SPANWISE FLOW STRUCTURES WITHIN A LAMINAR SEPARATIONBUBBLE ON AN AIRFOIL

Theodoros MichelisFaculty of Aerospace Engineering

Delft University of Technologyt.michelis@tudelft.nl

Kluyverweg 2, 2629HT, Delft,The Netherlands

Marios KotsonisFaculty of Aerospace Engineering

Delft University of Technologym.kotsonis@tudelft.nl

Kluyverweg 2, 2629HT, Delft,The Netherlands

Serhiy YarusevychDepartment of Mechanical and Mechatronics Engineering

University of Waterloosyarus@uwaterloo.ca

200 University Ave. W, Waterloo, Ontario, Canada, N2L 3G1

ABSTRACTThe present study considers the development of a Lam-

inar Separation Bubble on the suction side of a NACA0018airfoil under natural and forced conditions. Determin-istic forcing is applied by means of a two-dimensionalplasma actuator installed on the airfoil surface. The spatio-temporal characteristics of the bubble are measured usingtime-resolved, two-component Particle Image Velocimetryin streamwise and spanwise planes. Analysis of the re-sults shows that while the time-average bubble is stronglytwo-dimensional, the dominant coherent structures assumethree dimensional organisation in the vicinity of laminar-turbulent breakdown in both natural and forced conditions.

INTRODUCTIONA Laminar Separation Bubble (LSB) develops if a lam-

inar boundary layer is subjected to a sufficiently strong ad-verse pressure gradient. This causes separation, with sub-sequent laminar to turbulent transition of the shear layer.Increased mixing and energising of the separated shearlayer results in time-averaged reattachment, thus creatingthe LSB (e.g. Jones et al., 2010). This phenomenon is com-mon on the suction side of airfoils at low Reynolds numbersbased on chord length (Rec < 500,000). It is relevant for avariety of industrial applications spanning from unmannedaerial vehicles to gliders and wind turbine blades. Since aLSB is inherently unstable, it can lead to unwanted dynamiceffects such as stall, lift reduction, drag increase and noiseproduction. Consequently, detailed description of the dy-namics of LSBs is essential in order to effectively controlthem and has been a topic of extensive studies (e.g. Marxen& Henningson, 2011).

It is generally accepted that transition in the sepa-rated shear layer is governed by convective amplification ofdisturbances due to a Kelvin-Helmholtz instability mecha-nism (Boutilier & Yarusevych, 2012; Marxen et al., 2013).The later stages of amplification lead to turbulent break-down through the development of three-dimensional struc-

tures. Many studies focused on stability of LSBs involveeither periodic (Jones et al., 2010) or impulsive (Gaster& Grant, 1975; Michelis et al., 2017) forcing. The ma-jority of the available experimental investigations involvedthe two-dimensional description of the bubble topology inthe streamwise plane. In comparison, the description ofthe spanwise evolution of coherent structures in LSBs hasbeen considered only in a limited number of studies (e.g.Burgmann et al., 2006).

This work focuses on the characterisation of a LSBunder natural and forced conditions. Repetitive forcing ofthe LSB by means of a Dielectric Barrier Discharge (DBD)plasma actuator is applied in order to characterise the effectof natural and forced perturbations on the bubble dynamics.The emphasis is placed on the description of the spanwiseflow development, where strong three dimensional effectsare expected in the aft portion of the bubble (Marxen et al.,2013). The disturbance is introduced locally and in a two-dimensional manner. The resulting spatial and temporalresponse of the flowfield is captured with streamwise andspanwise time-resolved Particle Image Velocimetry (PIV)measurements.

EXPERIMENTAL SETUPExperiments are carried out in a closed-loop wind

tunnel with square cross-section of 610mm×610mm. ANACA0018 airfoil of 200mm chord is inserted in the testsection (figure 1). The airfoil is set at a geometric andaerodynamic angle of attack of 4◦ while the pressure sideboundary layer is tripped by means of a three-dimensionalroughness strip. This is done in order to avoid unsteadyeffects as well as trailing edge tonal noise emission. ACartesian coordinate system is defined with the origin atthe leading edge of the airfoil. The x, y and z axes corre-spond to streamwise, wall-normal and spanwise directionrespectively. The freestream velocity is set to U∞ = 9.2m/sresulting in a Reynolds number based on the chord of Rec =126,000. At this speed, the freestream turbulence intensity

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FOV laser

laser

Figure 1. Experimental arrangement. The green dashedvertical lines denote the streamwise extent of the spanwisefield of view (FOV).

is approximately 0.1%. For the selected conditions, a lami-nar separation bubble forms on the suction side, with meanseparation and reattachment points are at x/c ≈ 0.35 and0.53, respectively.

The laminar boundary layer is perturbed two-dimensionally by means of an Alternating Current Dielec-tric Barrier Discharge (AC-DBD) plasma actuator (Corkeet al., 2010; Kotsonis, 2015). It consists of two asymmet-rically placed self-adhesive copper electrodes separated bya Kapton R© dielectric layer. The electrodes are 10mm widein the streamwise direction, 30µm thick and 300mm long inthe spanwise direction, while the dielectric barrier is 120µmthick. The discharge gap is located at x/c = 0.3, upstreamof the separation point. The forcing signal is comprised ofrepetitive short pulses that are constructed by modulating a3.5kVpp and 5kHz sinusoidal carrier signal with a squaresignal of selected frequency. The modulation duty cycleis adjusted in regards to the pulse frequency, resulting in apulse width of 1ms.

Time-resolved Particle Image Velocimetry (PIV) mea-surements are carried out by employing two Photron SA4high-speed cameras with 200mm Nikkor macro lenses, setat an aperture of f/5.6. Illumination is performed by aPhotonics DM20-527 Nd:YLF laser, whose beam is trans-formed to an approximately 2mm thick light sheet. Asmoke generator uses water-glycol mixture to provide par-ticle seeding.

Two fields of view are captured at an acquisition fre-quency of 2kHz. The first lies in the x− y plane, at theairfoil midspan and is constructed by stitching images fromboth cameras, covering a field-of-view of 65mm× 22mm.The second view lies in the x− z plane, parallel to and ata distance of d = 21mm from the airfoil chord, capturing afield-of-view of 56mm×56mm (figure 1). In both cases, theacquired image pairs are processed with the LaVision Davis8.2 software using the multi-step interrogation algorithm(Scarano & Riethmuller, 2000) from an initial window of48×48 pixels to a final of 16×16 pixels with 75% overlap.As a result, vector fields of 161×473 and 247×247 vectorsare obtained for side and top views, respectively.

The results are presented on a surface-attached coordi-nate system (figure 1). The x coordinate runs tangent to theairfoil surface with an origin at the leading edge, while they coordinate is normal to the local tangent and is measuredfrom the airfoil surface (figure 1). The required scaling andgeometric transformation of the vector fields (dewarping)is applied to all instantaneous realisations of the measure-ments in the x− y plane. For the x− z plane measurements,no dewarping is applied. The z coordinate is running paral-lel to the airfoil leading edge, with an origin at the midspanof the model.

RESULTSUnforced bubble

All the results presented in this section pertain to Rec =126,000 and an angle of attack of α = 4◦. All dimensionalvariables are non-dimensionalised using the airfoil chord(c = 0.2m) and the freestream velocity (U∞ = 9.2m/s).

Figure 2 presents time-average velocity and velocityfluctuation fields for the unforced LSB, serving as the base-line for the present study. The velocity field in the stream-wise (x−y) plane is shown in figure 2a along with the time-average dividing streamline, indicating the outline of theLSB. The general topology of the bubble follows the wellknown definition of short LSBs by Gaster (1967). It is ev-ident that the mean separation point is not captured withinthe measurement domain. This is a necessary compromisefor achieving sufficient spatial resolution in the reattach-ment region of the bubble. Nevertheless, an approximationof the mean separation point can be produced, capitalisingon the nearly linear slope of the dividing streamline in thefore region of the bubble. Based on the extrapolated esti-mate of the mean separation point (xb

s = 0.29) and the meanreattachment point (xb

r = 0.54), the mean bubble length isestimated to be lb = 0.25. The maximum bubble height ishb = 0.07 and is located at x = 0.48.

Figures 2b and 2c demonstrate the standard deviationof streamwise (σu) and wall normal (σv) fluctuating veloc-ity fields respectively. The appearance of strong streamwiseand wall-normal fluctuations in the aft portion of the bubbleis attributed to vortex shedding, in line with previous in-vestigations on short LSBs (Yarusevych & Kotsonis, 2017).In particular, the topological arrangement of the streamwisefluctuations (figure 2b) reveals two distinct maxima in thevicinity of the maximum bubble height (x ≈ 0.5). In con-junction with the single maximum in wall-normal fluctua-tions located approximately along the mean displacementthickness (figure 2c), the overall organisation of the un-steady fluctuating fields in the streamwise plane suggeststhe existence of coherent vortical shedding in the aft-portionof the bubble (Hain et al., 2009).

Figure 2d presents the time-average velocity field inthe spanwise (x− z) plane. As mentioned earlier, the lasersheet in the x− z plane was placed parallel to the chord ofthe airfoil. As such the distance of the spanwise measure-ment plane from the airfoil surface is not constant along thestreamwise direction, due to the curvature of the airfoil. Inthe transformed and projected streamwise plane (dewarpedx− y plane) the measured x− z plane assumes a curvedshape. The intersection of the measured x− z plane withthe x−y plane is indicated in figure 2 by a dash-dotted line.

The time-average flow on the x− z plane demonstratesa high degree of two-dimensionality along the span (figure2d). The streamwise component of velocity is uniformlydecelerating along the x direction while the spanwise com-ponent is near-zero as evident by the quiver plot in figure2d. The overall behaviour of the time-average velocity inthe x− z measurement plane confirms the establishment ofspanwise invariant test conditions within the FOV. In con-trast, the both streamwise (σu) and spanwise (σw) velocityfluctuations (figures 2e and 2f) reveal pronounced spanwisemodulation. The combination of a highly two dimensionalmean flow (figure 2d) and pronounced spanwise modula-tion of the fluctuating field topology in the aft portion of thebubble merits further analysis.

In order to quantify the spectral content of the dom-inant velocity fluctuations in the aft portion of the bubble,

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Figure 2. Time-averaged velocity field of the unforced bubble in the (a) x− y plane and (d) x− z plane. Standard deviation ofthe velocity fluctuations in the (b-c) x− y plane and (e-f) x− z plane. M, # and O denote mean separation, maximum heightand reattachment respectively. Thick black line denotes dividing streamline and dashed line denotes displacement thickness.Black dash-dotted line denotes intersection of the x−y and x− z planes. White marker and vertical dashed line denote locationof velocity probes for spectral analysis of figure 3.

Figure 3. PSD of u′ in the (a) x− y plane and (b) x− zplane for the unforced case. Probe locations are indicatedin figure 2.

the time-resolved PIV measurements are capitalised. PowerSpectral Density (PSD) is computed using Welch’s methodfrom temporal signals of velocity components. Figure 3ademonstrates the PSD of the fluctuating streamwise veloc-ity measured in the streamwise plane (PSDx−y), with theprobe location identified by a white marker in figure 2b. Inorder to facilitate a comparison between the streamwise andspanwise measurement planes, the streamwise location ofthe probe corresponds to the location of the maximum bub-ble height and the wall-normal location corresponds to theintersection of the two planes. The spectrum in figure 3asuggests that velocity fluctuations in the aft portion of thebubble are associated with a relatively narrow band of fre-quencies laying within 12 < St = f c/U∞ < 17. Addition-ally, a highly energetic discrete peak appears at St ≈ 11.8corresponding to a physical frequency of 542 Hz.

The presence of a confined frequency band of unsteady

0.35 0.4 0.45 0.5 0.55 0.6

0

10

20

30

Figure 4. LST stability curve for the unforced case. Blackline denotes neutral curve (αi = 0). Dashed line denoteslocus of most unstable modes. Contour spacing is 0.1

fluctuations in the aft-portion of the bubble suggests a selec-tive amplification mechanism attested to the natural stabil-ity characteristics of the flow. This can be elucidated withthe use of Linear Stability Theory (LST) analysis (Mack,1984). The LST analysis is performed through solutions ofthe Orr-Sommerfeld equation, governing the developmentof small-amplitude perturbations in a time-invariant parallelflow. It has to be noted here that both assumptions of smallperturbation amplitude and parallel flow are challenged bythe inherent features of the bubble. Nevertheless, previousstudies have demonstrated the applicability of LST as a di-agnostic tool for accessing the stability of LSBs up to con-siderably late stages of transition (Michelis et al., 2017).

In the present study, the experimentally measured timeaverage PIV flowfield in the streamwise (x− y) measure-ment plane is used as the mean base flow for the LST anal-ysis. The Orr-Sommerfeld eigenvalue problem is solvedin spatial formulation where the real local Reynolds num-ber (i.e. based on the x location) and frequency are usedas known inputs. The eigenvalue is produced in the formof a complex wavenumber (α). The imaginary part ofthe wavenumber corresponds to the non-dimensional lo-cal growth rate (αi) associated with a given frequency.Negative values of αi denote unstable (i.e. amplifying)

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0 5 10 150

0.05

0.1Streamwise

Spanwise

Figure 5. Relative POD eigenvalues of the unforced case.

modes while positive values of αi denote stable (i.e. damp-ing) modes. Neutral modes correspond to zero imaginarywavenumber.

The LST results for the baseline flow are shown in fig-ure 4 in the form of a stability curve diagram. The flow isunstable at the upstream boundary of the measured FOV.The band of unstable frequencies spans from Stc ≈ 0 toStc ≈ 25 in a streamwise range of 0.35 < x/c < 0.45. Thecontour levels within the unstable region indicate the localgrowth rate (αi) and the locus of the most unstable modesis denoted in figure 4 by the dashed black line. In the re-gion upstream of the maximum bubble height (0.35< x/c<0.45) the most unstable frequency remains approximatelyconstant at Stc ≈ 11. This corresponds directly with thespectral peak in figure 3, linking the dominant velocity fluc-tuations in the aft portion of the bubble to the growth of nat-ural instabilities along the incoming boundary layer and theseparated shear layer (Marxen et al., 2013).

The respective PSD of streamwise fluctuating veloc-ity components measured in the spanwise (x− z) plane isshown in figure 3b. The corresponding velocity signalswere probed along the span (dashed line i figure 2b) atthe same streamwise location as that used for figure 3a.These are indicated with the vertical dashed line in figure2d. The results indicate that the power of fluctuations alongthe z direction is modulated in accordance with the topo-logical distribution of fluctuating velocity fields noted ear-lier in figures 2e and 2f. Nevertheless, despite the apparentmodulation of the fluctuation power, the corresponding fre-quency band and centre frequency appear largely invariantalong z, closely following the respective band in the x− yplane (figure 3a) and the LST predictions (figure 4). Theresults in figure 3 suggest that while there is strong three-dimensionality in the spatial topology of the fluctuating ve-locity field in the breakdown region of the bubble (figures2e-f), the dominant velocity fluctuations are associated witha common frequency band, evident in both streamwise andspanwise measurement planes. This implies that vorticalstructures shed in the aft portion of the bubble develop aconsistent spanwise modulation.

Proper Orthogonal Decomposition (POD) is utilised toreveal the presence and topology of the dominant coherentstructures in the LSB. For the present study, the snapshotmethod originally proposed by Sirovich (1987) is employedusing the ensemble of instantaneous snapshots acquired byPIV. Figure 5 shows the relative energy (λ ) of the fourteenmost energetic spatial modes in both streamwise and span-wise measurement planes. For both planes, the energy cas-cade reveals two pairs of modes dominating the fluctuat-ing velocity field. The cumulative energy of these first fourmodes is 37% of the total fluctuating energy for the stream-wise plane and 42% for the spanwise plane. A careful in-spection of the respective POD eigenfunctions reveals thatthe four most energetic modes for each measurement plane

Figure 6. Normalised POD eigenfunctions in the x− yplane for the unforced case. Same notation as figure 2.

Figure 7. Normalised POD eigenfunctions in the x− zplane for the unforced case.

represent pairs of harmonically coupled modes. The har-monic coupling manifests in the form of a π/2 phase shiftbetween the POD modes of each pair, a necessary conditionfor convective structures. As such, the following analysiswill focus on one spatial mode per harmonic mode pair, i.ethe first and third most energetic POD mode per measure-ment plane. Figures 6 and 7 show the spatial modes in thestreamwise and spanwise plane respectively. An importantnote to be made here is that the measurements and subse-quent POD analysis between the two measurement planesare uncorrelated. As such, there is no direct correspondencebetween POD modes in the x− y plane and POD modes inthe x− z plane other than their energy sorting. Subsequentanalysis will treat the two planes independently. To be notedthat all spatial POD modes are normalised to their respec-tive maximum.

The structure of the spatial POD modes Φ(1) and Φ(3)

shown in figure 6 corroborate the topology of the velocityfluctuations (figure 2b-c) and confirm the existence of co-herent shedding in the aft portion of the bubble. This isfurther elucidated in figure 7 which shows the spatial ar-rangement of modes Φ(1) and Φ(3) in the spanwise plane.As previously conjectured, the POD modes confirm the ex-istence of spanwise oriented vortical structures which un-dergo three-dimensional modulation in the streamwise di-rection. This is evident from distinct spanwise modulationsin the streamwise component of the spatial modes (figures7a and c) as well as the existence of a distinct spanwiseorganisation in the spanwise component (figures 7b and d).Additionally, it is striking to note the differences in the char-acteristic wavelengths between the first mode pair (Φ(1))and the second mode pair (Φ(3)). This suggests the exis-

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Figure 8. Statistic quantities of the forced LSB. Same notation as figure 2.

tence of multiple modes active in this region, supportingthe previously discussed spectral measurements (figure 3).

Forced bubbleIn order to investigate the origin of distinct spanwise

deformations of dominant coherent structures, the bubble isconditioned using deterministic impulsive forcing by meansof the installed plasma actuator. The frequency of suc-cessive pulses is chosen to be within the band of unstablemodes predicted by the LST analysis (figure 4) at St = 13( f = 600Hz). The time average velocity and velocity fluc-tuation fields for the forced bubble are shown in figure 8.In comparison to the baseline case (figure 2), forcing evi-dently results in the reduction of the bubble length to ap-proximately 80% and the reduction of the maximum heightto approximately 85% of the respective unforced values.This attributed to enhanced levels of velocity fluctuationsin both streamwise (figure 8b-c) and spanwise (figure 8e-f) planes, indicating higher amplitude of perturbations andearlier transition. An inspection of the spanwise plane mea-surements reveals the sustainment of the strongly two di-mensional mean flow. However, as for the baseline flow,the x− z topology of σu reveals strong spanwise modula-tion for both streamwise and spanwise components (figures8e and 8f).

The spectral analysis for the forced case has been ap-plied in a similar fashion as for the unforced bubble. ThePSD of the streamwise velocity fluctuations in the stream-wise plane is shown in figure 9a. While the previously iden-tified frequency band (figure 3a) is still visible, it is apparentthat the majority of fluctuating power is now highly con-centrated within a narrow band centred at Stc = 13, directlycorresponding to the forcing frequency. This indicates thelocking of the dominant velocity fluctuations on the actua-tion event. The spanwise spectral power distribution (figure9b), further confirms the strong individuation concentrationof the fluctuating energy along the span at the forcing fre-quency. Nevertheless, distinct spanwise modulation in thespectral content can be seen in figure 9b, similar to thoseobserved for the baseline case (figure 3c).

The selection of a single coherent fluctuating mode inthe spanwise plane due to the plasma forcing is further iden-

Figure 9. PSD of u′ in the (a) x− y plane and (b) x− zplane for the forced case. Probe locations are indicated infigure 8

0 5 10 150

0.2

0.4

Streamwise

Spanwise

Figure 10. Relative POD eigenvalues for the forced case.

tified by the cascade of POD modal energy shown in figure10. The first two POD modes in the spanwise plane are re-sponsible for approximately 63% of the total fluctuating en-ergy compared to 28% for the same modes in the unforcedbubble. In contrast, the energy cascade in the streamwiseplane appears to be weakly affected by the forcing.

Further analysis of the spatial topology of the first andthird POD modes for the streamwise and spanwise measure-ment planes is enabled by figures 11 and 12 respectively. Assuggested by the energy cascade, minor differences can be

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Figure 11. Normalised POD eigenfunctions in the x− yplane for the forced case. Same notation as figure 2.

Figure 12. Normalised POD eigenfunctions in the x− zplane for the forced case.

observed between the forced (figure 11) and unforced (fig-ure 6) cases in the streamwise plane. In contrast, the topo-logical effect of forcing on the POD modes in the spanwiseplane is drastic. More specifically, in the x− z plane, ampli-tude modulation is evident in both streamwise (figure 12a)and spanwise (figure 12b) vector components of the domi-nating mode, Φ(1). Strong modulation is also apparent forΦ(3), although it should be noted that the fluctuating energycontent of this mode is only 0.8% of the total turbulent ki-netic energy. The characteristic spanwise wavelength of theobserved modulations decreased compared to that seen forthe baseline case, likely due to the change in the streamwisewavenumber.

CONCLUSIONSThe present study investigated the spatial organisation

of shedding structures in the aft-portion of a Laminar Sep-aration Bubble. Statistical analysis reveals a rapid growthof velocity fluctuations, suggesting rigorous shedding andeventual transition. Spectral analysis confirms predictionsof LST in identifying a band of unstable frequencies perti-nent to the features of the baseline flow. POD analysis in thestreamwise plane confirms the manifestation of vortex shed-ding in the aft portion of the bubble. The POD analysis inthe spanwise plane shows that, while the dominant modesare coherent and monochromatic, they develop a three di-mensional amplitude and shape modulation in the spanwisedirection. This is present under natural unforced condi-tions within an otherwise strongly two-dimensional base-line flow.

The LSB was further conditioned by two dimensional

forcing applied upstream of mean separation using a plasmaactuator near the most amplified frequency. Under forcing,the shedding process locks to a single mode, while the co-herency in the spanwise plane increases considerably. Nev-ertheless, distinct spanwise deformation of the dominantstructures persists in the forced case. The aforementionedeffect provides insight into the origin of three-dimensionalbreakdown in LSBs. More specifically, while related to thedevelopment of disturbances upstream of separation, span-wise deformation of dominant rollers developing in the sep-arated shear layer is linked to the characteristics of thesestructures, persisting in both natural and forced bubbles.

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