Wing Rock Induced by a Hemisphere–Cylinder Forebody

Long-Kun Wei∗ and Bao-Feng Ma†

Beihang University, 100191 Beijing, People’s Republic of China

DOI: 10.2514/1.C032311

Thewing rock induced by a hemisphere–cylinder forebodywas investigated experimentally using an isolated delta

wing andwing body. For the deltawingwith sweep angle of 30 deg, no apparent limit-cycle wing rock occurs at angles

of attack of 0–90 deg. The mean roll angles exhibit nonzero values at angles of attack of less than 15 deg and become

zero at angles of attack of more than 15 deg. For the wing body with a hemisphere–cylinder forebody, apparent wing

rock exists at angles of attack of 0–90 deg; the wing rock is induced by the forebody. The phase diagrams showed that

the wing rockmotion is a typical limit-cycle oscillation at lower andmoderate angles of attack.With increasing angles

of attack, however, stochastic components in wing rockmotion are increased gradually, and the motion types start to

deviate from a limit-cycle oscillation. The phase-locked particle-image-velocimetry measurements for the wing body

revealed that the vortex pair over the forebody exhibits apparent dynamic hysteresis in position and strength during

wing rock, and the dynamic hysteresis of forebody vortices further influence flowfields over the wing, resulting in

asymmetric distributions of wing flow, which provides the driving moments sustaining the wing rock.

Nomenclature

D = diameter of cylindrical body, mmL = span length of wing, mmI� = I∕�ρL5�, nondimensionalmoment of inertia aboutX axis

p� = _ϕL∕U∞, nondimensional roll rate

ReD = U∞D∕ν, Reynolds number based on body diameterU∞ = freestream velocity, m∕sX = streamwise coordinate, mmα = angle of attack, degν = kinematic viscosity coefficient of air, m2∕sρ = density of air, kg∕m3

ϕ = roll angle, degω� = ωL∕U∞, nondimensional vorticity

I. Introduction

W INGS or wing bodies can produce “wing rock” around thebody axis at high angles of attack. Wing rock not only

severely limits the performance of aircraft but also influences theirflight safety. Thus,much attention has been devoted to understandingthe reason behind wing rock and to control it effectively, such asthrough blowing along leading edges of a wing or controllingforebody vortices [1,2]. Slender delta wings [3–7] are usually used assimplified models to study self-excited oscillation. The reason is thatthis phenomenon was first observed in an HP-115 research aircraftthat is used to test the low-speed aerodynamic characteristics ofslender delta wings during the development of the supersonicpassenger airplane Concorde. Researchers have since believed thatthe self-excited oscillations are produced primarily by wing vorticesover slender wings with sharp leading edges. Nevertheless, recentexperiments [8–11] showed that some nonslender wings exhibitrolling oscillations as well.Besides the rolling oscillations generated by isolated wings,

another category of self-excited oscillation is produced by a wingbodywhere the forebody vortices are able to induce drivingmomentson the wings. These driving moments trigger rolling oscillations,

regardless of whether the wings alone are able to oscillate. Brandonand Nguyen [12] originally found, by experiments, that even withvery low-sweep wings (26 deg), a generic wing body with slenderforebody could produce periodic oscillatory motions at high anglesof attack (AOAs). They found that the shape of the cross section offorebodies has an important effect on rolling oscillations. They alsofound that oscillatory motion starts at high AOAs and reaches asteady periodic oscillation with large amplitudes in considerablyshorter time relative to that of a slender wing (typically one to twoperiods). Ericsson [13] attributed the forebody-induced wing rock toasymmetric vortex flows over a slender forebody at high AOAs. Thephenomena of the asymmetric vortices over ogive cylinders or coneshave long been recognized [14,15]. The formation of the asymmetricvortices comes from sensitivity of vortex flow to apex irregularities.However, if the slender forebody is replaced with a hemisphere head,thewing rock canweaken but not disappear. Thevortex flow around ahemisphere cylinder is different from an ogive cylinder or cone, andso the reason for the wing rock induced by a hemisphere–cylinderforebody is not clear. Brandon and Nguyen [12] only showed thevariation of amplitudes of the wing rock with AOAs, and no furtherinformation is provided, and so the physical mechanism cannot beenidentified.In this investigation, an isolated cropped delta wing with low

sweep and a wing body with a hemisphere–cylinder forebody areaddressed experimentally. Through comparing the free-to-roll resultsof the isolated wing and the wing body, the sources for driving thewing rock can be determined, either from wings or from a forebody.Particle image velocimetry (PIV) has also been used to study flowmechanisms during the wing rock.

II. Experimental Setup

All experiments were performed in the D4 wind tunnel of theInstitute of Fluid Mechanics of Beihang University. The wind tunnelwas a low-speed, low-noise, and closed-return tunnel that can be runwith either open or closed test section. The open test sectionwas usedin our experiments. The section was 1.5 m wide, 1.5 m high, and2.5 m long, with turbulence level of less than 0.1% and maximumspeed of 60 m∕s. The introduction of the wind tunnel also can befound in [16,17]. Figure 1a showed the schematic diagram of theexperimental layout.A free-to-roll rig based onmechanical bearingswith high precision

was used for the wing rock experiments, as shown in Fig. 1b. Insidethe free-to-roll rig, a 12 bit digital optical encoder was installed torecord instantaneous roll angles. The sampled data were transferredto a host computer through a 16 bit digital input card at a samplingrate of 512 Hz. This rate is sufficiently fast to resolve all wing rockmotions. Roll angular rates were obtained using a fifth-order centered

Received 18 February 2013; revision received 20 June 2013; accepted forpublication 18 September 2013; published online 6March 2014. Copyright©2013 by Bao-Feng Ma. Published by the American Institute of AeronauticsandAstronautics, Inc., with permission. Copies of this paper may be made forpersonal or internal use, on condition that the copier pay the $10.00 per-copyfee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,MA 01923; include the code 1542-3868/14 and $10.00 in correspondencewith the CCC.

*Graduate Student, Key Laboratory of Fluid Mechanics, Ministry ofEducation.

†Associate Professor, Key Laboratory of Fluid Mechanics, Ministry ofEducation; bf-ma@buaa.edu.cn.

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Vol. 51, No. 2, March–April 2014

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difference scheme in terms of the histories of the roll angles. Beforethe difference calculation, a filtering procedure was in place becauseseveral adjacent data points in the histories of the roll angles wereprobably the same and formed many minor stages, owing to the highsampling rate. This effect is equivalent to high-frequency noise. Thisnoise had to be filtered through numerical filtering methods beforecalculating the roll angular rate to achieve better results, as performedby Arena and Nelson [6]. The numerical filter used is a low-pass andfinite-impulse-response filter, which merely smoothed the minorstages of roll angle histories and had no any influence on theamplitude and phase of raw signals. The frequencies of wing rock areobtained using the fast Fourier transformation (FFT) on the histories.FFT was performed based on the steady oscillation phase of wingrock, excluding the initial build-up phase. When the model wasreleased at certain roll angle, it needed to develop a period of time toreach steady oscillation. The values of roll angle over the initialperiod of time were removed in performing FFT because it wasinfluenced significantly by initial roll angles.Figure 2 shows experimental models. The isolated wingmodel is a

flat-plate delta wing with thickness of 4 mm and has doubly-beveledleading-edges of 45 deg and a sting support, as shown in Fig. 2a. Thewing body consists of a hemisphere–cylinder forebody and a wingwith the same geometry of the isolated delta wing. The wings areattached with their root chords parallel to the axis of the cylindricalbody with zero dihedral angle. The models were made of aluminumand mounted on the free-to-roll rig through cone-connection insidethe body. The axis of rotation for the model is along the centerline ofthe cylindrical body. The moment of inertia of the delta wing iwassI � 0.002 kg · m2 around the body axis, and the correspondingnondimensional moment of inertia was I� � 0.67 (airflow density,ρ � 1.225 kg∕m3; span length of wing,L � 300 mm). For thewingbody, I � 0.007 kg · m2, I� � 2.34. The moment of inertia wasestimated using CAD software.The PIV system used for the dynamic flowfields was a Dantec PIV

with dual 350mJNd:Yag lasers. Airflowwas seededwithmicrosized

oil particles generated by an atomizer and vegetable oil. The oilparticles were illuminated by a sheet of 3mm thick laser light. Imageswere taken using a Hisense 4M digital camera (12 bit,2048 × 2048 pixels) at a maximum 7 frames per second. Imagepairs were correlated to determine particle displacement and thenvelocity fields. We used 32 × 32 pixel interrogation windows and25% window overlap. The PIV measurement needed to besynchronously sampled with the model motion by an externaltriggering signal. Considering that the PIV sampling ratewas too low(only up to 7 Hz), however, phase-locked measurements wereperformed to obtain the instantaneous vortex structure for differentroll angles of the model. Twenty-five images were used to obtainphase-locked averaged results. A previous study [18] showed thatPIV results averaged using even 11 image pairs also can revealimportant characteristics of mean flowfields. Similarly, in recentstudies on pitching-up and rotating wings [19,20], 10 or 15instantaneous PIV images were used to construct a phase-averagedimage, and the vorticity patterns obtained are almost the same as theones obtained by averaging of less or more images.The free-to-roll and PIV measurements for the wing body were

conducted at ReD � 1.6 × 105 based on the body diameter(U∞ � 25 m∕s, kinematic viscosity coefficient � 1.39 × 10−5).Table 1 shows the repeatability of free-to-roll experiments with the

mean roll angle and rms of roll angle histories of wing rock. Table 2shows the precision of locked roll angles in PIV measurements. Theexperiments were run for seven times with the wing body atα � 35 deg. The results show the standard deviations are acceptable.The previous analysis [21] based on aerodynamic modeling

revealed that the wing rock motion is sensitive to the friction in thebearing. Therefore, a validation experiment was conducted using aslender wing with 80 deg sweep angle to evaluate the performance ofthe free-to-roll rig. This experiment has been extensively investigatedin the past years. Thus, the experimental data are available forcomparison. Figure 3a shows the geometry of the slender delta wingused, which is very similar to that by Levin and Katz [4]. We

DigitalEncoder

Support

ElectricBrake

Bearing

Stator Rotorlaser

a) b)

camera

U∞

Fig. 1 Experimental apparatus: a) model and PIV layout, and b) free-to-roll rig.

a) b)

30°

300

76.9

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Fig. 2 Experimental models: a) isolated cropped delta-wing with 30 deg sweep, and b) wing body with a hemisphere–cylinder forebody.

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primarily compared our resultswith theirs. Thevariation in amplitudeof thewing rockwith theAOA is shown in Fig. 3b. The results were invery good agreement with those of Levin and Katz. Hence, the free-to-roll rig is suitable for the study of the present investigation.

III. Results and Discussion

The free-to-roll results of the isolated deltawing andwing body arefirst presented. Subsequently, the PIV results of the wing body areshown to demonstrate the flow mechanisms during the wing rock.

A. Histories of Free-to-Roll Delta Wing

Figure 4 shows the equilibrium locations and the rms of the free-to-roll motion of the isolated delta wing at various AOAs. Thewing hadnonzero equilibrium locations at AOAs of less than 18 deg, which iscomparable to the results of Gresham et al. [10]. They studied thefree-to-roll characteristics of wingswith sweep angles of 40 to 70 degand found that wings with low sweep angles produce nonzero meanroll angles until the wings stalled where the mean roll angle is zero,whereas lower-sweep wings will be stalled earlier. The lowest-sweepwing with 40 deg sweep in their study stalled at 21 deg AOA. For thewing with 30 deg sweep in the present experiment, a stall angle ofapproximately 18 deg is reasonable. The standard deviations in theAOA range of 0 to 90 deg were very small. The typical histories in

Figs. 4b and 4c also show that the maximum amplitude of the free-to-roll wing was no more than 9 deg. More importantly, the phasediagram in Fig. 3d indicates that the slight fluctuations in roll anglehistories were not limit cycle oscillations because the trajectory linescannot be attracted to a closed orbit. In contrast, the fluctuationsexhibited apparent stochastic characteristics, and they were morelikely caused by intrinsic unsteadiness of flowfields after the wingstall but not by the coupling effect between the fluid and the wing.Thus, the motion patterns of the isolated delta wing were fixed-pointmotion with trivial stochastic fluctuations. This result is consistentwith that ofGreshamet al. [10],where the 40 deg sweepwing also hasextremely small amplitude of oscillations. In addition, the experimentof Gresham et al. [11] on cropped delta wings with 50 deg sweepangles showed that oscillatory motion gradually weakens asslenderness ratio increases. In this case, the side-edge vorticesseemed to stabilize the free-to-roll wing. Hence, for the presentcropped deltawing, the low sweep and side edges suppressed the self-excited oscillation from occurring.

B. Histories of Free-to-Roll Wing Body

Figure 5 shows roll angle histories of the free-to-roll wing bodywith a forebody. It can be seen that apparentwing rock exists at anglesof attack of 0–90 deg, as shown in Fig. 5a. In particular, theamplitudes of wing rock are larger at AOAs of 30–35 deg, andFigs. 5b–5e further show the variation of roll angle with time atvarious AOAs. Through comparing the free-to-roll results of theisolated wing and wing body, it can be concluded that the wing rockof the wing body is induced by the hemisphere–cylinder forebody.Themean roll angle slightly deviates from zero value at AOAs of lessthan 45 deg and becomes zerowith increasing AOAs. Figure 6 showsthe frequency characteristics of wing rock of the wing body. Thefrequency spectrum based on FFT shows an apparent dominantfrequency (taking the case of 30 deg AOA as an example), whichindicates that the wing rock is a type of periodic motion, as shown inFig. 6a. The dominant frequency is increased roughly with AOAs,with the exceptions between 30 and 40 deg AOAswhere the frequen-cies exhibit a decrease abruptly. The frequency decrease correspondsto the amplitude increase at Fig. 5a, and themodel requiresmore timeto roll through the roll angles.Figure 7 shows the phase diagrams of the free-to-roll wing body at

various AOAs. The phase diagram in Fig. 7a indicates that the slightfluctuations at AOA � 10 deg in roll angle histories were not limitcycle oscillations because the trajectory lines cannot be attracted to aclosed orbit. The phase diagram atAOA � 35 deg indicates that thewing rock is a typical limit-cycle oscillation, as depicted in Fig. 7b, inwhich the asymptotic behaviors of the phase trajectories form aclosed orbit, independent of initial values. However, with increasingangles of attack further, stochastic components in wing rock motionare increased gradually, and the motion types deviate from a limit-cycle oscillation, as shown in Figs. 7c–7e. However, theseapproximate closed-orbits are still abstractors because, even given a

Table 1 Mean roll angle and standarddeviation

Case Mean roll angle RMS

1 2.4 46.62 2.7 46.23 1.7 45.34 2.8 45.35 1.2 45.06 2.0 45.47 2.7 45.6Standard deviation 0.6 0.6

Table 2 Mean locked-phase roll angle and standarddeviation

Case Mean locked roll angle Standard deviation

ϕl � 0��� 0.01 0.3ϕl � 30��� 29.9 0.3ϕl � 60��� 60.1 0.3ϕl � 30�−� 30.0 0.3ϕl � 0�−� 0.0 0.3ϕl � −30�−� −30.1 0.3ϕl � −60��� −60.0 0.3ϕl � −30��� −29.9 0.3

600

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45°

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, d

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Present Experiment

b)

Levin and Katz [4]

Fig. 3 Validation of free-to-roll rig: a) slender delta wing with 80 deg sweep angle, and b) variation in amplitude of the wing rock with AOA.

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larger initial roll angle, the wing body remain to be abstracted to thesame region, as depicted in Fig. 7d. Particularly, the motion types atFig. 6e already are not periodic close orbits any more obviously.

C. Particle-Image-Velocimetry Results of Free-to-Roll Wing Body

The dynamic PIV measurements were carried out with a phase-locked method during the free-to-roll motion of the wing body.Figure 8 shows the typical history of wing rock used for PIVmeasurements, in which phase-locked roll angles also are markedschematically. The final PIV snapshot is an average result with 25image pairs obtained by the phase-locked method.Figure 9 shows the sectional vector fields, streamlines, and

vorticity contours when thewing body passes through zero roll anglein a positive (�) and negative (−) direction. Near zero roll angle, thewing body exhibits higher rolling rates, and so dynamic effects offlowfields are more apparent. Regardless of the vector fields orstreamline graphs, it is easy to identify a vortex pair over the body.The vortex pair is produced by the hemisphere–cylinder headbecause the leading-edge shear layers from the wing are clear, whichcannot form concentrated vortices or the wing vortices have brokendown, and the flowfields over the wing exhibits completelyseparating flowpatterns after vortex breakdown.The forebody vortexpair is asymmetric in position, and the left and right vortex is unequalin size, and so the vortex strength is also asymmetric. The orientationof the vortex asymmetry varies with rolling directions, and for apositive roll, the left vortex from a rear view is higher in position andlarger in size, but for aminus roll, the right vortex is higher and larger.The dynamic asymmetry of vortices comes from the dynamichysteresis of flow, which is similar to the case of the wing rock ofslender wings studied by Arena and Nelson [6]. The hysteresis effectof vortices can provide negative damping moments sustaining wingrockmotion. However, in the study of Arena andNelson, the vorticesyielding dynamic hysteresis are leading-edge vortices over slenderdelta wings, but the present ones are forebody vortices. Theasymmetric vortex pair will further interact with the flowfields overthe wing, leading to asymmetric load distributions on the left and

right half of the wing. The asymmetric loads provide negativedamping moments sustaining the wing rock.Figure 10 shows the variation of sectional flowfields in a period

of wing rock. It can be seen that the level and orientation of theasymmetric forebody vortices induced by dynamic effects arechangedwithwing rock. The associated flowfields over thewing alsobecome asymmetric.

D. Analysis on Physical Mechanism of Wing Rock of Wing Body

The wing rock can be taken as a type of nonlinear oscillation,and so the physicalmechanism driving thewing rock can be analyzedby an analogy to general oscillation systems. However, the couplingeffects of fluid flow and motion are necessarily considered.According to the concepts of general oscillation systems in thetextbooks of flight dynamics [22] and physics [23], the rollingmoments that sustain the oscillations of the wing body can be brokendown into restoring moments and damping moments. The restoringmoments are determined by stationary flowfields. They depend onroll angles. Hence, the restoring moments will be produced when thewing body is positioned statically at a certain roll angle and at certainAOAs. The damping moments are generated by the history effects ofthe flowfields (i.e., the dynamic hysteresis or time lag of the flow).The decomposition of rollmomentswas also taken in themodeling ofwing rock [21,24].The rolling moments sustaining wing rock entirely come from the

wing loads because the fuselage is an axisymmetric body, whichcannot produce any moments by pressure integration. The rollingmoments on the wing are induced by both the flowfields of the wingitself and the inducing effect of forebody vortices on the wing. Forsimplicity, wing flow only refers to the flowfield around an isolatedwing. The roles of forebody vortices include two aspects: the directimpact of forebody vortices on the loads of the wing and theinteraction on the original wing flow. Both roles of forebody vorticeson rolling moments are difficult to distinguish. Hence, in the presentstudy, we generally attributed both to the role of the forebodyvortices. The contribution of the flow around the isolated wing to the

10 20 30 40 50 60 70 80 90-60

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Fig. 4 Free-to-roll results of delta-wing: a) mean roll angle vs AOA with standard deviation bars, b) history at α � 55 deg and c) α � 70 deg, andd) phase diagram of Fig. 4c.

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rolling moments is readily determined, because the current cropped-delta-wing has no wing rock. As the wing is set at certain initial rollangles, it will converge to certain roll angles. Therefore, the isolated

wing is necessarily exerted on the statically stabilizing restoringmoments and the positive dampingmoments duringmotion. The twotypes of moment primarily come from the static switching of wing

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Fig. 5 Histories of wing rock of wing body: a) rms and mean roll angle, b) roll angle vs time at α � 10 deg, c) α � 35 deg, d) α � 50 deg, ande) α � 80 deg.

0 1 2 3 4 50

20000

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nitu

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f , h

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α , deg

Fig. 6 Frequency characteristics of wing rock of wing body: a) frequency spectrum at α � 30 deg, and b) variation of dominant frequencies with AOA.

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flowfields with roll angle and dynamic hysteresis, respectively. Thestatic switching of wing flow is the variation of moment directionswith statically changing roll angle.When thewing body takes certainroll angle, the wing vortex at the higher side of the wing will moveaway from the wing surface, and at the lower side, the wing vortexwill approach the wing surface. Therefore, the wing loads at left andright sides are asymmetric, and the orientations of the asymmetricloads depend on that roll angle is positive and negative. With themodel oscillating, the orientations of wing flow and associated loadswill switch between positive and positive values. The kind ofswitching is not caused by dynamic effects of wing flow,which existswhen roll angle is altered statically (no roll rate). In the present study,the dynamic hysteresis of the wing vortices produces positivedamping, although the vortices probably have broken down. FromFigs. 8 and 9, the shear layers from the leading edge of the wing areclearly visible.For limit-cycle oscillations, the rollingmoments during oscillation

consist of statically stabilizing restoring moments, negative dampingmoments at low roll angles, and positive damping moments at highroll angles. The statically stabilizing restoring moments are causedby the switching of the wing flow with the roll angle. The negativedamping moments triggering the destabilization of the wing body at

low roll angles are uniquely contributed by the dynamic hysteresisof the forebody vortices because wing flow only produces positivedamping moments. The positive damping moments at high rollangles are caused by the dynamic hysteresis of both thewing flow andthe forebody vortices.

-15 -10 -5 0 5 10 15-0.010

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φ , deg

Fig. 7 Phase diagrams of wing rock of wing body: a) α � 10 deg, b) α � 35 deg, c) α � 50 deg, d) α � 50 deg and intial roll angle 60 deg, ande) α � 80 deg.

0.0 2.5 5.0 7.5 10.0-80

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eg

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Fig. 8 Roll angle as a function of time for PIV phase-lockedmeasurements at α � 35 deg.

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Fig. 9 PIV results for wing body with −X∕D � 1.9 and α � 35 deg, from rear view: a) sectional velocity vector fields, b) streamlines at ϕ � 0���,c) sectional velocity vector fields, and d) streamlines at ϕ � 0�−�.

Fig. 10 Sectional flowfields of wing body at −X∕D � 1.9 during wing rock at α � 35 deg, from rear view.

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IV. Conclusions

The wing rock induced by a hemisphere–cylinder forebody wasinvestigated experimentally. Some conclusions can be draw asfollows.For the isolated cropped delta wing with sweep angle of 30 deg, no

apparent limit-cyclewing rock occurs at angles of attack of 0–90 deg.Although there are slight fluctuations in amplitude, the fluctuationsare not limit-cycle oscillations in terms of phase diagrams but arestochastic oscillations. Themean roll angles exhibit nonzero values atangles of attack of less than 15 deg and become zero at angles ofattack of more than 15 deg.For the wing body with a hemisphere–cylinder forebody, apparent

wing rock exists at angles of attack of 0–90 deg. Thewing rock of thewing body is induced by the forebody through comparing the free-to-roll results of the isolated wing and wing body. In particular, theamplitudes of wing rock are larger at angles of attack of 30–35 deg.The phase diagrams indicate that thewing rock is a typical limit-cycleoscillation at lower and moderate angles of attack. However, withfurther increasing angles of attack, stochastic components in wingrock motion are increased gradually, and the motion types deviatefrom a limit-cycle oscillation. The frequencies of wing rock increasewith increasing angles of attack, with the exceptions at 30–45 degangles of attack.The phase-locked PIVmeasurements duringwing rock of thewing

body reveal that the hemisphere–cylinder forebody can generate apair of forebody vortices. The forebody vortex pair exhibits apparentdynamic hysteresis in position and strength duringwing rock, and thedynamic hysteresis of forebody vortices further influence flowfieldsover the wing, resulting in asymmetric distributions of wing flow,which provides the moments sustaining the wing rock.

Acknowledgment

The project is supported by the National Natural ScienceFoundation of China under grant 11272033.

References

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