STUDIES ON BYPASS TRANSITION OF A BOUNDARY LAYER SUBJECTED TO LOCALIZED PERIODIC EXTERNALDISTURBANCES
K. FUNAZAKI, Y. WAKITA AND T. OTSUKIDEPARTMENT OF MECHANICAL ENGINEERING
IWATE UNIVERSITYMORIOKA, JAPAN
Proceedings ofASME Turbo Expo 2004
June 14-17, 2004, Vienna, Austria
GT2004-53305
Proceedings of ASME Turbo Expo 2004 Power for Land, Sea, and Air
June 14-17, 2004, Vienna, Austria
GT2004-53305
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ABSTRACTThis study aims at clarification of wake-induced bypass transition
process of a boundary layer on a flat plate with no pressure gradient.Special attention is paid to inception as well as growth of a turbulentspot created by the incoming wake as an external disturbance. To meetthis goal a unique wake generator is invented to create an isolatedturbulent spot. A multi-probe sensor with seven single-hot-wire probesis used to measure wake-affected boundary layer. The wake generatorconsists of a disk, pillars and a very thin wire with a small sphere on it.The sphere on the wire generates periodic wakes behind it when itpasses across the main flow in front of the test flat plate. These spherewakes impinge the flat plate in a spatially and timewisely localizedmanner so that the wakes periodically leave narrow affected zonesinside the boundary layer. The observations confirm that an isolatedturbulence spot emerges from each of those wake-affected zones. It isalso found that the turbulent spot observed in this study bears a closeresemblance to the conventional turbulent spot that takes a shape ofarrowhead pointing downstream.
INTRODUCTIONThis study deals with a unique attempt to elucidate a mechanism
of bypass transition of a boundary layer induced by periodic wakepassing. Originating from the investigation done by Klebanoff [1],free-stream turbulence (FST) induced bypass transition has been at-tracting a lot of attention from researchers and designers. Recent well-organized experiments [2][3] and sophisticated CFD studies [4] haverevealed a very likely scenario for FST- induced bypass transition.According to the scenario, streaks first appear in the boundary layersubjected to FST. These streaks are unstable themselves, therefore at alocation downstream of the leading edge the streaks break down, lead-ing to the generation of turbulent spots. Besides, many studies havebeen also made on effects of wakes moving over the boundary layer,and it is found that turbulent patch, which could be regarded as amal-gamated turbulent spots following the precedent wake, plays an im-portant role in the wake-induced boundary layer transition. Recently,applying their DNS code to unsteady analyses of flat-plate boundarylayers subjected to incoming wakes from moving bars, Wu et al. [5]suggested that ‘puffs’, instead of the streaks for FST case, were ob-served and could be regarded as a transition precursor. The puffs, whichdo not seem to be properly defined yet, have streaky structure similarwith the streaks for FST case, as shown in Figure 1. Despite thosefindings, however, a plausible scenario is not established for incep-tion and growth of wake-induced turbulent spot. Furthermore, limited
- Copyright@2004 by ASME
knowledge is available on any precursor of wake-induced turbulentspot and the growth of the turbulent spot. Discussion on what is themost influential factor among several candidates such as wake turbu-lence, velocity deficit or pressure fluctuation is also unsettled.
This study aims at clarification of wake-induced bypass transi-tion process of a boundary layer on a flat plate with negligible pres-sure gradient by tracing the development of a wake-induced turbulentspot. To meet this goal a unique wake generator is invented to createan isolated turbulent spot since it is quite difficult to distinguish oneturbulent spot from another within the turbulent patch that usuallyappears under the influence of two-dimensional bar wakes. The wakegenerator consists of a disk, pillars and a very thin wire (piano wire of0.1 mm diameter) with a small sphere on it. The sphere on the wiregenerates periodic wakes behind it when it passes across the mainflow in front of the test flat plate. These sphere wakes impinge the flatplate in a spatially and timewisely localized fashion so that the wakesperiodically leave narrow affected zones in a periodic manner insidethe boundary layer. Turbulence spots are then expected to emerge fromthose wake-affected zones. A multi-probe sensor with seven single-hot-wire probes is used to measure the wake-affected boundary layer.As an attempt to identify the turbulent spot from the signals a flowacceleration parameter is introduced in the present study in conjunc-tion with local turbulence intensity or velocity fluctuation.
'Puff'DNS (Wu et al.)
Exp. (Kittichaikarn et al.)
'Puff'
Figure 1 ‘Puffs’; one scenario for transition presursor(Wu et al. [5])
EXPERIMENTAL SETUPTest ApparatusTest Model Figure 2 shows the test facility used in this study. Asshown in Figure 3, the test duct contained a sharp-edged acrylic-acidresin flat plate of 860 mm length and 460 mm width, which was thetest model. The test duct with sharp-edged inlet was inserted into thetransition duct with about 10 mm clearance between the test and thetransition ducts. The transition duct was equipped with a slot of 35mm width, through which cylindrical bars on the wake generatorpassed. The test model was slightly tilted by 0.5 deg so that the flowchannel above the model gradually became narrow towards the exit ofthe duct. In fact, the distance between the model leading edge and theupper plate of the test duct was 150 mm, whereas the distance be-tween the model rear end and the upper plate was 142.5 mm. Thistilting, in conjunction with the screen attached to the exit of the testduct, was employed to avoid leading edge separation. The slope (i.e.curved wall) was located below the test model. It also ensured preven-tion of the flow separation at the model leading edge by promotingoutflow over the slope thanks to the Coanda effect. Oil-flow visual-ization confirmed that these efforts successfully eliminated the lead-ing edge separation.
As shown in Figure 3, the test model had an injection hole of 0.5mm diameter located 120 mm downstream of the model leading edge.In most cases this hole was carefully sealed to avoid any unintentionalboundary layer transition due to the hole itself. This injection holewas used only to create a series of turbulent spots by intermittent airinjection from this hole, which was connected to a speaker systemdriven by a function generator. Besides, Figure 2 showed two rows ofpressure taps at the both sides of the centerline of the test model. Thesepressure taps are provided for future experiments to investigate ef-fects of pressure gradient upon the wake-induced boundary layer tran-sition, therefore these taps were not used this time and were also sealedwith great care.
Wake Generator This study featured a unique wake generator using asphere as wake-generating object. The wake generator comprised of adisk, four cylindrical bars with a diameter of 7 mm, a very thin steelwire (hard drawn steel wire or piano wire, JIS SWP-B) of 0.1 mmdiameter and three plastic spheres of 5 mm diameter. The sphere hadvery smooth surface. Each of the cylindrical bars had a small straighthole through which the piano wire passed. The wire eventually took ashape of square, and the sphere was tightly glued on the middle ofeach of the side of the square. The length of the diagonal of the wiresquare was determined so that the wake generating square moved acrossthe centerline of the test model, meaning that the sphere wake washighly likely to impinge the test model surface on its centerline. Se-lection of wire diameter was one of the key factors in the design of thewake generator from various points of view. To minimize any effectof wire wake, which was of no concern to the present study, the wireneeded to be as thin as possible. On the other hand, since tension ap-plied to the wire was to be maximized in order to increase lowestnatural frequency of the wire vibration, a relatively thick wire waspreferable for reducing the tensile stress. The wire diameter, 0.1 mm,was finally determined from a trade-off between these conflicting de-sign requirements. Two pegs for guitar were equipped on the disk inorder to adjust the wire tension, which was checked by monitoring thenatural frequency of the wire. The lowest natural frequency of thewire was estimated to be about 460 [Hz] when the tension of 22 [N]was applied to the wire. Since the disk rotated by 435 [rpm] and eachsegment of the wire accordingly experienced fluid force of 7.25 Hz,this natural frequency was high enough to avoid resonance. Disk rota-tion direction was easily reversed in order to achieve two types ofinteraction of wake with the boundary layer. An optical tachometermonitored the rotational speed, at the same time generating trigger
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pulses as data synchronizing signal. The distance between the planeof disk rotation and the model leading edge was 180 mm.
Multi-channel Sensor Flow measurement was made by use of a 7chhot-wire sensor shown in Figure 4. From simultaneous velocity ac-quisition inside the wake-affected boundary layer on the test model,this measurement aimed at exploration of the existence of any precur-sor leading to wake-induced turbulent spot as well as at clarificationof the growth of the turbulent spot. This sensor, shown in Figure 3,consisted of a light-weight frame, seven active hot-wire probes of Itype (Dantec 55P11, 5 [ m m] wire diameter and 1.9 [mm] probe bodydiameter) and two inactive dummy probes, all probes being equippedon a thin horizontal bar with equal spacing of 5 mm. These two dummyprobes were to ease any unfavorable effects of side flow around thesensor upon the right- and left-end active probes. Those hot-wire probeswere inclined by 60 [deg] from the pillar of the sensor for minimizingblockage effect of the sensor. The sensor was tightly fixed to one endof a connecting rod, the other end of which was fastened to the tra-versing unit. Great care was also paid to the horizontal alignment ofthe probes. This probe alignment was verified through a preliminarymeasurement of a laminar boundary layer, eventually yielding satis-factory agreement among all velocity profiles obtained from the probesin the sensor [6]. The center probe, channel #4, was located almostalong the centerline of the test model. Accordingly the sphere wakeand an isolated turbulence spot induced by the wake were expected tobe captured by the center probe in the sensor with great possibility.
Inlet velocity Uin
was measured by a Pitot tube that was located inthe middle of the test duct. The flow field was almost uniform alongthe spanwise direction, especially at the front half of the test duct,where the velocity variation lay within about 2% of the inlet velocity(Takahashi [6]). The head of the Pitot tube aligned itself with the lead-ing edge of the test model. As for the probe calibration, taking advan-tage of the uniformity of the flow field of the test duct, each of theprobes was in-situ calibrated. The output from each of the probes wascorrelated with the velocity in the test duct, this relationship beingable to be approximated by a 4-th order polynomial with excellentagreement.
Data ProcessingEnsemble-Averaging With the trigger signal from the optical tachom-eter, all signals from the hot-wire probes were converted simultaneouslyto digital data by a high-speed A/D converter with 50 [kHz] samplingfrequency and 14 bit resolution, then the digital data were stored intoPC. Each of the realizations acquired by k-th probe in the sensor,u x y ti
k( ) ( ), ; , contained 8192 words digitized data, and the total num-ber of the realizations, N , was 100. From these data, ensemble-aver-aged velocity and turbulence intensity were calculated, respectively,as follows;
u x y tN
u x y tkik
i
N( ) ( )=
( ) = ( )Â, ; , ;1
1, (1)
Tu x y tU x N
u x y t u x y tk
ek
kik
i
N( )( )
( ) ( )=
( ) =( ) -
( ) - ( )ÏÌÓ
¸̋˛
Â, ; , ; , ;1 1
1
2
1(2)
where U xek( ) ( ) was the time-averaged local velocity measured by the
k-th probe at the location distanced by 20 [mm] from the model sur-face. Velocity perturbation was also defined as the velocity deviationfrom the time-averaged velocity over one wake passing period, thatis,
Figure 5 Three images of the same turbulent spotinduced by air injection, the images being depicted using
turbulence intensity (top), acceleration factor (middle)and acceleration factor with raw velocity data instead of
smoothed ensemble-averaged velocity (bottom)
0 50 100 150 200
30
20
10
0
-10
-20
-30
z(m
m) 4.0
2.5 5.0 7.5 10.0 12.5 15.0
0 50 100 150 200
30
20
10
0
-10
-20
-30
z(m
m) 0 500 1000 1500 2000
0 50 100 150 200
30
20
10
0
-10
-20
-30
z(m
m)
x - xref (mm)
0 500 1000 1500 2000
x - xref (mm)
x - xref (mm)
Turbulence Intensity
Acceleration Factor using Smoothed Ensemble-Averaged Velocity
Acceleration Factor using Raw Velocity
(3).
Acceleration Factor To identify a turbulent spot from the acquiredvelocity data, a newly defined index called acceleration factor wasemployed in this study, in conjunction with the ensemble-averagedturbulence intensity (Eq.(2)). Since detailed information on this indexwas well-documented by Takahashi [6] and Wakita [7], only brief ex-planation is given in the following.
The acceleration factor, abbreviated to AF hereafter, was definedfor the ensemble-averaged velocity data from the k-th probe by
AF x y t u x y t t u x y t tksm sm
k k( ) ( ) = +( ) - ( )ÊËÁ ˆ
¯˜
( ) ( ), ; , ; , ;D D , (4)
where u x y tsmk( ) ( ), ; was an ensemble-averaged velocity smoothed by
use of a 25-point scheme as follows;
u x y t u x y t t u x y t t
u x y t t u x y t t u x y t t
u x y t t
smk k
k k k
k
k( )( ) = ±( ) + ±( ) +
±( ) + ±( ) + ±( ) +
±( ) +
( ) ( )
( ) ( ) ( )
( )
, ; { , ; , ;
, ; , ; , ;
, ;
1
72912 3 11
6 10 10 9 15 8
21 7
D D
D D D
D 2828 6 36 5
45 4 52 3 57 2
60 61
u x y t t u x y t t
u x y t t u x y t t u x y t t
u x y t t u x y t
k k
k k k
k k
( ) ( )
( ) ( ) ( )
( ) ( )
±( ) + ±( ) +
±( ) + ±( ) + ±( ) +
±( ) + ( )
, ; , ;
, ; , ; , ;
, ; , ; }
D D
D D D
D
.
(5)
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Table 1 Test conditions
Figure 6 Schematic representation of interactionbetween the sphere wake and the boundary layer
(unit in mm)
The smoothing procedure was found to be necessary in this study be-cause of the fact that even small noise in the velocity signal exhibiteda considerable contribution to the evaluation of AF.
Performance of Acceleration Factor Prior to applying this index towake-affected boundary layer measurement, the performance of theindex in extracting a turbulent spot was examined through a prelimi-nary test where a series of single turbulent spot were created by inter-mittent jet injection from the injection hole nearby the leading edge ofthe test model.
Figure 5 shows three images of a turbulent spot identified usingthe ensemble-averaged turbulence intensity, acceleration factor definedby Eqs. (4) and (5) and acceleration factor using raw velocityu x y ti
k( ) ( ), ; in Eq. (5) instead of the smoothed ensemble-averaged ve-locity u x y tk( ) ( ), ; . The abscissa and the ordinate of Figure 5 arestreamwise and lateral distances, respectively, where the streamwisedistance was not the actual length but calculated one from the elapsedtime from a reference instance of the measurement and the free-streamvelocity. Note that scaling factors for each of the axes in Figure 5 aredifferent. Besides, since it was relatively long distance from the injec-tion hole before the turbulent spot started to take a well-known arrow-
Inlet velocity 17.5 m/s
Sphere moving velocity
Uin
Us 18.0 m/s
Sphere moving direction Upwards (Reverse)
Reynolds number based onplate lengthReynolds number based on spherediameter and relative velocity
head shape [8] and the lateral extent of the turbulent spot exceeded themeasurable range of the multi-channel sensor mentioned above, thedata used in Figure 5 were acquired by another type of 7ch hot-wireprobes with wider probe spacing of 10 [mm]. The top image of Figure5 clearly indicated that the present multi-probe sensor successfullycaptured the arrowhead-like turbulent spot pointing downstream interms of ensemble-averaged turbulent intensity. One can also notice asolid line surrounding the highly turbulent zone, which is an iso-valueline of 4% turbulence intensity and will be used in the following dis-cussion. As seen in the middle of Figure 5, the acceleration factor alsoprovided a similar contour of turbulent spot to that obtained using theturbulence intensity, in particular, at the front part of the turbulentspot. On the other hand, the bottom image of Figure 5 demonstratedthat the acceleration factor using raw velocity data was also useful tocapture even a shape of a turbulent spot, although the extracted imagebecame somewhat jaggy.
Figure 8 Iso-surfaces of 2% ensemble-averagedturbulence intensity showing wake turbulence and
turbulence spread within the boundary layer(top : top view / bottom : side view)
Figure 10 Autocorrelation of the signal measured by #4probe (center probe) of the sensor
Figure 9 Contours of ensemble-averaged turbulenceintensity associated with the stationary wake measured
on several measurement planes (unit in mm)
x = -60 x = -40 x = -20 x = 0
x = 20 x = 40 x = 80 x = 100
y
z
x[mm]
x[mm]
Leading Edge
102 106 110 114 118 122 126[msec]
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-
Test Conditions Table 1 shows all test conditions examined in thisstudy. Inlet velocity U in was unchanged and 17.5 [m/s], and inlet free-stream turbulence level was about 0.5%. The disk rotational speedwas 435 [rpm], resulting in the sphere moving velocity U s was 18.0[m/s]. Wake angle lw , shown in Figure 6, was then -45.8 [deg]. Thesphere moved upwards in front of the test model. This movement waspreviously called ‘reverse rotation’ [14]. Prior to this unsteady mea-surement, stationary wake effects upon the boundary layer on the testmodel were investigated by fixing the sphere upstream of the leadingedge, as shown in Figure 6.
Measurement locations The present experiment could be divided intotwo parts, i.e., stationary sphere case and moving sphere case. In theformer case the measurement area extended from x = -60 [mm] tox = 120[mm] in the streamwise direction and from y = 0 1. [mm] toy = 35[mm] in the heightwise direction. The latter case covered thearea ranging from x = 25 [mm] to x = 205 [mm] and fromy = 0 1. [mm] to y = 10[mm].
Uncertainty AnalysisUncertainty analysis of the measured velocity was made in a rather
simplified manner based on the guidance proposed by Yavuzkurt [18].It was found that uncertainty in the velocity data originated mostlyfrom the calibration procedure of the each of the hot-wire probes inthe multi-channel sensor. As mentioned above, the reference velocityfor the probe calibration was measured by the Pitot tube that was con-nected to a pressure transducer with ± 0.4 [Pa]. This led to ± 0.8 [m/s]error in the reference velocity. Therefore, percentile uncertainty of theinstantaneous velocity, which varied from location to location, was,for example, about 5% for x = 100[mm] and y = 1 0. [mm], while theuncertainty was about 24% measured at y = 0 2. [mm] for the same x .
Steady-State MeasurementPrior to the measurements of wake-affected boundary layers,
steady-state boundary layer measurement was carried out. Figure 7shows a comparison between the Reynolds number based the mea-sured momentum thickness and its analytical counterpart using theBlasius solution, in conjunction with calculated 99% boundary layerthickness. The measurement reasonably agreed with the analytical so-lution.
RESULTS IN THE STATIONARY SPHERE CASEBefore examining effects of the moving wake, preliminary stud-
ies were made to understand the structure of sphere wake using a sta-tionary sphere, then to clarify how the stationary sphere wake inter-acted the flat plate boundary layer. For this purpose the sphere wasfixed at a position suitable to make the stationary wake impinge theleading edge of the test model. Reynolds number based on the inlet
Figure 11 Close-up of the contours of the ensemble-averaged turbulence intensity measured at x =-60 (left)and an example of one-sided vortex shedding from a
sphere at Re = 300 (Johnson and Patel [11]) (right)
velocity and the sphere diameter Red was then 5800. Figure 8 shows
top and side views of the stationary sphere wake interacting the testmodel, where the wake was represented by iso-value surfaces of 2%turbulence intensity measured behind the sphere. Similarly, Figure 9illustrates contours of turbulence intensity associated with the wakemeasured on y-z measurement planes from x = -60 [mm] to x = 100[mm]. It is clear from these images that the stationary wake impingedthe test model at an acute angle, which was because of the modelinclination against the incoming flow as well as downwash near theleading edge due to the flow being discharged from the lower part ofthe test duct. These figures also exhibited a minor spanwise drift ofthe wake centerline at the upstream of the test model, which wasstraightened after the leading edge of the model. Figure 9 also depictsthat the wake size was about 2 times the sphere diameter and the maxi-mum turbulence intensity inside the wake was about 3% when thewake hit the test model surface. The top view of the wake in Figure 8,in conjunction with the lower contours in Figure 9, shows that the
Figure 12 Interaction of the flat-plate boundary layer withthe sphere wakes measured at x=25[mm] and y=0.2[mm]
(represented in terms of the acceleration factor,ensemble-averaged turbulence intensity and velocity
perturbation)
Wire Wake Trace
Spere Wake Footprint
Acceleration Factor
Turbulence Intensity
Velocity Perturbation
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6
wake-affected zone with relatively high turbulence intensity gradu-ally grew, spreading in the lateral direction inside the boundary layer.This zone resembled a turbulent wedge. However, a rough estimationusing the top view of Figure 8 revealed that its spreading half anglewas about 3 [deg], which was smaller than that of a conventional tur-bulent wedge induced by a 3D roughness [9].
Figure 10 presents an example of autocorrelation of the velocitysignal measured by #4 probe (center probe) of the sensor. The sensorwas located 40 [mm] upstream of the leading of the test model with 15[mm] vertical distance from the surface. The occurrence of periodicpeaks in this autocorrelation could be attributed to vortex sheddingfrom the sphere, and the reduced frequency of the vortex shedding,i.e., Strouhal number, was roughly estimated to be 0.14. According tothe study by Achenbach [10], the vortex shedding from the spherewas very periodic at Re above 6000 and its Strouhal number rangedfrom 0.125 to 0.20. Thus the present case almost agreed with this find-ing by Achenbach.
The flow field around and behind the sphere is known to be verycomplicated with one-sided or two-sided vortex shedding [11]. A nu-merical example of one-sided hairpin-like vortex shedding from asphere is displayed on the right of Figure 11. Although the presentmeasurement technique using a standard single hot-wire probe wasnot able to capture such a detailed coherent structure inside the spherewake, one may notice from close inspection of the data, e.g., the con-tours of the ensemble-averaged turbulence intensity measured atx = -60 [mm] (on the left of Figure 10) that the sphere wake was ac-
companied with relatively high turbulence zones designated as R-Land T-B, where R and L mean right-hand and left-hand sides whenlooking upstream, respectively. The feature of the sphere wake ap-pears to indicate two-sided vortex shedding mode, however, muchstill remains uncertain because of lacking relevant experimental data.
RESULTS IN THE MOVING SPHERE CASEDisturbance Detection
Figure 12 demonstrates the interaction of the flat-plate boundarylayer with the wakes from the sphere that moved upwards in front ofthe flat plate, expressed in terms of the acceleration factor, ensemble-averaged turbulence intensity and velocity perturbation on z-time do-main. These data were measured near the leading edge ( x = 25 [mm])and very close to the model surface ( y = 0 2. [mm]). It is obvious fromthis figure that the acceleration factor successfully detected the foot-print of the sphere wake on the test model much clearer than the tur-bulence intensity or velocity fluctuation did. The acceleration factoralso captured the traces associated with the thin wire, while the othertwo indices only detected very obscure images of the wire wakes. Sincethe wire moved only outside the circle of the sphere trajectory, thetrace of the wire wake took shape of a parabolic curve that shouldhave been in principle tangent to the line of z = 0. The velocity per-turbation contours indicate that the sphere wake mostly induced flowdeceleration on the wall, while the arrival of the bar wake first gener-ated flow deceleration, followed by the acceleration.
Although the acceleration factor based on the smoothed ensemble-averaged velocity proved its capability to capture a turbulent spot, thepresent authors finally decided to rely mainly on the turbulent inten-sity for detecting the emergence of a turbulent spot, while the accel-eration factor was used especially to track the incoming sphere as wellas wire wakes. This was because the difference in sensitivity to theincoming wakes between the acceleration factor and the turbulenceintensity, which was found by chance, could provide a useful tool fordistinguishing any flow event related to transition onset from the ex-ternal disturbances.
The sphere wake and the wake-affected zone were designed topass through the middle of the sensor, i.e., z = 0 . However, a closeinspection revealed that the sphere moved slightly right-hand side ofthe sensor symmetric plane, which was due to the centrifugal force
Figure 13 Snapshots of iso-value surfaces of the acceleration factor and ensemble-averaged turbulence intensity for theupward movement case, showing the appearance of an isolated turbulence spot beheath the sphere wake
effect acting on the sphere. In any cases, it was observed that the spherewake hit the test model surface as a localized external disturbance.
Turbulent Spot InceptionEnsemble-Averaged Quantities Figure 13 demonstrates the spherewake interaction with the boundary layer on the test model, using aseries of snapshots of the acceleration factor using the smoothed en-semble-averaged velocity as well as ensemble-averaged turbulenceintensity in terms of iso-value surfaces depicted in the spatial domainextending from x = 75[mm] to x = 205 [mm], from y = 0 toy = 5[mm] and from z = -15[mm] to z = 15[mm], respectively. Themeasurement domain in this figure is not properly scaled. Note that
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the inflow came from the left side of the domain. The iso-values of theacceleration factor and the ensemble-averaged turbulence intensitywere 750 and 4%, respectively. Note that the threshold for the turbu-lence intensity was previously adopted by one of the authors [12] todetermine the extent of a turbulent spot. Consequently, it appears thatthese snapshots correspond to sequential photo-images of the flowfield taken from a flow visualization using dye or smoke.
The fourth snapshot in Figure 13 captured the incoming spherewake on the most upstream measurement plane. The subsequent snap-shot detected a localized turbulent zone just beneath the sphere wake,as marked by a small circle. The sphere wake, embodied by the iso-value surface of the acceleration factor, appeared to trail its near-wall
end over the test surface containing this tiny turbulent zone. The tur-bulent zone gradually delayed from the advection of the mainbody ofthe sphere wake, at the same time, it grew as it moved towards thedownstream. Recalling the fact that the longitudinal scale of the mea-surement domain in Figure 13 was shrunken by a factor of more than4 in comparison with the spanwise (z) scale, the isolated turbulentzone created by the incoming sphere wake could be characterized byan elongated structure in the streamwise direction. In this sense, theturbulent zone, which was identified through the ensemble-averagedturbulence intensity, bore a close resemblance to the puff as shown inFigure 1. One should also remember that the each of the hot-wire probeswas distanced from the neighboring probes by 5 mm, therefore thesensor employed in this study was inherently unable to resolve theobserved turbulent zone into the streaky structure that would be ex-pected to reside there.
As the turbulent zone was drifted towards the downstream, its lee-ward side (the side pointing downstream) tended to lift off from thesurface as indicated by an arrow in 21) or 22) of Figure 13. This liftoff was clearly confirmed in 23) of Figure 13, also illustrating thelateral spread of the windward side of the turbulent zone (the sidefacing upstream) in comparison with its leeward side. These featuresallow us to draw a conclusion that the wake-induced turbulent zonearound x = 190 [mm] was likely to become a single turbulent spotthat seemed to take a shape of a conventional arrowhead pointing down-stream. This observation could be reconfirmed by Figure 14 showingensemble-averaged turbulence intensity contours on y = 0.2 [mm] andy = 1.4 [mm] expressed in the space (z) - time domain. The profile ofthe high turbulent zone on y = 1.4 [mm] was featured with an arrow-head-like shape pointing downstream, and the profile surely precededits lower counterpart on y = 0.2 [mm] by about 4.5 [msec]. This timedifference corresponded to the length of about 58 mm, estimating fromthe Blasius solution that the velocity difference between the two loca-tions was about 13 [m/s]. Since the spanwise scale of the turbulencezone, i.e., turbulent spot on y = 0.2 [mm] was about 31 [mm], thesemi-apex angle of the turbulence spot was tan-1 (15.5/58) = 15 [deg],which was almost the same as that of a conventional turbulent spot[15].
It seems that the above-mentioned findings conflicts with the find-
y=0.2
y=1.4
4.49msec
31
Figure 14 Ensemble-averaged turbulence intensitycontours for x = 190[mm] on two measurement locations(y = 0.2[mm] and y = 1.4[mm]) expressed in the space (z) -
time domain
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ing in DNS work by Wu et al. [5]. In fact, they found in their analysesdealing with wake-boundary layer interaction that the turbulent spotinduced by any external disturbances like free-stream turbulence hadan arrowhead pointing upstream because breakdown occurred in theouter layer. In thinking of this disagreement, one should understandseveral differences between the studies by Wu et al. and by the presentauthors. The DNS work mainly employed bar wakes as external dis-turbance impinging the surface, which could be termed ‘normal rota-tion case’ according to Funazaki et al. [14]. On the contrary, only ‘re-verse rotation case’ was thoroughly investigated in this study.
Actually, the normal rotation case, where the sphere moved down-
Acceleration Factor
Turbulence Intensity
y [m
m]
y [m
m]
t [msec]
t [msec]
sphere wakebar wake bar wake
bar wake bar wake
sphere wake
Acceleration Factor
Turbulence Intensity
y [m
m]
y [m
m]
t [msec]
t [msec]
bar wake bar wake
bar wake bar wake
sphere wake
sphere wake
(a) normal rotation (sphere moving downwards)
(b) reverse rotation (sphere moving upwards)
Figure 15 Contours of acceleration factor and ensemble-averaged turbulence intensity for the normal and reverserotaion cases measured at x = 130[mm] expressed in the
Figure 16 Raw signals of the velocity data simultaneously acquired by the seven hot-wire probes that were placed aroundy/ddddd* * * * * = 1.3 at several streamwise measurement locations
wards instead, had been once tried, ending up with a serious problem.Figure 15 shows contours of the acceleration factor using the smoothedvelocity as well as ensemble-averaged turbulence intensity drawn onthe space (y) and time domain for the normal rotation case at x = 130[mm], in comparison with the corresponding contours for the reverserotation case. Due to the effect of ‘negative jet’ [19], which is an ap-parent jet inside the wake viewed from the mean flow, the wakes forthe normal rotation case created turbulent zones that lasted much longernear the test surface than those for the reverse rotation case. These
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enlarged wake and their followers, i.e., calmed regions seemed to in-terfere with the subsequent turbulent zones generated by the spherewakes. This was clearly confirmed in the acceleration factor, in par-ticular, the area marked by a circle where the acceleration factor be-came very small. Therefore, it was concluded that the present wakegenerator was not suitable for observing the transitional process of thenormal rotation case. Modification on the wake generator is now un-der way.
Raw signal investigations As shown in the above, the sphere wake hitthe test model surface as a localized external disturbance, creating anisolated turbulent spot where a criterion for the spot generation wasmet. Since one of the final goals in this and any future studies hasbeen and will be to find out this criterion, it was important to detectthe existence of any precursor of the wake-induced turbulent spot aswell as the turbulent spot itself, particularly from the raw velocitydata from the seven probes. Because the amount of the all raw datawas too huge to be checked, a limited number of the data were se-lected to be examined in search of the spot precursor and the spot.This selection process was based on an assumption that the point-likedisturbance from the moving sphere locally and temporarily acted likefree-stream turbulence which was believed to bring about streaks in-side the boundary layer, leading to so-called Klebanoff modes (seeLuchini [12], for example). The Klebanoff modes, which characterizea laminar boundary layer under the influence of free-stream turbu-lence and can be regarded as an ensemble-averaged view of the in-stantaneous streaks [4], have the peak of streamwise velocity fluctua-tion at y d * = 1.3, where d * is the displacement thickness. In expec-tation of any analogy between the free-stream turbulence and the mov-ing sphere wake, the velocity data measured around y d * = 1.3 wereselectively examined.
Figure 16 illustrates raw signals of the velocity data simultaneouslyacquired by the seven hot-wire probes that were placed around y d * =1.3 at several streamwise locations. Note that the displacement thick-ness was found to be determined by use of the Blasius solution, whichwas also based on the study done by Takahashi [6]. Three sets of theraw signals, each of which was randomly picked up out of 100 datasets, are shown here for each of the streamwise locations. The spherewake created velocity dips between two adjacent bar wakes aroundx = 70 [mm], where the velocity dips did not contain any high-fre-quency fluctuations. As could be easily imagined, such smooth dipstended to be replaced by high-frequency fluctuations as x increased.One may see that there were large differences in the velocity fluctua-tion among the randomly selected three data sets for each measure-ment location. This means that the sphere wake stochastically left somedistinct traces of the interaction inside the boundary layer. Spiky fluc-tuations emerged as indicated by arrows within the velocity dips forx = 130 [mm] ( Req =239), followed by the appearance of high-fre-quency fluctuations thereafter. A close inspection into the raw signalsrevealed that such spiky fluctuations began to be identified after x =100 [mm] ( Req =209). Although these spiky fluctuations seemed tobe closely related to a precursor of turbulent spot or the spot onsetitself, more detailed and systematic investigations over the entire rawvelocity data are needed to verify this supposition.
Transition Onset In the above, the transition onset was observed aroundReq =210 ~240. Mayle’s correlation for the transition Reynolds num-ber [16],
Re Tutrq , = -400 5 8, (5)
in conjunction with the experimental finding that Tu inside the spherewake apart from the test surface was about 3% as shown in Figure 9 orFigure 13, yielded a reasonable prediction, Re trq , =201. On the otherhand, the correlation of Abu-Ghannam and Show,
Re etrTu
q ,.= + -163 6 91 , (6)
provided Re trq , =213, which seems a better prediction than that of theMayle’s correlation.
It appears that some discussion is necessary here on whether dif-ferences in wake structure between a sphere wake and a rather con-ventional bar wake with quasi two-dimensionality may have any im-pact upon the transition onset. In fact, as Koyabu et al. [20] recently
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pointed out, even weak bar wakes with maximum Tu of 5% causedboundary layer transition earlier than expected from the Mayle’s cor-relation, which was different from the finding in the present spherewake cases. However, as mentioned above, most of the experimentsin this study were executed for the reverse rotation case, not for thenormal rotation case, so that fair judgement should be suspended untilsufficient amount of velocity data that are free from the disturbance ofthe bar wakes become available, in particular for the normal rotationcase. Actually, according to Funazaki et al. [14], followed numeri-cally by Wu et al. [5] and experimentally by Koyabu et al. [20], adistinct difference has been confirmed in transitional behavior of wake-affected boundary layer between the normal and the reverse rotationcases, usually resulting in delayed transition onset in the reverse rota-tion case.
CONCLUSIONS This study aimed at clarification of wake-induced bypass transi-
tion process of a boundary layer on a flat plate using the moving sphereas wake generator in order to create a localized external disturbance.The multi-probed sensor was employed to capture any preceding flowevent to turbulent spot onset, the structure of the spot, in addition tothe spot onset itself. The important findings are summarized as fol-lows.(1) The periodically incoming sphere wake left a localized external
disturbance acting on the laminar boundary layer, eventuallycreating a ‘puff-like’ elongated flow phenomenon inside theboundary layer.
(2) An isolated turbulent spot began to appear around x = 100 ~ 130[mm], corresponding to Reynolds number based on momentumthickness Re trq , of 210 ~ 240. The two correlations, Mayle, Abu-Ghannam and Show, were able to provide reasonable predictionsof the transition onset even in the case of sphere wake-boundarylayer interaction.
(3) It was revealed from the detailed inspection of the three-dimensional structure of the turbulent spot using the ensemble-averaged turbulence intensity that the turbulent spot created bythe localized external disturbance was likely to take a shape ofarrowhead pointing downstream like a conventional turbulent spot.
ACKNOWLEDGMENTSThe authors acknowledge the financial support to this study from
the Ministry of Education, Culture, Sports, Science and Technologyof Japan. The authors are also grateful to F. Saito for his cooperationin making the test apparatus. Lastly, the authors are greatly indebtedto the reviewers for their invaluable suggestions and comments toimprove the quality of this paper.
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