gt200 5-68603

Proceedings of GT2005ASME Turbo Expo 2005: Power for Land, Sea and Air

June 6-9, 2005, Reno-Tahoe, Nevada, USA

GT2005-68603

Intermittent Behavior of the Separated Boundary Layeralong the Suction Surface of a Low Pressure Turbine Blade under

Periodic Unsteady Flow Conditions

B. Öztürk, M. T. Schobeiri, David E. AshpisTurbomachinery Performance and Flow Research Laboratory National Aeronautics and space Administration

Texas A&M University John H. Glenn Research Center at Lewis FieldCollege Station, Texas Cleveland, OH 44135-3191

ABSTRACTThe paper experimentally and theoretically studies

the effects of periodic unsteady wake flow andaerodynamic characteristics on boundary layerdevelopment, separation and re-attachment along thesuction surface of a low pressure turbine blade. Theexperiments were carried out at Reynolds number of110,000 (based on suction surface length and exitvelocity). For one steady and two different unsteadyinlet flow conditions with the corresponding passingfrequencies, intermittency behavior were experimentallyand theoretically investigated. The current investigationattempts to extend the intermittency unsteady boundarylayer transition model developed in previously to theLPT cases, where separation occurs on the suctionsurface at a low Reynolds number.

The results of the unsteady boundary layermeasurements and the intermittency analysis werepresented in the ensemble-averaged, and contour plotforms. The analysis of the boundary layer experimentaldata with the flow separation, confirms the universalcharacter of the relative intermittency function which isdescribed by a Gausssian function.

NOMENCLATURE

b intermittency wake widthc blade chordcax axial chordC threshold leveldR rod diameter

LSS suction surface lengthM number of samplesN number of wake cyclesReLSS Reynolds number based Re = L88Vd /v

SB blade spacingSR rod spacings streamwise distance from the leading edge

of the bladeso streamwise distance from the leading edge

to the trailing edge of the blades distance from plate leading edge(mm)S(t) criterion functionSsm(t) smoothed-criterion functiont time (s)T time for one revolution of wake generatorTu reference turbulence intensity<Tu> ensemble-averaged turbulence intensityU belt translational velocityVax axial velocityVexit exit velocityV velocityv fluctuation velocityy lateral distance from plate surface (mm)< 'y (t)>max maximum ensemble-averaged

intermittency< 'y (t)>min minimum ensemble-averaged

intermittency'y) time-average intermittency< 'y (t)> ensemble averaged intermittencyP relative turbulence intermittencyC nondimensional coordinate, y/b

Copyright © 2005 by ASME

< kinematic viscosity of air (m2/s)> Transformed coordinate, E2 = t SR /tiD density of air (kg/m3)F length spacing ratio, s 0/SR

J one wake passing periodRA Zweifel coefficient

S reduced frequency

INTRODUCTION

In recent years, gas turbine engine aerodynamicistshave focused their attention on improving the efficiencyand performance of the low pressure turbine (LPT)component. Previous research has shown that areduction in the blade numbers can be achieved withoutsubstantially sacrificing the efficiency of the LPTblading. For aero-engines this reduction contributes toan increase in thrust/weight ratio, thus reducing the fuelconsumption. Contrary to the high pressure turbine(HPT) stage group that operates in a relatively highReynolds number environment, based on the operatingconditions, the LPT experiences an adverse change inReynolds number ranging from 50,000 to 250,000.Since the major portion of the boundary layer,particularly along the suction surface is laminar, the lowReynolds number in conjunction with the local adversepressure gradient makes it susceptible to flowseparation, thus increasing the complexity of the LPTboundary layer aerodynamics. The periodic unsteadynature of the incoming flow associated with wakes thatoriginate from upstream blades substantially influencesthe boundary layer development including the onset ofthe laminar separation, the extent of the separationbubble, and its turbulent re-attachment. Of particularrelevance in the context of LPT aerodynamics is theinteraction of the wake flow with the suction surfaceseparation bubble. While the phenomenon of theunsteady boundary layer development and transition inthe absence of the separation bubbles has been thesubject of intensive research that has led to betterunderstanding of the transition phenomenon, graspingthe multiple effects of mutually interacting parameterson the LPT boundary layer separation and their physicsstill requires more research. To fully understand thebasics involving the separation bubble phenomenon, anintermittency analysis has been employed to extend theintermittency unsteady boundary layer transition modeldeveloped in [1], [2], [3] to the LPT cases, whereseparation occurs on the suction surface at a low

Reynolds number.Studies by Abu-Ghannam and Shaw [4], Gostelow

and Blunden [5], and Dullenkopf and Mayle [6], wereconducted to determine the effect of free-streamturbulence and pressure gradient on the spot productionrate and the intermittency factor. Significantcontributions to steady and unsteady boundary layerresearch was made by Pfeil and his co-researchers ([7],[8], [9], [10], [11]). Pfeil and Herbst [12], utilizing thesquirrel cage-type wake generator and a flat plate,developed a wake-induced transition model that is nowgenerally accepted as accurate. They also showed thatthe boundary layer grew naturally in between theinduced transition regions by wakes. Comprehensiveinvestigations on the effect of periodic unsteady flow ona curved plate were performed by Schobeiri and Radke[13], and Schobeiri et al. [14]. They showed that anincrease in wake passing frequency as a result ofreducing the wake spacing results in changing the waketurbulence structure, and also a shift of transition regiontowards the leading edge. Experiments for the effect ofunsteady wake flow on the boundary layer transitionwere also conducted by Walker [15], Paxson and Mayle[16], and Orth [8]. Paxson and Mayle investigated theeffect of unsteady passing wakes on the laminarboundary layer near the stagnation region. Dullenkopfand Mayle [3] proposed a time averaged transitionmodel. Few of these researchers have addressed theeffect of wake frequency and the structure on theboundary layer transition.

The transition process was investigated by Emmons[17] through the turbulent spot production theory. Thistheory was later promoted by Dhawan and Narasimha[18], who found the intermittency factor for naturaltransition. Unlike the steady boundary layer transitioncase, the calculation of intermittency function under theunsteady flow situation is a difficult task because of thefree-stream turbulence distribution, which is periodicallychanging from almost non-turbulent to high turbulentintensity values. The process of turbulent/non-turbulentdecisions from the instantaneous signals measured underthese unsteady conditions is reviewed by Hedley andKeffer [19]. They proposed derivatives of velocitysignals as the detector function to identify the turbulentand non-turbulent parts in the signals. This method wasalso used by Antonia and Bradshaw [20], Kovasznay, etal. [21], and Bradshaw and Murlis [22]. Mayle andPaxson [13] and Mayle [23] used a similar method forunsteady flows.

Developing an unsteady transition model is essentialto accurately predict the unsteady boundary layercharacteristics such as skin friction and heat transfer


coefficients. With an appropriate transition model, it ispossible to numerically solve the boundary layerequations using different methods such as thoseproposed by Launder and Spalding [24], Crawford andKays [25], and Schmidt and Patankar [26].Implementing such a model in an unsteady Navier-Stokes code enables reliably predicting theturbomachinery profile loss coefficients and thus, theefficiency.

Based on the fundamental investigations of thevelocity and the turbulence structure of the impingingwakes and their interaction with the boundary layer,Chakka and Schobeiri [1] developed an intermittencybased unsteady boundary layer transition model. Theanalysis revealed a universal pattern for the relativeintermittency function for all the frequencies andpressure gradients investigated. However, the aboveinvestigations were not sufficient to draw anyconclusion with regard to an eventual universalcharacter of the relative intermittency function. Furtherdetailed investigations of the unsteady boundary layeron a high Reynolds number turbine cascade by Schobeiriet al. [27], [28] and its subsequent analysis [2] and [3]verified the universal character of the relativeintermittency function.

The current investigation attempts to extend theintermittency unsteady boundary layer transition modeldeveloped by Schobeiri and his coworkers ([1], [2], [3])to the LPT cases, where a massive separation occurs onthe suction surface at a low Reynolds number at thedesign and off-design points. Furthermore, theexperimental results are intended to serve as benchmarkdata for a comparison with numerical computation usingDNS or RANS-codes.

EXPERIMENTAL RESEARCH FACILITY

To investigate the effect of unsteady wake flow onturbine and compressor cascade aerodynamics,particularly on unsteady boundary layer transition, amulti-purpose large-scale, subsonic research facility wasdesigned and has been taken into operation since 1993.Since the facility in its original configuration is describedin [27], [28] and [29] only a brief description of themodifications and the main components is given below.The research facility consists of a large centrifugalcompressor, a diffuser, a settling chamber, a nozzle, anunsteady wake generator, and a turbine cascade testsection as shown in Figure 1. The compressor with avolumetric flow rate of 15 m3/s is capable of generatinga maximum mean velocity of 100 m/s at the test sectioninlet. The settling chamber consists of five screens and

one honeycomb flow straightener to control theuniformity of the flow.

Two-dimensional periodic unsteady inlet flow issimulated by the translational motion of a wakegenerator (see Figure 2), with a series of cylindrical rodsattached to two parallel operating timing belts driven byan electric motor. To simulate the wake width andspacing that stem from the trailing edge of rotor blades,the diameter and number of rods can be varied. The roddiameter, its distance from the LPT blade leading edge,the wake width and the corresponding drag coefficientis chosen according to the criteria outlined by Schobeiriet al. [30]. The belt-pulley system is driven by an electricmotor and a frequency controller. The wake-passingfrequency is monitored by a fiber-optic sensor. Thesensor also serves as the triggering mechanism for datatransfer and its initialization, which is required forensemble-averaging. This type of wake generatorproduces clean 2-dimensional wakes, whose turbulencestructure, decay and development is, to a great extent,predictable [30]. The unsteady boundary layer transitionand heat transfer investigations [1], [2], [27], [28]performed on this facility serve as the bench mark datafor validation of turbulence models, transition models,and general code assessments.

To account for a high flow deflection of the LPTcascade, the entire wake generator and test section unitincluding the traversing system, was modified to allowa precise angle adjustment of the cascade relative to theincoming flow. This is done by a hydraulic platform,which simultaneously lifts and rotates the wakegenerator and test section unit. The unit is then attachedto the tunnel exit nozzle with an angular accuracy lessthan 0.05 o, which is measured electronically.

The special design of the facility and the length ofthe belts (Lbelt = 5,000 mm) enables a considerablereduction of the measurement time. For the presentinvestigation, two clusters of rods with constantdiameter of 2 mm are attached to the belts as shown inFigure 2. The two clusters with spacings S R = 160 mmand SR = 80 are separated by a distance which does nothave any rods, thus simulating steady state case (SR =—). Thus, it is possible to measure sequentially the effectof three different spacings at a single boundary layerpoint. To clearly define the influence domain of eachindividual cluster with the other one, the clusters arearranged with a certain distance between each other.Using the triggering system mentioned above and acontinuous data acquisition, the buffer zones betweenthe data clusters are clearly visible.


OStatic pressure blade © Timing belts. rod attachments O Inlet nossle © Large silence chamber with

O2 Blade with hot film sensors © Transition duct 10 Hydraulic cylinders 14 honcyope and five screens

Telesc

O3 Wake generating rods O Straight duct 1© Pivot point 16 Honeycomb flow straightener

® Wake Traversing systemenerator © Wake generator a—motor 1® Traversing slotsg O

Figure 1. Turbine cascade research facility with the components and the adjustabletest section

6.5

6.250=3.18 w

S3= 80 mm E 6

'5.75

5.5

725 750 t(f11S)

775 600

6.5

6.25H

C1=1.59 -1^6S2=160 mm

X5.75

5.5

425 450 t(fns)

475 500

6.5

6.25

0=0.0 6S1= ∞

5.5

75 100 t(I11/S)

125 150

Figure 2. Wake Generator


Table 1: Parameters of turbine cascade test section

Parameters Values Parameters Values

Inlet velocity Vin = 4 m/s Inlet turbulence intensity Tuin = 1.9 %

Rod translational speed U = 5.0 m/s Blade Re-number Re = 110,000

Nozzle width W = 200.0 mm Blade height hB = 200 mm

Blade chord c = 203.44 mm Cascade solidity a = 1.248

Blade axial chord cax = 182.85mm Zweifel coefficient *A = 1.254

Blade suction surface length LSS = 270.32 mm Cascade angle cp = 55°

Cascade flow coefficient (D = 0.80 Cascade spacing SB = 163 mm

Inlet air angle to the cascade " 1 = 0° Exit air angle from the cascade "2 = 90°

Rod diameter DR = 2.0 mm Rod distance to lead. edge LR = 122 mm

Cluster 1 (no rod, steady) SR = — mm parameter steady case 0.0

Cluster 2 rod spacing SR = 160.0 mm parameter for cluster 1 1.59

Cluster 3 rod spacing SR = 80.0 mm parameter for cluster 2 3.18

The data analysis program cuts the buffer zones andevaluates the data pertaining to each cluster.Comprehensive preliminary measurements were carriedout to make sure that the data were exactly identical tothose, when the entire belt length was attached withrods of constant spacing, which corresponded to eachindividual cluster spacing. The cascade test sectionshown in Figure 1, located downstream of the wakegenerator, includes 5 LPT blades with a height of 200.0mm and the chord of 203.44 mm. For boundary layerinvestigations, five identical “Pak B” airfoils designed byPratt & Whitney were implemented whose cascadegeometry is given in Table 1.

The blade geometry resembles the essential featuresuch as the laminar boundary layer separation that isinherent to typical LPT blades. The blade geometry wasmade available to NASA researchers and academia tostudy the specific problems of LPT flow separation, itspassive and active control and its prevention. As shownin [27], this blade number is necessary and sufficient tosecure a spatial periodicity for the cascade flow. Theperiodicity is demonstrated by the pressure distributionsof the blade number 2 and 4, shown in Figure 1 Theseblades were specially manufactured for measurement ofpressure and showed identical pressure distributions. A

computer controlled traversing system is used tomeasure the inlet velocities and turbulence intensities, aswell as the boundary layers on suction and pressuresurfaces. The traversing system is vertically mounted onthe plexiglass side wall. It consists of a slider and a leadscrew that is connected to a DC-stepper motor with anencoder and decoder. The optical encoder provides acontinuous feedback to the stepper motor for accuratepositioning of the probes. The system is capable oftraversing in small steps up to 2.5 µm, which isspecifically required for boundary layer investigationswhere the measurement of the laminar sublayer is ofparticular interest.

INSTRUMENTATION, DATA ACQUISITION,AND DATA REDUCTION

The data acquisition system is controlled by apersonal computer that includes a 16 channel, 12-bitanalog-digital (A/D) board. Time dependent velocitysignals are obtained by using a commercial 3-channel(TSI), constant temperature hot-wire anemometersystem that has a signal conditioner with a variable lowpass filter and adjustable gain. A Prandtl probe, placedupstream of the diffuser, monitors the reference velocity


at a fixed location. The pneumatic probes are connectedto high precision differential pressure transducers fordigital readout. Several calibrated thermocouples areplaced downstream of the test section to constantlymonitor the flow temperature. The wake generatorspeed and the passing frequency signals of the rods aretransmitted by a fiber-optic trigger sensor. The passagesignals of the rods are detected by the sensor using asilver-coated reflective paint on one of the belts. Thissensor gives an accurate readout of the speed of thewake generator and the passing frequency of the rods.The signals of the pressure transducers, thermocouples,and trigger sensors are transmitted to the A/D board andare sampled by the computer. To ensure the cascadeperiodicity, the second and fourth blades areinstrumented each with 48 static pressure taps. Twoadjacent blades are used for boundary layermeasurement. The taps are connected to a scanivalve,which sequentially transferred the pressure signals toone of the transducers that was connected to the A/Dboard.

The unsteady data are taken by calibrated, customdesigned miniature, single hot wire probes. At eachboundary layer position, samples were taken at a rate of20kHz for each of 100 revolutions of the wakegenerator. The data were ensemble-averaged withrespect to the rotational period of the wake generator.Before final data were taken, the number of samples perrevolution and the total number of revolutions werevaried to determine the optimum settings forconvergence of the ensemble-average.

For the steady state case, the instantaneous velocitycomponents are calculated from the temperaturecompensated instantaneous voltages by using thecalibration coefficients. The instantaneous velocity canbe represented in the following form:

(1)

where is the mean (time-averaged) velocity and v isthe turbulent fluctuation component. The mean velocity,also known as the time-average, is given by:_MV = 1- F V, (2)

where M is the total number of samples at one boundarylayer location. The root mean square value of theturbulent velocity fluctuation is:

M _

V = 1 (V. - V)Z(3)J

and the local turbulence intensity is defined as:

Tui.= v x 100 = 1 1 (V.- Ff x 100 (4)V V Mi=1

For unsteady cases, the ensemble-averaged velocity,fluctuation velocity, and the turbulence intensity werecalculated from the instantaneous velocity samples by:

N

VP) _ < M )> = -E V (tt) (5)NJ_1

Ar

1V#) = <VXt^)> = E [V_.J (ti) - < mi)>] 2 (6)NJ_1

<vt(t^>=(t;)> _ <Tu^.(t=)> = x100 (7)(tp

where N= 100 is the total number of wake generatorperiods and M the number of samples taken per period.<Vi (ti)> is the reference ensemble averaged velocity forthe particular boundary layer traverse.

INTERMITTENCY ANALYSIS

The intermittency distribution, which identifieswhether the flow is laminar or turbulent inside theboundary layer, is calculated following the method ofHedley and Keffer [19]. Instantaneous velocities areused to identify this intermittency distribution. Theinstantaneous velocity is sensitized to increase itsdiscriminatory capabilities between turbulent and non-turbulent parts of the signal. For this purpose, themultiplication of the first derivative of the velocity signaland the velocity signal is used for further analysis. Thisis called the detector function, S(t). Several otherdetector functions were used by Kowasznay et al. [21 ]and Antonia and Bradshaw [20].

S(t)= u anat 1 (8)

Though sensitized detector function separates theturbulent and non-turbulent zones of the fluid, there is


still some overlap between two near the origin. Thediscrimination between the two zones of the flow will beideal when the overlap between the two distributions isminimal or zero. To eliminate the disturbing effects ofthe velocity signal peaks, a smoothing procedure isapplied to the S(t) signal: The mean value of tenconsecutive S(t) values is calculated and the ten valuesare substituted by their mean value of S sm(t).

After smoothing the detector function, a thresholdlevel C is then applied to the smoothed detector functionto distinguish between true turbulence and the signalnoise.

1 when Sjt) z C,I(fl- 0 when S„„(t) < C. (9)

After applying the threshold level to the detectorfunction S(t), the result is a random square wave with0's representing the laminar case and 1's representing theturbulent behavior of the boundary layer. A thresholdlevel, C, of 1.2 is used for all the data on the suctionsurface. In the absence of length scales, this value ischosen from visual observations. Several other values ofC are tested and little qualitative difference is seen in theintermittency distribution during transition. Though theintermittency values vary with different values of C, theimportant parameters like start and end of transition arenot effected by C. The resulting square wave afterapplying the threshold is ensemble- averaged to get theensemble- averaged intermittency as follows:

<Yi(tr)> - 1t qo (10)ni=1

Where n is the number of revolutions of the wakegenerator for which the data are collected. For time-averaged intermittency, <( i(ti)> is integrated withrespect to time to arrive at:

T

y = T f <yXtf)>dt (11)r=o

Figure 3 show the processing of instantaneousvelocities.

8

7

6

^ 5

4

3

2 0 1 23 4t/τ

10

8 S(t)S

sm(t)

6

4 ^^ I

2

0 0 1 2 3 4t/τ

1

0.8

0.6

0.4

0.2

0 0 1 2 3 4t/τ

1

0.8

0.6

0.4

0.2

00 1 2 3 4t/τ

Figure 3. Calculation of ensemble-averagedintermittency function from instantaneousvelocities for Q=1.725 at y=0.720 mm.

RESULTS AND DISCUSSION

Time Averaged Velocity and IntermittencyDistributions

The effect of the wake frequency on the time-averaged velocity profiles and fluctuation velocitydistribution are presented for one steady and twounsteady inlet flow conditions on the suction surfacealong 31 streamwise locations for the Reynolds numberof 110,000. The steady state case serves as the referenceconfiguration. After completing the velocitymeasurements, the boundary layer coordinates weretransformed into a blade orthogonal coordinate system.Velocities at blade normal positions were obtained byinterpolating their transformed values. The resultsshowed almost no difference between the interpolatedand non-interpolated velocity data. Experimentalinvestigations were performed for three different valuesof Q = 0.0, 1.59, and 3.18. These values cover thereduced frequency range encountered in LPT-designand off-design operation conditions.

The velocity fluctuation and intermittencydistributions are shown in Figures 4 to 6 at 6representative streamwise locations for upstream regionof the separation bubble, where the flow is attached.Upstream of the separation bubble at s/s o= 0.52 and alsoat its immediate proximity s/s o=0.588, the velocity


distributions inside the boundary layer experience aslight decrease with increasing the reduced frequency.Inside the separation bubble at s/s 0=0.705, a substantialinfluence of the wake frequency is observed. The higherwake frequency introduces a fluctuation kinetic energyinto the boundary layer trying to reverse the separationtendency. As it can be seen from the velocitydistribution profiles in Figure 4, the onset and the lengthof the separation bubble are not changed. However,there is a slight change of the bubble height. This showsthat the wake flow does not have the capability tosuppress the separation bubble. It only reduces theseparation bubble height. In the downstream of theseparation bubble, where the flow is fully reattached,s/so= 0.951, the impact of the wake on the boundarylayer is reduced. This effect is clearly shown in thevelocity distribution at s/s o=0.951. According to theprevious investigations reported in [28] on a HP-turbine cascade, an increased wake frequency causesturbulence fluctuations to rise inside and outside theboundary layer. However, in the LPT- case with theboundary layer separation, once the boundary layer isre-attached and the velocity distribution assumes a fullyturbulent profile, no major changes are observed neitherin the velocity nor in the fluctuation distribution, Figure5. The time averaged intermittency distributions areshown in Figure 6 for several streamwise locations.Upstream of the separation bubble, the intermittency isvery low through s/s o= 0.502. Close to the separationleading edge at s/so=0.52 a sudden increase ofintermittency is observed that indicates a change in flowstate from a transitional to a fully turbulent state. AsFigure 6 shows, inside the separation bubble ats/so=0.705 intermittency changes drastically for all threefrequency cases. An initial increase in intermittency isinfluenced by the shear layer responding with a slightdecrease in intermittency. For a streamwise location ofs/so=0.705, this occurs at a lateral position of y = 8 mm.Outside the bubble, the intermittency increasesapproaching a value close to unity. This indicatives thecontinuation of a transition process that started at thebubble leading edge above the shear layer that separatesthe separation zone with the external flow. A similarsituation is observed further downstream at s/so= 0.767.Once the separation bubble is left behind ( s/so=0.951),the effect of the shear layer is still felt. Moving from thewall, intermittency increases, reaches a peak atapproximately y = 15 mm. It experiences a relaxationwith a minimum value of < ,y(t)> = 0.5 whichcorresponds to the shear layer intermittency value. Fromthis point on, the transition process along the shear layerdetermines the intermittency picture. It is worth noting

that in all cases depicted in Figure 6, highestintermittency occurred in steady case with Q = 0. Insidethe bubble, the wake effect seems not be strong,however, outside the bubble, the well known becalmingeffect makes itself felt in terms of reducing theintermittency.

Ensemble-Averaged Intermittency Distribution

The temporal-spatial contours of the ensemble-averaged intensity distribution at three different lateralpositions for two reduced frequencies are presented inFigure 7. The wakes periodically disturb the boundarylayer with the high turbulence intensity cores. As it isseen in Figure 7, the first three wakes are shown forbetter comparison of the effects of the impinging wakefrequency. In these figures, the wakes with the highlyvortical cores display intermittency values close to unityindicating the turbulent character of the boundary layerat the particular instant of time that the wake impingeson the surface. Intermittency is approximately equal tozero outside the wake region near the leading edgeshowing the non-turbulent behavior of the flow. Thewakes represented by thin strips pass through theturbine blade channel and periodically switch theboundary layer from laminar to turbulent and vice versadepending on the presence of the wakes. At s/so= 0.52,the visibility of the wake is vanished due to theseparation bubble. As explained earlier, the separationbubble starts at s/so= 0.52 and extends up to s/s o= 0.746,thus occupying more than 24% of the suction surfaceand forming a massive separation. At s/s o= 0.746, theintermittency field in Figure 7(a) shows the stagnantfluid region, which indicates the development of atransition and re-attachment. Increasing Q to 3.18causes an earlier mixing of the impinging wakes, whichleads to a complete degeneration of the deterministicperiodic flow into a stochastic turbulent flow.

Relative Intermittency Distributions

The intermittency distributions in Figure 7 clearlyshow the unsteady nature of the boundary layertransition. In this form, however, they cannotquantitatively describe the complex unsteady transitionprocess. To establish the basic relations essential for aquantitative description of the unsteady boundary layertransition, we resort to the fundamental studies bySchobeiri and his co-workers ([14], [27], [30]) that dealwith the physics of steady and unsteady wakedevelopment in a curved environment. These studiesshow that the turbulence structure of the steady and


0

9 ° ov0 00

0 00u8 ° Ov ° norod

° pv p 160mm7 0 0o 80mm

6 0 ovo Oo

5 o ov°Ov

4 °ov0 w

3 0°d

2

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0 0 0.1 .2 0.3 0.4v0 s)

5 v

0o

90

00 °0 °v

8 0 norod°0v o 160mm7 o 0 80mm

6 0 ovv

5 °° o v°4 o0v

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Ov

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1,yy,vv

9"^^

00 0.1 0. v 03m/s)

0.4 0.5

oo

norod0 160mmV 80mm

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Re=110,000, s/s o=0.502 Re =110,000, s/so=0.52 Re =110,000, s/so=0.58810

V10 a 10

9 a 9 g 9

0 08 ° norod ° °

0 160mm a8 o 1wmam o

8 0 19omm7 80mm e 7 80mm e 7 80mm

2 4 6 8

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CE 5

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3 O 3 30

1 1 1

0 002 4 6 8 002 4 6 8

V(m/s) V(m/s) V(m/s)

Re=110,000, s/s o=0.705 Re =110,000, s/so=0.767 Re =110,000, s/so=0.95120 30

18

16 orod25

norodp 160mm O 160mm14 v 80mm

20 v 80mm

12

10 15

8r

6 ° °o Oo vOV 10

4 v°pv00v 52

002 4 6 8 002 4 6 8V(m/s) V(m/s)

Figure 4: Distribution of time-averaged velocity along the suctionsurface for steady case Q=0 (S R= 4) and unsteady cases Q=1.59(SR= 160 mm) and Q=3.18 (SR= 80 mm) at Re=110,000

Re=110,000, s/so=0.502 Re=110,000, s/s o=0.52 Re=110,000, s/so=0.588

,000,s20

18

16 norodO 160mm

14 v 80mm

12

10

8

6 00^.G4 ° 0

00

.0

2 v

0 0 0.5v(m/s)

1

Re =110,000, s/so=0.76730

25norod

0 160mm

20v 80mm

15

10

5

em °°

00 0.5 1 1.5v(m/s)

0,000,

no rodp 160mmv 80mm

Figure 5: Distribution of time-averaged fluctuation rms velocity alongthe suction surface for steady case Q=0 (S R=—) and unsteady casesQ=1.59 (SR= 160 mm) and Q=3.18 (SR= 80 mm) at Re=110,000

9 Copyright © 2005 by ASME

Re=110,000, s/s0=0.50210

9 mm

8 m o no rod

010 160 mm

7 o 80 mm

^ 6Oa

E 5 o E

4

3m

2

1

0 0.25 0.5 0.75 1⎯γ

Re=110,000, s/s0=0.70520

18 00016 o no rod w°So°O

160mm14 o 80 mm v°^

12 ^O Oo°o

o10 U1 ^

⎯γ

⎯γ

Re=110,000, s/s0=0.767

Re=110,000, s/s0=0.951

no rod

no rodO 160 mm O 160 mm

0 80mm o 80mm

Re=110,000, s/s0=0.52 Re=110,000, s/s0=0.588

no rod m 8 no rodO 160 mm ® O 160 mmo 80 mm ® 7 v 80 mm

® 6m

m^ E 5

a.

1

1

γ γ γ

Figure 6: Distribution of time-averaged intermittency along the suctionsurface for steady case Q=0 (S R=—) and unsteady cases Q=1.59 (S R= 160mm) and Q=3.18 (SR= 80 mm) at Re=110,000

unsteady wake flow is determined by the wake defect,which is a Gaussian function. Following the abovestudies, we define a dimensionless parameter:

tUw tSR _ L2 fb tib b

with b -- r ^z (12)

-m

that relates the passing time, t, of a wake impinging onthe plate surface with the wake passing velocity in thelateral direction, Uw, and the intermittency width, b.The latter is directly related to the wake widthintroduced by Schobeiri and his co-workers [30]. In ananalogous way to find the defect function, we define therelative intermittency, P, as:

(13)

In the above equation, is the time dependent

ensemble-averaged intermittency function, whichdetermines the transitional nature of an unsteadyboundary layer. The maximum intermittency

exhibits the time dependent ensemble-

averaged intermittency value inside the wake vorticalcore. Finally, the minimum intermittency

represents the ensemble- averaged

intermittency values outside the wake vortical core.Figure 8 exhibits the maximum and minimum ensemble-averaged intermittency inside and outside the wakevortical core.

A representative relative intermittency function, P,is shown in Figure 9 (a, b, c, d) for a frequency value ofQ=1.59 at a lateral distances from the blade surface ofy =0.858, 0.996, 5.3, and 9.3 mm, with thedimensionless longitudinal distance s/s o as a parameter.The above lateral distances are representative forintermittency distributions inside, within and outside theseparation bubble over the entire suction surface. Thesymbols represent the experimental data. As seen, forthe reduced frequency of Q=1.59, the measured relativeintermittency functions follow very closely a Gaussiandistribution, given by:

r = e -C2 (14)


(a)3

2.5

2

Z 1.5

1

0.5

52=1.59, y=1.341 mm 52=3.18, y= 1.341 mm

<Kt)>1.000.940.870.810.750.690.620.560.500.440.370.310.250.190.120.060.00

(b)3

<Kt)>

1.00 2.50.950.880.820.76

0.70 20.640.570.51

0.45 1.50.390.320.26

0.20 10.140.070.00

0.5

(c)3

2.5

2

Z 1.5

1

0.5

(e)3

2.5

2

Z 1.5

1

0.5

s/so

52=1.59,y=1.755 mm

0.2 0.4 0.6 0.8s/so

52= 1.59, y=6.1 mm

(d)3

<Kt)>

1.00 2.50.950.890.820.76

0.70 20.640.570.510.45 a 1.50.390.320.26

0.20 10.140.070.00

0.5

(f)3

<Kt)>

1.00 2.50.950.890.820.76

0.70 20.640.570.510.45 a 1.50.390.320.26

0.20 10.140.070.00

0.5

s/so

52=3.18, y= 1.755 mm

0.2 0.4 0.6 0.8s/so

52=3.48, y=6.1 mm

<Kt)>1.000.940.870.810.750.690.620.560.500.440.370.310.250.190.120.060.00

<Kt)>1.000.950.880.820.760.690.630.570.500.440.380.320.250.190.130.060.00

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8s/so s/s o

Figure 7. Ensemble-averaged intermittency factor in the temporal-spatial domain at different y positionsfor Q=1.59 ( S R= 160 mm), and Q=3.18 ( SR= 80 mm)


and represented by the solid curve. Here, C is the non-dimensionalized lateral length scale from Eq. (12).Using this function as a generally valid intermittencyrelationship for unsteady wake flows, the intermittencyfunction <( i(ti)> is completely determined if additionalinformation about the minimum and maximumintermittency functions <Y(t.) > and <Y (t.) >

i i max i i min

are available. Figure 11 shows the time-averagedintermittency distribution for one steady or no rod caseand two unsteady cases on the suction surface, as afunction of s/s o at different normal positions from theblade. Upstream of the leading edge of the separationbubble, the time averaged intermittency is determined bythe laminar nature of the boundary layer, which exertsa strong damping effect on the impinging wakefluctuations as extensively discussed in [29].Approaching the bubble leading edge a steep increase inintermittency indicate a strong turbulent fluctuationwithin the separation bubble. This exactly correspondsto the findings plotted in Figure 5. Close to the wall ( y= 0. 1, 0. 720) the intermittency peak is embedded in theseparation bubble as shown in Figure 11. Movingtoward shear layer causes an increases the value of thepeak intermittency. At s/s o = 0.705, where the separationbubble height reaches its maximum, the intermittencyapproaches its minimum and increases again to reach thesecond maximum. The change of the intermittency stateis reflected in Figure 10, which was extensivelydiscussed in [29].

0.9

0.8

0.7

0.6

0.5v

0.4

0.3

0.2

0.1

2 3t/τ

Figure 8. Maximum and minimum intermittencies aty=0.1 mm and s/s o= 0.383

The distributions of and

in streamwise direction are plotted in Figure 12 for Q =1.59 and 3.18 on the suction surface. The distributionof corresponds to the condition when the

wake with its high turbulence intensity core impinges onthe plate surface. Once the wake has passed over thesurface, the same streamwise location is exposed to alow turbulence intensity flow regime with anintermittency state of , where no wake

present. As shown in Figure 12, outside the separationzone the minimum intermittency tends to

i i min

follow the course of steady (no wake) intermittencydistribution. The final state of does not

approach the fully turbulent value of 1.0 due to thewake calming effect.

CONCLUSIONS

A detailed experimental and theoretical study of thebehavior of the separation bubble on the suction surfaceof a highly loaded LPT blade under periodic unsteadywake flow is presented. The measurements were carriedutilizing a custom designed hot-wire probe. One steadyand two different unsteady inlet wake flow conditionswith the corresponding passing frequencies, the wakevelocity and the turbulence intensities were investigatedby utilizing a large-scale, subsonic research facility. Twodimensional wakes were generated by cylindrical rodsattached to two parallel timing belts performing acontinuous translational motion in front of the turbinecascade. The results of the unsteady boundary layermeasurements and the intermittency analysis werepresented in the ensemble-averaged, and contour plotforms. The analysis of the boundary layer experimentaldata with the flow separation, confirms the universalcharacter of the relative intermittency function which isdescribed by a Gausssian function.

The minimum intermittency factor, <,y min>,represented the intermittency, when the boundary layeris subjected to the wake external region. While upstreamof the separation bubble, the minimum intermittency<(min>, resembles the distributions found in [1], [2] and[3], within the separation bubble a steep drop followedby a moderate increase dictates the intermittencypicture.


(a)

10

9

8

7

6

EE

5

4

3

2

1

s/so

Ω=1.59, t/τ=1(c)

10

9

8

7

6EE 5r

4

3

2

1

Ω=1.59, t/τ=0.25

s/so

Ω=1.59, t/τ=0.75

(b)

10

9V/U

∝ 8

o"oeeo

7o.0.830.76 60.69 E0.62 EO 5o. T0.480.40 40.330.26 30.190.12

2

1

(d)10

9

V/U∝ 81.07

1.000.93 70.860.800.73 60.66 E0.60 E 50.530.460.39 40.330.26

30.190.13

2

1

Ω=1.59, t/τ=0.50

(a)1

0.9

Ω=1.59, y= 0.858 mm (b)1

0.9

Ω=1.59, y=0.996 mm

exp(- ζ2 ) exp(- ζ 2 )

0.8

q a§o=0.069I i t, 0.1 21T it, 0.8

[1 s/so =0.069

s/so= 0.121

V s/so=0.216

0.7IL D s/s

o= 0.320

Q s/so= 0.898 0.7

D s/so= 0.320

Q s/so= 0.401

0.6Q s/s

o=0.951

0.6s/s

o=0.519

s/so= 0.805

V s/so=0.951

c. 0.5 c. 0.5

0.4 0.4

0.3 0.3

0.2 0.2

0.1 0.1

0 -1 0 12 0-2 -1 0 1 2

ζ ζ

(c) Ω=1.59, y= 5.3 mm (d) Ω=1.59, y=9.3 mm1 1

- exp(- ζ2 )0.9 q s/s

o=0.069 0.9

0.8 ps/s

o=0.121

s/so=0.216 0.8

D s/so=0.320

0.7 Q s/so=0.401 0.7

s/so=0.616

0.6 s/so

= 0.766 0.6

[. 0.5 [. 0.5

0.4 0.4

0.3 0.3

0.2 0.2

0.10.1

00-2 -1 0 1 2

ζ

Figure 9. Relative intermittency as a function of s/s o for unsteady frequency ofQ=1.59 (SR= 160 mm) at (a) y=0.858 mm, (b) y=0.996 mm, (c) y=5.3 mm, and (d)y=9.3 mm at Re=110,000

s/s o s/so

Figure 10. Ensemble-averaged velocity contours along the suction surface for different s/s o with time t/ tias parameter for Q=1.59 (S R= 160 mm), Re=110,000 (time-averaged separation bubble for Q=1.59marked red)


(b

0

0

0

0

0

0

0

0

0

0

0

0

0

a 0

0

0

0

0

(a)y=0.1 mm

9 no rod9 160 mmv 80 mm

y=0.720 mm

B no rodE 160 mmv 80 mm

(c)

0

0

0

0

0

0

0

0

0

0.2 0.4 0.6 0.8s/so

y=1.045 mm

9 no rod9 160 mmv 80 mm

0.2 0.4 0.6 0.8s/so

y=1.410 mm

B no rodE 160 mmv 80 mm

(d)

0

0

0

0

a 0

0

0

0

0

s/so s/s o

(e)

y=2.1 mm y=10.1 mm

0

0 $ no rod

$ no rod9 160 mm E 160 mm

0 v 80 mm

v 80 mm

0

0

0

0

0

0

s/so s/s o

Figure 11. Time-averaged intermittency as a function of s/s o at different lateral positions for steady caseQ=0 (SR=—) and unsteady cases Q=1.59 (SR= 160 mm) and Q=3.18 (SR= 80 mm) at Re=110,000


(b

0

r

0

^E

0

0

0

0

0

0

0

(d

0

r

0

^E

0

0

0

0

0

0

0

(f)1

0.9

0.8

0.7

r 0.6

rE 0.5

0.4

0.3

0.2

0.1

52= 1.59, y=0.765 mm

El vmax

vmin^— vavg

i m 1

0.4 0.6 0.8s/s

o

52= 1.59, y= 1.410 mm

E3 vmaxe vmin

v vavg

s/so

52= 1.59, y= 10.1 mm

B vmax0 vmin

v vavg

52=3.18, y=0.765 mm

$ vm ax

vmin

vavg

0.2 0.4 0.6 0.8s/s

o

52=3.18, y= 1.410 mm

El vmax

vmin

v vavg

s/so

52=3.18, y= 10.1 mm

B vm ax

vmin

v vavg

s/s o s/so

Figure 12. Maximum, minimum and time-averaged intermittency as a function of s/s o at different lateralpositions for steady case Q=0 (SR=—) and unsteady cases Q=1.59 (S R= 160 mm) and Q=3.18 (SR= 80mm) at Re=110,000


A more detailed picture of the intermittencybehavior inside the laminar, separation, and the turbulentregion is given by the time averaged intermittency.Upstream of the separation bubble the intermittency isdetermined by the laminar nature of the boundary layer,which exerts a strong damping effect on the impingingwake fluctuations as extensively discussed in [29].Approaching the bubble leading edge a steep increase inintermittency indicates a strong turbulent fluctuationwithin the separation bubble. Close to the wall, theintermittency peak is embedded in the separation bubble.Moving toward the shear layer causes an increase in thevalue of the peak intermittency. The intermittencyapproaches a minimum, where the separation bubbleheight reaches its maximum.

UNCERTAINTY ANALYSIS

The Kline and McClintock [31] uncertainty analysismethod was used to determine the uncertainty in thevelocity after calibration and data reduction for thesingle-wire probe. In addition, the uncertainty in theheat transfer measurements was also determined. TheKline and McClintock method determines theuncertainty with a 95% confidence level. Theuncertainty in the velocity for the single-wire probe afterthe data reduction is given in Table 3. As shown, theuncertainty in the velocity increases as the flow velocitydecreases. This is due to the pneumatic pressuretransducer having a large uncertainty during calibration.Table2: Uncertainty in velocity measurement for hot-wire probe.

U (m/s) 3 5 12

G)U/U (%)red 5.78 2.41 1.40

ACKNOWLEDGMENTS

The presented study is a part of an ongoing LPT-aerodynamics project executed by the NASA GlennResearch Center. The authors were supported by NASACooperative Agreement NCC3-793 monitored by Dr.David Ashpis. The support and the permission forpublication is gratefully acknowledged. The authors alsogratefully acknowledge Pratt&Whitney for providingthe research community with the blade coordinates.

REFERENCES

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“Effect of unsteady wake passing frequency onboundary layer transition, experimentalinvestigation and wavelet analysis,” ASME PaperNo. 95-GT-437.

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[16]Paxson, D.E., Mayle, R.E., 1991, “LaminarBoundary Layer Interaction With an UnsteadyPassing Wake,” Journal of Turbomachinery, Vol.113, pp. 419-427.

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[27]Schobeiri, M. T., Pappu, K., Wright, L., 1995,“Experimental Sturdy of the Unsteady BoundaryLayer Behavior on a Turbine Cascade,” ASME 95-GT-435, presented at the International Gas Turbine

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