the newborn vortex becomes stronger,and wing-rock patterns become fixed-points,chaotic oscillations,and limit-cycled oscillations.With a further backward movement of the wing,the vortices arefar away from the upper surface of the wings,and the motions exhibit divergence,limitcycled oscillations and fixed-points.For a rearmost location of the wing,the wing body exhibits stochastic oscillations and fixed-points.

Acknowledgement

The project was supported by the National Natural Science Foundation of China(No.11272033).

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Ma Baofengis an associate professor at Institute of Fluid Mechanics in Beihang University.His main research interests include the investigation of unsteady separated flows and vortex flows in aerodynamics using experimental and computational methods.

2 October 2015;revised 21 March 2016;accepted 28 March 2016

Available online 26 August 2016

Aerodynamics;

Experiments;

Unsteady flow;

Vortex flow;

Wing rock

©2016 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/).

*Corresponding author.Tel.+86 10 82338344.

E-mail address:bf-ma@buaa.edu.cn(B.Ma).

Peer review under responsibility of Editorial Committee of CJA.