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STUDIES ON TURBULENCE STRUCTURE OF BOUNDARY LAYERS DISTURBED BY MOVING WAKES
K. Funazaki and Y. Aoyama
Iwate University
Morioka, Japan
Proceedings ofASME TURBO EXPO 2000May 8-11, 2000, Munich, Germany
2000-GT-0272
ABSTRACTAn attempt is made to measure wake-affected boundary layers on
a flat plate by means of a split-film probe. Although a number of stud-ies have been made to reveal the transitional behavior of boundarylayers subjected to periodic wake passing, much is still unknown onthe turbulence structure of those boundary layers. It is because mostof the studies measured the boundary layers by single hot-wire probe.This measurement therefore aims at the determination of the turbu-lent structure of the incoming wakes as well as the disturbed bound-ary layers mainly in terms of ensemble-averaged Reynolds shear stressand turbulence intensity. Unsteady velocity vectors associated withthe wakes and wake-induced turbulence patch (a number of turbulentspots) are also determined in detail. In comparison to a conventionalhow-wire probe, the probe used in this study is less sensitive to fluc-tuations of high frequency and less accurate in the near-wall measure-ment due to its relatively large diameter of its sensor. However, newand important information is obtained on the structure of wake-in-duced turbulence patch, which provides more insight into the wake-induced boundary layer transition than before. In addition, the mea-sured velocity field following the turbulent patch indicates a clearimage of calmed region.
NOMENCLATUREA Bi i, : constants of sensor (i)b1 2 : semi-depth width of bar waked : diameter of wake-generating barEi : voltage output from sensor (i)fi θ( ) : a function of flow angle for sensor (i)ni : constant (power) of sensor (i)Ri : resistance of sensor (i)
T : wake-passing periodt : timeTu t( ) : ensemble-averaged turbulence intensityUe : velocity at the outer edge of boundary layerU t( ) : velocity magnitudeu t v t( ) ( ), : streamwise and transverse velocity components
′ ′( )u v t : ensemble-averaged Reynolds shear stressx : longitudinal distance from the leading edge of the modelXd : distance between the bar and the model leading edgexs : surface length measured from the leading edge of the modely : distance from the surface of the test modelδ99 : boundary layer thicknessν : kinematic viscosity
θ t( ) : flow angle
superscript
- 1
1
: ensemble-averaged value
: time-averaged value
′ : fluctuation measured from the average
INTRODUCTIONBoundary layer transition induced by periodic wakes moving over
airfoils in axial-turbomachines has been attracting much attention fromvarious fields of researches during the last two decades, and a largeamount of information on the wake-induced transition is now beingcomplied, mostly from experimental activities, into a database (Forexample, Chakka and Schobeiri (1999), Kittichaikarn et al. (1999),Kim and Crawford (1999), Funazaki and Koyabu (1999), as relevantand recent studies). Despite these efforts, because of the utilization ofunidirectional probes or surface sensors in the experiments, only lim-ited knowledge is available on turbulence structure of the wake-af-fected boundary layers. Therefore, to the authors’ best knowledge, veryfew studies have been done to clarify time-resolved Reynolds stressdistributions within the boundary layers or the structure of a wake-induced turbulent patch, clustered turbulent spots, in detail. Let usbriefly discuss on this turbulent patch. Figure 1 is a schematic expres-sion of the turbulent patch given by Hodson et al. (1992). This figuregives us an idea on how turbulent spots are generated under the wake,however, the situation is not as simple as depicted in Figure 1. Somestudies (Makita and Nishizawa (1998)(1999)) using two small pulsejets have revealed that interaction between two identical and neigh-boring turbulent spots changed the growth pattern of each of the tur-
Figure 1 Schematic of turbulent patch under a wake(Hodson et al. (1992))
- Copyright@2000 by ASME
Copyright (C) 2000 by ASME
bulent spots in comparison with that of an isolated turbulent spot. Theinteraction became more complicated when the turbulent spots didnot emerge simultaneously. From these experiments using only twoturbulent spots, one can easily imagine that a number of turbulentspots must be interacting with each other in a very complex mannerunder the wake, then characterize the resultant turbulent patch andeventually affect transitional behavior of wake-disturbed boundarylayer. This indicates the importance of exploring the structure of wake-induced turbulent patch for better understanding of boundary layertransition in turbomachines.
This study was the authors’ first attempt to conduct two-compo-nent velocity measurements using a split-film probe upon transitionalboundary layers on a flat plate which were subjected to periodic wakepassage, aiming at the clarification of the structure of the wake-af-fected boundary layer. The split-film probe was employed for theboundary layer measurements in consideration of its small size whichenabled it possible to be positioned close to a wall (Bruun (1995)).
EXPERIMENTS
Test ApparatusFigure 2 shows the test section and the measuring system. The test
model, which was already used in the study of Funazaki and Koyabu(1999), had an elliptic leading edge of 75 mm long axis and 15 mmshort axis, followed by two flat plates. The total streamwise length ofthe model was about 1000 mm and the span was 200 mm wide. Mov-ing bars on the rotating disk generated periodic wakes that impingedthe model surface. The bar diameter d was 5 mm. While the streamwisedistance between the wake-generating bar and the model leading edgeXd was usually 300 mm, this distance was changed in a case to exam-
ine the effect of the wake turbulence intensity on the transition of theboundary layer. Revolution direction of the disk could be reversed,which changed the interaction between the wake and the boundarylayer through so-called negative jet effect (Funazaki et al. (1997a)).An optical tachometer detected the disk rotational speed.
Two-channel Constant-Temperature-Anemometry system(Kanomax model 1010) was used for the velocity measurement, wherea temperature compensation unit (Kanomax model 1020) measuredthe free-stream temperature as shown in Figure 2. A PC-controlleddigitizer (Autonics APC-204) acquired all three analog signals fromthe system with 50kHz sampling frequency. The optical tachometergenerated a pulse per revolution that triggered the data acquisition. Atraverse unit placed the split-film probe, whose detail will be given inthe following, to a specified point within the accuracy of 0.05 mm.
Split-Film ProbeMeasurement Principle Figure 2 also shows the split-film probe usedfor the boundary layer measurements (TSI Model 1287). The sensingpart of this probe is a small crystal-fiber rod of 0.15 mm diameter, onwhich two electrically insulated thin films are deposited as sensor.The principle of two-dimensional velocity measurement by means ofthe split-film probe is as follows.
Suppose that each of the outputs from the sensing films can beexpressed as the product of two functions of flow velocity U andflow angle θ , respectively, we have a following expression (Bruun(1995)).
E
RA B U f T Ti
ii i
ni s a
ii
2
= +( ) ( ) −( )ˆ θ , (1)
where Ei : output from the sensor, Ri : operational resistance of thesensor, Tsi
: sensor temperature, Ta : ambient temperature, Ai, Bi,
- 2 -
2
Uθ
Figure 2 Test model and measurment system with theclose-up of the split-film sensor (TSI Model 1287)
ni : sensor constant, and suffix i (= 1, 2) indicates the sensor number.The angular function fi θ( ) represents the effect of the movement ofthe stagnation point on the sensor rod due to the flow angle variation,and is approximated by a linear function as follows:
ˆ ( ) ( ) ( )( )
( )( )
( )
f a a aa
aa a
a f
ii i i
i
ii
i
ii
θ θ θ θ
θ
( ) = + = +
= +( )
≡ ( )
0 1 01
00
0
1 1
. (2)
Substitution of Eq. (2) into Eq. (1) yields the following equation,
E
RA B U f T Ti
ii i
ni s a
ii
2
= +( ) ( ) −( )ˆ ˆ θ , (3)
where a A Aii i0
( ) ˆ≡ , a B Bii i0
( ) ˆ≡ . When θ =0 in Eq. (3), we have
E
RA B U T Ti
ii i
ns a
ii
20θ = = +( ) −( )ˆ ˆ . (4)
Calibration using the above equation provides the sensor constantsAi , Bi , ni . The function fi θ( ) is also experimentally determined fromthe following equation,
f E T T E T Ti i s a i s ai iθ
θ θ( ) = −( ) −( )= =2
0
20 . (5)
Eliminating θ from Eqs. (3) for i = 1 and i = 2, the following equa-tion for the velocity U is derived as
ˆ ˆ ˆ ˆ ˆB Ba
aU A B
a
aB e Un n n
1 22
12 1
2
11 2
21 11 2 1−
+ −
−
+
Split-FilmSensor
Wake Temp. Probe
Digitizer
Temp. Unit
Cylinder
xy
L
ReverseRotation
Screen
Motor-DrivenTraversing Unit
Test Model
NormalRotation
Personal Computer
Trigger
Amemometer 1
Amemometer 2
Xd
Copyright (C) 2000 by ASME
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0.80
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0.90
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1.00
1.05
1.10
1.15
1.20
-30 -20 -10 0 10 20 30
f 1(˘)
f2 (
˘)
˘[ ]
θ
Figure 4 Example of experimentally determined angularfunctions of the sensors
+ −
−
+ −
ˆ ˆ ˆ ˆ ˆA Ba
aB e U A A
a
an
1 22
12 1
21 2
2
11 12
,(6)
+ − =a
aA e A e2
12 1
21 2
2 0ˆ ˆ
eE
R T Te
E
R T Ts a s a12 1
2
122 2
2
2=
−( ) =−( ), .
The above equation can be iteratively solved by Newton’s method toobtain U . The flow angle θ is then obtained from Eq. (3).
Calibration The split-film probe was carefully calibrated in the po-tential core of free jet from the contraction nozzle of the calibrationtunnel. This tunnel could set the jet velocity with about ± 2% accu-racy. As the first step, the probe holder of the calibration system fixedthe probe so that the probe axis became almost perpendicular to thejet, which meant θ = 0. The voltage outputs from the two sensorswere acquired as the jet velocity was changed. Note that the air tem-perature was also measured simultaneously. Figure 3 shows one ofthe results obtained through this calibration. The calibration curves inthis figure followed the experimental data quite well, proving the va-lidity of the expression in Eq. (1). Then the probe holder pitchwisely
- 3
0
0.005
0.01
0.015
0.02
0
0.005
0.01
0.015
0.02
0 5 10 15 20 25 30 35
E1^
2/R
1/(T
s-T
a) E2^2/R
2/(Ts-T
a)
U[m/s]
Figure 3 Example of the probe calibration
3
tilted the probe in order to determine the angular function fi θ( ) in Eq.(5). Due to a mechanical constraint of the holder, the probe inclinedby ± 25°. Two output signals and the jet temperature were simulta-neously obtained using the above-mentioned measurement system.Figure 4 demonstrates an example set of the experimentally deter-mined angular function f1 θ( ) and f2 θ( ) for the sensor 1 and sensor2, respectively. This graph revealed that the both function linearlyvaried with θ within the range tested, as expected in the above.
Operation One thing we had to pay attention to was the thermal inter-action between the two heated films. To avoid this, the operationalresistance of each of the films was selected so that the sensor tempera-tures were kept equal to each other.
Data ReductionEnsemble-averaged velocity components u t( ) , v t( ) , and turbu-
lence intensity Tu t( ) were calculated from the records U tk ( ) and θk t( )( k m= 1,..., , m = 128) as follows:
˜ cosu tm
U t tkk
m
k( ) = ∑ ( ) ( )=
1
1θ , sinv t
mU t tk
k
m
k( ) = ∑ ( ) ( )=
1
1θ , (7)
Tu tm
u t v t Uk kk
m
in( ) = ′ ( ) + ′ ( ){ }∑=
122 2
1 , (8)
where ′ ( ) = ( ) − ( )u t u t u tk k ˜ and ′ ( ) = ( ) − ( )v t v t v tk k ˜ . Reynolds shearstress was also defined in an ensemble-average fashion as
′ ′( ) = ′ ( ) ′ ( )∑=
u v tm
u t v tk kk
m1
1 . (9)
Flow Conditions and Measurement PointsInlet flow velocity Uin was 20 m/s and the background turbu-
lence level was about 0.8 %. When using a turbulence grid, the turbu-lence level slightly increased up to 1.2%. Test conditions for the mea-surements of wake-disturbed boundary layers are listed in Table 1.The most upstream measurement point was at x = 0.078 for the regu-lar configuration of the test model, i.e., X dd = 60. The measure-ment points at each of the streamwise positions located over the zoneextending from y = 0.2 mm to y = 15 mm, clustering near the sur-face. Two wake-generating bars were attached on the rim of the diskrotating at 1200 rpm in the present case, which led to the bar speed ofabout 45m/s at the mean radius of the bar. The resultant unsteady flowfluctuated at the wake-passing frequency of 40 Hz.
Uncertainty AnalysisUncertainty associated with the velocity measurement by use of
the split-film probe seemed to consist of two major parts: calibrationerror and error arising from the probe itself. The calibration error af-fected the uncertainty of the velocity magnitude U through the em-pirical constants such as ni in Eq. (6). Some numerical investiga-tions revealed that the error in U caused by the uncertainty of theempirical constants was about 2.5%. The angular error in θ estimatedfrom Eq. (3) was about 3.5%.
As for the error caused by the probe itself, it has been realized thatthe greatest uncertainty of the split-film probe originates from its com-plex thermal response (Bruun (1995)) and, similar to any other hot-film probes, the split-film probe suffers from its poor frequency-re-sponse characteristics in comparison with hot-wire probes. In that senseit was important to understand how the split-film probe followed theunsteady flow caused by the wake passing for clarification of the un-certainty. However, it was actually a difficult task to make such an
Copyright (C) 2000 by ASME
estimation rigorously. A simple approach taken in this study to mea-sure the probe frequency response was to compare the data obtainedwith the split-film probe with those acquired with a proven technol-ogy, i.e., a single hot-wire probe. Figure 5 shows a comparison ofensemble-averaged velocity data obtained using the two differentmethods. It seemed that the velocity deficit of the split-film probebecame about 5% smaller than that of the hot-wire probe, however,the both data almost coincided with each other, which might be thanksto relatively low frequency of the velocity fluctuation caused by thewake. This implies that the split-film probe was able to respond to thevelocity fluctuation encountered in the present study as fast as a hot-wire probe, at least in the ensemble-average sense.
RESULTS
Velocity Distribution over the Test ModelSince there were no pressure holes on the test model, the velocity
distribution over the model was analytically evaluated from a poten-tial flow code. Figure 6 is the calculated velocity distribution, show-ing that the velocity rapidly accelerated nearby the leading edge, fol-lowed by a gradual decrease. Boundary layer analyses revealed thatno separation was expected on the model, which was also verified bythe oil-flow visualization in the preliminary test.
Steady Flow MeasurementsWake Profile Measurements To check the soundness of the probe andthe above-mentioned procedure for determining velocity and flowangle, bar wake measurements were conducted with one of the wake-generating bars being placed horizontally along with the duct centerplane. Note that the test model located at the far downstream of thetest duct and the split-film probe was at 300 mm behind the bar. Fig-ure 7 shows the measured distribution of time-averaged Reynolds shearstress inside the stationary wake normalized with the square of veloc-ity defect, in comparison with the theory of Schobeiri et al. (1996).The experimental data almost matched the theory, however, there arosesome discrepancies over the region y b1 2 = 0.0 - 1.0, which wereattributed to slight vertical non-uniformity of the mean flow inside theduct.
Flat-Plate Boundary Layer Measurements Figure 8 shows astreamwise velocity profiles at x = 0.15 and x = 0.25 on the testmodel for no grid condition. Also shown is the Blasius solution, where
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0.9
0.95
1
1.05
1.1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Split-Film ProbeHot-Wire Probe
U /
Uin
time [s]
Figure 5 A comparison between the time-varying velocitymeasurements obtained by a single hot-wire probe and
the present split-film probe
4
η was defined as
η ν= y U xe s . (10)
Most of the measured data at x = 0.15 followed the Blasius solutionexcept for the data obtained very close to the surface. These discrep-ancies occurred where η < 1.5, which corresponded to about y < 0.5mm. This indicates that the data obtained near the wall ( y < 0.5 mm)were less accurate. The data at x = 0.25 exhibited a slight deviationfrom the Blasius solution, suggesting the onset of boundary layer tran-sition around there. Figure 9 presents the velocity traces acquired atx = 0.25 and x = 0.30 for several transverse locations from the sur-
face. One can notice the appearance of ‘wave packet’-like patterns inthe near-wall traces, which eventually evolved to be a turbulent spotas seen in the traces for x = 0.30. Figure 10 displays boundary layer
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-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
-4 -3 -2 -1 0 1 2 3 4
Schobeiri et al (1996)
Exp.
uuuu’’’’vvvv’’’’ //// ∆ UUUU2222
y / b1/2
300
y
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6
Ue
x
x
Figure 6 Velocity distribution on the test model obtainedbya potential flow code
1
2
3
4
Table 1 Test conditions for unsteady flow measurements
direction gridcase #
normal none 60
normal none 100
reverse none 60
normal yes 60
X dd
Figure 7 Reynolds shear stress inside the bar wake
Copyright (C) 2000 by ASME
6
8
10
12
14
16
18
20
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x = 0.30
U [m/s]
Time[s]
6
8
10
12
14
16
18
20
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x = 0.25 0.20.30.40.50.60.70.80.91.0
U [m/s]
Time[s]
0 0.2 0.4 0.6 0.8 1 1.20
2
4
6
8
10
12x = 0.25
Exp.Blasius solution
u / Ue
η
no grid
Figure 8 Velocity profiles measured at x = 0.15 (left) and x = 0.25 (right) for no grid condition, with Blasius solution
0 0.2 0.4 0.6 0.8 1 1.20
2
4
6
8
10
12x = 0.15
Exp.Blasius solution
u / Ue
η
no grid
Figure 9 Traces of streamwise velocity component measured at x = 0.25 (left) and x = 0.30 (right) for no grid condition
thicknesses measured for low (no grid) and moderate (with grid) free-stream turbulence conditions, accompanied with calculated laminarboundary layer thickness. The measured data for the no grid conditiondeviated from the calculation from x = 0.4, which almost correspondedto the observations of the velocity traces mentioned above.
Unsteady Flow MeasurementsCase 1 - Baseline Measurements - Figures 11 and 12 exhibit contoursof ensemble-averaged turbulence intensity and Reynolds shear stressmeasured at several streamwise locations, respectively, where the ab-scissa is the elapsed time from the trigger point and the ordinate is thedistance from the test surface. The turbulence intensity contours inFigure 11 indicated the incoming wakes on the test model as well asthe turbulence spots growing beneath the wakes. One can spot theoccurrence of a zone with relatively high turbulence intensity, i.e.,turbulent patch, at x = 0.078, which grew in the cross-flow andstreamwise directions. Since the value of the Reynolds shear stresssinusoidally varied with time in the free-stream away from the testsurface, the turbulent patch observed in Figure 11 could be identifiedmuch clearer in Figure 12 as negative value zone of ′ ′( )u v t under thewake. This intense shear zone, taking the shape of iceberg, dominatedthe near-wall region beneath the wake. This turbulent patch movedwith the wake, its height and length being enlarging. It was also foundthat the Reynolds shear stress tended to have relatively large magni-
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5
0
0.002
0.004
0.006
0.008
0.01
0 0.2 0.4 0.6 0.8 1
laminar (Cal.)Exp. (no grid)Exp. (grid)
δ 99
x
Figure 10 Boundary layer thicknesses with and withoutturbulence grid
tude at the front portion of the turbulent patch.To examine the flow structure near the wake and the wake-in-
duced turbulent patch in more detail, the wake-perturbed velocity fieldfrom which the time-averaged velocity field was extracted was super-imposed on the Reynolds shear stress contours at x = 0.15 and x =0.30 as seen in Figure 13. Note that a velocity vector directed to the
-
Copyright (C) 2000 by ASME
right means a decrease in velocity. It is clear that the incoming wakefor the normal rotation case first induced velocity increase, which wasfollowed by the decrease in the velocity. A close inspection of thevelocity vectors revealed that the perturbed velocity vectors inside thewake had the velocity components towards the test surface, whichwas marked with the circle D in the upper of Figure 13. These phe-
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0.00 0.01 0.02 0.03 0.04
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m]
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8.0
10.0
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14.0
16.0
time [s]
y [m
m]
Figure 11 Time-resolved turbulence intensity contoursmeasured at several streamwise locations (case 1)
x = 0.10
x = 0.15
x = 0.20
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0.00 0.01 0.02 0.03 0.04
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time [s]
y [m
m]
x = 0.078
6
nomena were due to the negative jet effect of the wakes. Inside theturbulent patch that followed the wake, marked with the circle A, thewake-affected velocity field exhibited considerable deceleration incomparison to the time-averaged velocity field. The accelerating zonemarked with the circle C, which seemed to correspond to a calmedregion, then appeared after the precedent intense shear zone near the
-0.6
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y [m
m]
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time [s]
y [m
m]
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2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
time [s]
y [m
m]
Figure 12 Time-resolved Reynolds shear stress contoursmeasured at several streamwise locations (case 1)
x = 0.10
x = 0.078
x = 0.15
x = 0.20
Copyright (C) 2000 by ASME
Figure 13 Time-resolved Reynolds shear stress contours measured at x= 0.15 (upper) and x = 0.30(lower), with velocityvectors induced by the wake and the turbulent patch (case 1)
0.00 0.01 0.02 0.03
2.0
4.0
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12.0
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16.0
time [s]
y [m
m]
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C
D
A
B
X = 0
0.00 0.01 0.02 0.03
2.0
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6.0
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12.0
14.0
16.0
time [s]
y [m
m]
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Reynolds stress
E F
X = 0
test surface. Similar statements can be applied to the data at x = 0.30,except for the facts that the wake-induced intense shear zone as seenin the circle E as well as the subsequent flow-accelerated region des-ignated with the circle F significantly grew while they moved from x= 0.15 to x = 0.30. The other point to be mentioned on these contoursis positive value zones of ′ ′( )u v t occurring under the leading and trail-ing edges of the turbulent patch. Although the near-wall flow mea-surements by use of the split-film probe was likely to contain largeerrors, it appears that these zones had some physical meanings in con-nection with the wake-affected flow field and the resultant turbulentpatch. In addition, it is evident that the near-wall vectors beneath theturbulent patch marked with circle A or E had upward velocity com-ponents.
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7
Some discussions are necessary on turbulent patch. As mentionedearlier in this paper, the authors defined that the turbulent patch was acluster of turbulent spots randomly generated under the wake, as de-picted in Figure 1. Unfortunately it was not possible to distinguishone turbulent spot from others inside the turbulent patch, however, itseems useful to compare the structure of the measured turbulent patchwith that of a well-documented turbulent spot for the discussion de-scribed in the following. Figure 14 shows a typical streamwise pertur-bation velocity field associated with a turbulent spot, which was re-ported by Makita and Nishizawa (1998). Note that this spot was cre-ated by pulse air injection from a small hole. Also shown in Figure 13is the streamwise perturbation velocity field of the turbulent patch,where the ordinate is the distance normalized with the steady bound-
Copyright (C) 2000 by ASME
ary layer thickness. In general the features of the both streamwise per-turbation velocity fields resemble each other in terms of the appear-ance of the velocity deceleration, followed by the acceleration, i.e.,calmed region. In addition, the bottom of each of the deceleration zoneslocated around y δ = 0.5. On the other hand, one can also identifysome differences. For example, the bottom of the deceleration zone ofthe turbulent patch was considerably flat and large in comparison tothat of the turbulent spot. One plausible explanation for this differ-ence was the effect of several turbulent spots coexisting or being mergedin the turbulent patch. It also seemed convincing that the negative jeteffect contributed to the difference, however, much remains unknownyet.
Case 2 - Effects of Decayed Wake- Figures 15 demonstrates Reynoldsshear stress contours and streamwise perturbation velocity contoursobtained for the case 2; the axial distance between the moving bar andthe test model enlarged by 200 mm. Again the ordinates are normal-ized with the steady boundary layer thicknesses, respectively, whilethe upper limit of the measured areas are all the same (8 mm). Notethat the boundary layer measurement near the leading edge becameenabled in this case. Due to this enlargement, the peak value of thewake turbulence Tumax decreased from 5% down to 4%. It appears
Figure 14 An example of ensemble-averaged streamwisevelocity perturbation(upper) turbulent spot (Makita and Nishizawa (1998)(lower) turbulent patch at x = 0.15 (case 1)
y / δ
0.5
0.0
2.0
1.0
1.0
2.0
-1.0
-2.0
-3.0
0.02 0.03 0.04
1.0
2.0
3.0
4.0
5.0
time [s]
-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0U - Uave [m/s]
- 8
8
that the occurrence of turbulent patch under the wake could not beclearly observed at least until x = 0.075. This was a contrast to thedata for the case 1, meaning delay of the wake-induced transition. Theshear stress contour at x = 0.10 provides a clear image of a growing
1.0
0.0-1.5
-1.0
-0.50.5
1.0
0.000 0.010 0.020
1.0
2.0
3.0
4.0
5.0
6.0
time [s]
y / δ
Figure 15 Time-resolved Reynolds shear stress distribu-tions superimposed with streamwise velocity perturba-tion contours measured at several streamwise locations
(case 2)
-1.0
0.0
0.5 0.0
-0.5
0.00 0.01 0.02
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time [s]
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time [s]
y / δ
x = 0.10
x = 0.075
x = 0.05
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time [s]
y / δ
x = 0.15
-0.3 -0.2 -0.1 -0.0Reynolds Shear Stress
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Copyright (C) 2000 by ASME
turbulent patch underneath the wake. Comparing the contours of theReynolds shear stress and streamwise perturbation velocity at x =0.05 or 0.075, it did not seem that the small velocity dip appearingaround y δ = 1.0 had a direct relationship with a turbulent patch ofhigh shear stress.
Figure 16 Time-resolved turbulence intensity contoursmeasured at several streamwise locations (case 3)
2.0
4.0
0.00 0.01 0.02 0.03 0.04
2
4
6
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12
14
16
time [s]
y [m
m]
x = 0.078
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time [s]
y [m
m]
x = 0.10
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time [s]
y [m
m]
x = 0.15
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time [s]
y [m
m]
0 2 4 6 8Turbulence Intencity [%]
x = 0.20
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9
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time [s]
y [m
m]
-1.0 -0.8 -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6 0.8Reynolds Shear Stress
-0.2
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time [s]
y [m
m]
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m]
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time [s]
y [m
m]
Figure 17 Time-resolved Reynolds shear stress contoursmeasured at several streamwise locations (case 3)
x = 0.20
x = 0.15
x = 0.10
x = 0.078
Case 3 - Effect of the Direction of the Bar Movement - Figures 16 and17 display contours of ensemble-averaged turbulence intensity andReynolds shear stress measured at several locations for the reverserotation case. Comparisons of these contours with those in Figures 11and 12 reveals that the wake duration for the reverse rotation case
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Copyright (C) 2000 by ASME
Figure 18 Reynolds shear stress contours at x= 0.15 (left) and x = 0.30(right), with velocity vectors (case 3)
0.0050 0.0100 0.0150 0.0200
2.0
4.0
6.0
8.0
time [s]
y [m
m]
-1.0 -0.8 -0.6 -0.4 -0.2 -0.0Reynolds Shear Stress
x = 0.15A
B
C
Wake
0.0175 0.0225 0.0275 0.0325
2.0
4.0
6.0
8.0
time [s]
y [m
m]
-1.0 -0.8 -0.6 -0.4 -0.2 -0.0Reynolds Shear Stress
x = 0.30
WakeD E
F
became shorter and shorter as it moved downstream. Accordingly,wake-induced turbulent patches gradually lagged behind the preced-ing wakes, lastly separated each other. This was quite in contrast tothe normal rotation case (case 1). Impacts of the bar movement direc-tion upon the wake-induced transition were first reported by Funazakiand his colleagues (1996)(1997a), and reconfirmed by Kittichaikarnet al. (1999). Figure 18 explains the separation between the wake andthe turbulent patch more clearly, where ensemble-averaged Reynoldsshear stress contours at x = 0.15 and x = 0.30 for the reverse rotationcase were shown along with their perturbed velocity vectors. The tur-bulent patch was characterized as the intense shear stress zone as wellas decelerated zone. The perturbation velocity vectors exhibited sev-eral interesting features to note. Due to the upward fluid motion insidethe wake (positive jet effect), the vectors beside the wake, as markedwith A and B, were directed toward the wake. These movements con-sequently induced the flow that went beyond the turbulent patch fromthe backside of the patch as indicated in the circle B for x = 0.15 or inthe circles D and E. Upward vectors underneath the turbulent patchwere again observed as seen in the circle C or F likewise in the case 1measurements (see Figure 19 as the close-up of the right-side con-tours in Figure 12 for the sake of a direct comparison with Figure 18).A comparison between Figure 18 and Figure 19 yields that the wake-induced turbulent patch for the normal rotation seemed larger thanthat of the reverse rotation. It could be possible to image that the in-coming wake of the normal rotation contributed to this differencethrough generating turbulent spots under the front portion of the wake.Otherwise, as indicated by Kittichaikarn et al. (1999), broadly-dis-tributed virtual origins of the turbulent spot had some influences onthe difference in growth rate of the turbulent patch, although furtherstudies are still necessary to verify these suppositions.
Case 4 - Effect of Free-Stream Turbulence - Figure 20 shows theensemble-averaged Reynolds shear stress contours and the perturbedvelocity vectors for the case using the turbulence grid, where the wake-generating bar moved in the normal direction. Due to the enhancedfree-stream turbulence, the level of the background shear stress in-creased. Comparing the contour and the velocity vectors with those ofthe case 1 (or Figure 19), the size of the turbulent patch became smallerand the shear stress level in the patch was considerably low for thecase 4. In addition, the upward movement under the patch was calmeddown. It is also evident that the front side of the wake bent in the
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thickened boundary layer, as seen in the circle A. These changes seemedto be related to the production rate of the turbulent spots. Finally onecan notice the appearance of a small dip of the shear stress as well as
Figure 19 Close-up of Reynolds shear stress contoursand perturbation velocity vectors at x= 0.30 (case 1)
Figure 20 Close-up of Reynolds shear stress contoursand perturbation velocity vectors at x= 0.30 (case 4)
0.00250 0.00750 0.01250 0.01750
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4.0
6.0
8.0
time [s]
y [m
m]
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x = 0.30
0.0000 0.0050 0.0100 0.0150
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time [s]
y [m
m]
-1.0 -0.8 -0.6 -0.4 -0.2 -0.0Reynolds Shear Stress
x = 0.30
A
B
0 Copyright (C) 2000 by ASME
the acceleration zone behind the turbulent patch marked with the circleB. Again this indicates the existence of the calmed region.
DiscussionIn the last section of this paper, the authors discuss the develop-
ment of the calmed region following the wake-induced turbulent patch.The existence of the calmed region was identified in the perturbationvelocity data as shown in Figure 14, however, it seems useful to checkthe calmed region from another point of view, such as in terms ofReynolds shear stress. Figure 21 shows Reynolds shear stress aty=0.5mm for the case 1 displayed on x-time diagram, where the re-gions with negative value of the Reynolds shear stress are depictedwith shaded region and those with positive Reynolds shear stress aremarked with lines. Also shown are the three straight lines that repre-sent trajectories of the fluid particles moving at 100%, 55% and 30%free-stream velocity over the flat plate, Ue(=22m/s), respectively. Thefront of the negative value region moved almost along with the free-stream and the rear of the region moved much slower. These featuresmatched those of turbulent spots, as indicated by Halstead et al. (1997).The other point to be noted here is the appearance of the positiveReynolds shear stress behind the wake-induced turbulent patch. It isclear that the rear end of the positive Reynolds shear stress regionsmoved almost at 30% free-stream velocity, which corresponded to therear end speed of calmed region (Halstead et al. (1997)). In addition,according to the study of Wang and Keller (1999), non-turbulent mo-tion of the transitional boundary layer contributed to the appearanceof positive Reynolds shear stress in the boundary layer. These find-ings therefore implies a possibility that the positive value regions werestrongly related to the calmed region, although further studies areneeded to verify it. Figure 22 represents that the wake-affected turbu-
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Figure 21 Reynolds shear stress measured at y=0.5mm(case 1) on x-time diagram
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x [m]
t / T
-0.20 -0.15 -0.10 -0.05 -0.00Reynolds shear stress
Ue (=22m/s)
55% Ue30% Ue
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lence intensity measured at y=0.5mm (case 1) on x-time diagram, withcontours of the positive Reynolds shear stress. The behavior of thehighly turbulent regions resembled that of turbulent spots, similar tothe negative Reynolds shear region. Since the positive shear stressappeared over the regions of low turbulence intensity on the x-timediagram, it seems that those regions were not in ‘true turbulence’ statebut were caused by the fluctuation of the non-turbulent (irrotational)flow of the boundary layer.
CONCLUSIONSThis study aimed at clarifying the turbulent structure of the wake-
affected boundary layers at several flow conditions by the measure-ment of the flow field including wakes using the split-film probe. Anew procedure was developed to calculate two velocity componentsfrom the two signals of the probe, whose validity was verified in thisstudy to some extent. Despite the shortcoming of the probe especiallyin the very near-wall measurements, the probe successfully, and seem-ingly for the first time, revealed time-resolved two-dimensional fluidmotions around the wake and its induced turbulent patch. At the sametime, the authors believe that the measurements helped the readers tograsp the evolutional process of the wake-induced turbulent patch morevividly by looking at the ensemble-averaged Reynolds shear stress inthe flow field. Although the coverage of the measurements was farfrom satisfaction for extraction of any decisive conclusions, majorfindings in the present study, which are itemized in the following,provide an insight into this complicated flow event.
(1) The structure of the measured turbulent patch resembled a singleturbulent spot generated by pulse air injection to some extent, how-
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x [mm]
t/T
0.00 1.00 2.00 3.00 4.00 5.00 6.00Tu [%]
Ue (=22m/s)
55% Ue30% Ue
Figure 22 Turbulence intensity measured at y=0.5mm(case 1) on x-time diagram, overlaid with contours of the
Reynolds shear stress
Copyright (C) 2000 by ASME
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ever, the bottom of the decelerated zone associated with the turbulentpatch extended larger than that of the turbulent spot.
(2) As previously reported in several literatures, separation of thewake from the following turbulent patch was confirmed again in thereverse rotation case. The detected velocity vectors also indicated posi-tive jet -like fluid motion near the wake, while the negative jet effectwas observed in the normal rotation case. These relative motion nearthe wake seemed to affect the structure of the turbulent patch.
(3) Under the enhanced free-stream turbulence case the measuredturbulent patch was smaller and exhibited relatively low level ofReynolds shear stress inside.
(4) Ensemble-averaged Reynolds shear stress could be a usefulindex to identify the development of the wake-induced turbulentpatches as well as the calmed regions behind the patches.
ACKNOWLEDGMENTThe authors are indebted to E. Koyabu for his technical advice to
the measurements.
REFERENCESBruun, H. H., 1995, "Hot-Wire Anemometry," Oxford University
Press.Funazaki, K., 1996, "Studies on Wake-Affected Heat Transfer
around the Circular Leading Edge of Blunt Body," Trans. ASME Jour-nal of Turbomachinery, Vol. 118, pp. 452-460.
Chakka, P. and Schobeiri, M. T., 1999a, "Modeling UnsteadyBoundary Layer Transition on a Curved Plate Under Periodic UnsteadyFlow Conditions: Aerodynamic and Heat Transfer Investigations,"Trans. ASME Journal of Turbomachinery, Vol. 121, pp. 88-97.
Funazaki, K., Kitazawa, T., Koizumi, K. and Tanuma, T., 1997a,"Studies on Wake-Disturbed Boundary Layers under the Influencesof Favorable Pressure Gradient and Free-Stream Turbulence - Part II :Effect of Free-Stream Turbulence," ASME Paper 97-GT-451.
Funazaki, K., Kitazawa, T., Koizumi, K. and Tanuma, T., 1997b,"Studies on Wake-Disturbed Boundary Layers under the Influencesof Favorable Pressure Gradient and Free-Stream Turbulence-Part I :Experimental Setup and Discussions on Transition Model," ASMEPaper 97-GT-452.
Funazaki, K. and Koyabu, E., 1999, "Effects of Periodic WakePassing Upon Flat-Plate Boundary Layers Experiencing Favorable andAdverse Pressure Gradients ," Trans. ASME Journal ofTurbomachinery, Vol. 121, pp. 333-340.
Halstead, D.E., Wisler, D.C., Okiishi, T.H., Walker, G.J., Hodson,H.P. and Shin, H.-W., 1997, "Boundary Layer Development in AxialCompressors and Turbines: Part 1 of 4 - Composite Picture," Trans.ASME, Journal of Turbomachinery, Vol. 119, pp.114-127.
Hodson, H. P., Addison, J. S. and Shepherdson, C. A., 1992, "Mod-els for Unsteady Wake-Induced Transition in Axial Turbomachines,"Journal de Physique III, Vol. 2, pp. pp. 545 - 574.
Kim, K. and Crawford, M. E., 1999b, "Prediction of TransitionalHeat Transfer Characteristics of Wake-Affected Boundary Layers,"ASME Paper 99-GT-45.
Kittichaikarn, C., Ireland, P. T., Zhong, S. and Hodson, H. P., 1999,"An Investigation on the Onset of Wake-Induced Transition and Tur-bulent Spot Production Rate using Thermochromic Liquid Crystals,"ASME Paper 99-GT-126.
Makita, H. and Nishizawa, A., 1998, "Interaction between TwoHorizontally Displaced Turbulent Spots," JSME Transaction (B) (inJapanese), Vol. 64, pp. 3682-3689.
Makita, H. and Nishizawa, A., 1999, "Effects of Mutual Interac-tion between Turbulent Spots on Their Streamwise Growth," JSME
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Transaction (B) (in Japanese), Vol. 65, pp. 573-580.Schobeiri, M. T., John, J. and Pappu, K., 1996, "Development of
Two-Dimensional Curved Channels: Theoretical Framework and Ex-perimental Investigation," Trans. ASME Journal of Turbomachinery,Vol. 118, pp. 506-518.
Wang, T. and Keller, F.J., 1999, "Intermittent Flow and ThermalStructures of Accelerating Transitional Boundary Layers: Part 2 - Fluc-tuating Quantities," Trans. ASME, Journal of Turbomachinery, Vol.121, pp. 106-112
Copyright (C) 2000 by ASME
