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Lothar Hilgenfeld

Michael Pfitzner

Institut fuer Strahlantriebe,Universitaet der Bundswehr Muenchen,

Werner-Heisenberg-Weg 39,85579 Neubiberg, Germany

Unsteady Boundary LayerDevelopment Due to WakePassing Effects on a HighlyLoaded Linear CompressorCascadeThe effects of wake passing on boundary layer development on a highly loadedcompressor cascade were investigated in detail on the suction side of a compressorThe experiments were performed in the High Speed Cascade Wind Tunnel of the Ifuer Strahlantriebe at Mach and Reynolds numbers representative for real turbomaery conditions. The experimental data were acquired using different measurementniques, such as fast-response Kulite sensors, hot-film array and hot-wire measuremThe incoming wakes clearly influence the unsteady boundary layer development.forced transition in the boundary layer is followed in time by calmed regions. Lapressure fluctuations detectable in the ensemble averaged Kulite data reveal the exiof coherent structures in the boundary layer. Distinct velocity variations inside the boary layer are amplified when approaching the blade surface. The time–mean momentumthickness values are reduced compared to the steady ones and therefore clarify thtential for a loss reduction due to wake passing effects.@DOI: 10.1115/1.1791290#

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Introduction

The periodic disturbances caused by wake shedding ofstream blade rows and their downstream migration are a msource of unsteadiness in turbomachines. This inherently unstflow plays a significant role in the loss generation process of aturbomachinery blades. The boundary layer transition on thefile from laminar to turbulent and the subsequent growth ofboundary layer thickness are the main source of loss generaand significantly affected by the unsteadiness of the flow.

Over the past years many experimental investigations oninfluence of wake passing on the boundary layer developmenreported in the literature. Fundamental studies along flat plwere performed, e.g., by Pfeil and Herbst@1#, Pfeil et al.@2# andOrth @3#. Mayle @4# gives an excellent overview of the fundametal transition modes relevant in turbomachines. The transiprocess is influenced by several factors like the freestream tulence, the pressure gradient and the strength of the incomwakes. An increase in wake passing frequency has the same eas a higher free stream turbulence level~Schobeiri et al.@5#!.Due to the periodic wake passing, a combination of several tsition modes can occur resulting in a multimode transition pcess. The maybe most comprehensive basic research work oboundary layer development on compressor and turbine bladue to wake passing effects were carried out by Halstead et al@6#.They clarify the fundamental effects regarding to wake passlike the early onset of transition in the wake-induced path,suppression of a laminar separation bubble and the existencecalmed region. The calmed region partially suppress laminar sration due to its higher shear stress level and delays the ons

Contributed by the International Gas Turbine Institute~IGTI! of THE AMERICANSOCIETY OF MECHANICAL ENGINEERSfor publication in the ASME JOURNAL OFTURBOMACHINERY. Paper presented at the International Gas TurbineAeroengine Congress and Exhibition, Vienna, Austria, June 13–17, 2004, Pape2004-GT-53186. Manuscript received by IGTI, October 1, 2003; final revisiMarch 1, 2004. IGTI Review Chair: A. J. Strazisar.

Copyright © 2Journal of Turbomachinery

rom: http://turbomachinery.asmedigitalcollection.asme.org/ on 07/08/201

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transition in regions where under steady inflow conditionsflow is fully turbulent. Thus the profile losses can be reduced.

Measurements of the blade row interactions in axial comprsors were carried out, e.g., by Walker et al.@7# and Mailach andVogeler @8#. Recent hot-wire measurements within the boundlayer on the blade surface of a multi-stage axial compressor wperformed by Shin et al.@9#. However, most of the boundary layeinvestigations were conducted in low speed wind tunnel flowslow speed research compressors. Only few investigationsavailable for compressible, high-speed compressor flow, seeexample, Teusch et al.@11,10#.

Considering these effects in current aerodynamic design mods, reliable transition and turbulence models in unsteady Ccodes, which consider the effects of wake passing, are necesNevertheless numerical code validation has still to be performbased on experimental test cases. Hence, one objective opresent investigation is to provide a detailed unsteady databasnumerical code validation. The present work contributes to tobjective as part of a joint research effort on unsteady flowsturbomachines. An overview of the complete project and its scis given by Hourmouziadis@12#. For this reason experimental investigations focusing on unsteady boundary layer developmdue to wake passing have been performed on a highly loalinear compressor cascade at Mach and Reynolds numbers rsentative for real turbomachinery conditions.

Experimental Setup

Compressor Cascade. The measurements were performeda large scale compressor cascade called V103-220 consistinthree NACA 65 blades which represent the mid-span of thesection of a stator blade in a highly loaded axial compressor. Othe center blade is used for the measurements. To achieve a hresolution of the boundary layer effects, a blade chord lengthl 5220 mm was chosen. The design conditions with an inlet Manumber of Ma150.67 and a Reynolds number based on the bla

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chord length of Re15450,000 lead to a fully subsonic cascaflow. The geometrical data of the cascade, the definitions of anand distances and the design conditions are displayed in FiThe measurements have been performed at Reynolds numbe450,000 and 700,000.

The Wake Generator. The periodically unsteady flow causeby the relative motion of rotor and stator rows and its influencethe compressor cascade is simulated by a moving bar type wgenerator with a bar diameter ofdbar52 mm. Acton and Fottner@13# explain this so-called EIZ~Erzeuger Instationaerer Zustroemung; see Fig. 2! and its constructional principles in more detaThe cylindrical steel bars create a far wake very similar to theproduced by an actual airfoil~Pfeil and Eifler@14#!. Preliminarytests showed that the wakes shed by bars of 2 mm diameterepresentative for the wakes of the V103 profile geometry reging the wake width. The distance ratio between the bars andcascade inlet plane is aboutxax/ l ax50.38. Two different barpitches of 40 mm and 120 mm were used, resulting in aspacing to blade pitch ratiotbar/t of 1/3 and 1, respectively. Thebelt mechanism drives the bars with speeds of up to 40 m/s.the present investigation Strouhal numbers based on the clength and the axial inlet velocity between 0.22 and 1.32 are gerated for the investigated test cases.

It should be noted that the maximum bar speed together wthe axial velocities is still too slow to produce a Strouhal numand inlet velocity triangle representative for modern compressThe wakes in the rig enter the cascade passage almost parathe blades, whereas the data acquired with this setup cannotransferred directly to real turbomachines. The measurem

Fig. 1 Compressor cascade V103-220

Fig. 2 Wake generator „EIZ… with installed compressor cas-cade

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should be considered as basic investigations of the unsteadytimode transition process. Since the main purpose of the expmental investigations is to provide a database for numerical flsolvers, the angle of the incoming wakes is not essential forvalidation of transition modeling in unsteady Navier–Stokcodes.

Test Facility. The experiments were carried out in the HigSpeed Cascade Wind Tunnel of the Institut fuer Strahlantriebthe Universitaet der Bundeswehr Muenchen. The wind tunnean open-loop test facility located inside an evacuable prestank ~Fig. 3!. Mach and Reynolds number in the test section cbe varied independently by lowering the pressure level insidetank and keeping the total temperature constant by means oextensive cooling set-up, therefore allowing to simulate realbomachinery conditions~Sturm and Fottner@15#!. All tests wereperformed with a constant total temperature of 303 K. The turlence intensity in the test section is adjusted by fitting a turbulegrid upstream of the nozzle.

Measuring Techniques. The experimental data acquired provide time-averaged as well as time-resolved information regardthe boundary layer development on the suction side of a compsor blade.

The time-averaged loading of the compressor blade was msured by means of static pressure tappings on both the suctionthe pressure side at the mid-span connected to a Scanivalvetem. These pneumatic data were recorded via computer coand represent mean values. The time-resolved compressor ploading was determined from a total of 10 Kulite fast-responpressure sensors embedded into the suction side of the cblade. Prior the measurement, each Kulite sensor is calibrinside the pressure tank.

To document the unsteady inflow conditions, triple hot-wmeasurements were taken upstream of the cascade inlet at aspan at aboutxax/ l ax520.16. The probe employed in the preseinvestigation consists of three sensing tungsten wires of 5mmdiameter with a measuring volume of approximately 1 mmdiameter. A single hot-wire anemometer system was used tolyze the boundary layer in the turbulent part of the compresblade suction side. After passing an anti-aliasing filter, theemometer output signals are digitized with a sampling frequeof 60 kHz and stored together with other peripheral data. Atailed description of the measuring system and the evaluationcedure of the velocity vector is given in Wolff@16#. The relativeerror of the hot-wire velocity is estimated to be less than 5%;absolute angle deviation of the 3D system is less than 1 deg.

Surface mounted hot-film sensors are used to measurequalitative distribution of unsteadiness and the quasi wall shstress on the suction side. The entire length of the suction sur

Fig. 3 High speed cascade wind tunnel

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is covered with a total of 56 gauges1 at the midspan with theirspacing varying between 2.5 and 5 mm. The sensors consist0.4 mm thin nickel film applied by vapor deposition process oa polyamide substrate. They were operated by a consttemperature anemometer system in sets of 12 sensors and losimultaneously at a sampling frequency of 50 kHz.

As shown, e.g., by Hodson@17#, the boundary layer characteistics can be derived directly from the anemometer output andnot necessarily require an extensive calibration procedure.quasi-wall shear stress QWSS is determined by the output volE and the output voltage under zero flow conditionsE0 accordingto Eq. ~1!

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A once-per-revolution trigger mechanism ensured that the wpassing effects were studied for wakes produced by identical bProcessing of the raw data was done using the well-establisPLEAT technique~Phase Locked EnsembleAveraging Tech-nique, Lakshminarayana et al.@18#! in order to separate randomand periodic signals. The time-dependent signal b is composea periodic componentb̃ and the turbulent componentb8 accordingto Eq. ~2!

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A total of 300 ensembles was logged with each run and evated for quasi-wall shear stress, random unsteadiness RMS~3!, and skewness, Eq.~4!, where the variableb represents theanemometer output voltage. To be able to compare the hot-sensors, the resulting RMS values were normalized with theemometer voltage at zero flow, thereby eliminating the influeof manufacturing differences between the gauges.

Results

Inflow Conditions. To provide a comprehensive unsteadata set for numerical modeling of wake passing, the inflow cditions for the cascade have to be investigated in detail. Thesemble averaged results at design inlet flow conditions, a bar pof 40 mm (tbar/t51/3) and a bar speed of 20 m/s (Sr150.66) areshown as an example in Fig. 4, where the normalized inflowlocity, the turbulence level Tu based on the local flow velocity athe inflow angleb1 are plotted for four bar passing periodst/T.

The velocity deficit in the wake reaches about 12% of theflow velocity. The turbulence level rises from about 6% bacground level to 9.5% in the bar wake and correlates withvelocity during the wake passing period. Compared to steadyflow conditions with a freestream turbulence intensity of 3.5the overall turbulence intensity in the unsteady case is substalarger. The reduction in flow velocity also affects the veloctriangle and results in a periodic increase of the inflow angleaboutDb52 deg during every wake passing. Note that the ablute value of the inlet flow angle diverges from the geometric flangle that should result from the installation. This is due toloss of mass flow through the gaps at the upper and lower en

1Only 33 gauges are used during the present investigation.

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Unsteady Pressure Measurements.The measurements werperformed at different inlet Mach and Reynolds numbers in cjunction with two bar pitches and velocities. To get an impressof the cascade flow at design conditions with an inlet Mach nuber of Ma150.67 and an inlet Reynolds number of R15450.000, the mean blade loading in terms of the isentropic pfile Mach number distribution is plotted in Fig. 5. Both steady aunsteady inflow conditions, measured with conventional stapressure tappings technique and fast-response Kulite sensorshown. The unsteady runs are performed attbar/t51/3 (tbar540 mm) and tbar/t51 (tbar5120 mm) at bar speeds ofubar520 m/s, resulting in Strouhal numbers of Sr150.66 and Sr150.22, respectively, based on axial inlet velocity.

The differences compared to the steady inflow case are duechange of the inlet flow angle due to the moving bars. The mKulite data~filled symbols! show an excellent agreement with thvalues obtained from the static pressure tappings. At unsteinlet flow conditions, the separation bubble on the suction sstarting at aboutxax/ l ax50.40, is somewhat reduced comparedthe steady case due to the time averaging of the periodicallytached flow.

Fig. 4 Unsteady inflow conditions; design inlet conditions

Fig. 5 Isentropic profile Mach number distribution at designinlet conditions

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As an example of the ensemble averaged unsteady surfacesures measured on the suction side, the isentropic profile Mnumber distribution obtained from the Kulite data is given in F6 for a bar pitch of 120 mm (tbar/t51) and a bar speed of 40 m/(Sr150.44). In this space–time contour plot, nondimensionalizwake passing timet/T along the ordinate is plotted over the nodimensionalized axial chord length along the abscissa. Thetailed view shows the profile Mach number at four different timsteps during one wake passing period. Near the leading edgeare only small differences from the mean value, but the paswake leads to a periodical reduction of the separation bubStarting in the region of the separated flow at aboutxax/ l ax50.40, large amplitude pressure oscillations with high frequeoccurs. To get more information about these pressure oscillatia detailed look at the time traces is needed. A selection of typraw Kulite signals together with the ensemble averaged onesshown in Fig. 7 for one sensor atxax/ l ax50.65.

The large pressure fluctuations are visible in the raw sigAlthough the ensemble averaging process reduces randomtuations, the large amplitude and high frequency fluctuationssustained in the average traces. This is an indication that tfluctuations are generated by deterministic coherent structurethe flow. The period is approximately 35% of the bar passperiod. The entire ensemble averaged pressure traces measuthe suction side are shown in Fig. 8, which represent the sdata as in Fig. 6. The magnitude of the pressure fluctuations,

Fig. 6 Contour of unsteady isentropic profile Mach number

Fig. 7 Unsteady pressure signals at x ax Õ l axÄ0.65

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indicated as solid lines, are arbitrary but congruent along theface location, which is indicated as dash–dotted lines.

Also drawn in Fig. 8 are two lines representing the trajectorythe freestream velocityU` and the speed of sound. The origin othe high fluctuations is located in the region of the separated lanar flow at about 42% axial chord length. The onset of the flowing downstream fluctuations are concordant with tfreestream trajectory, thus they are controlled by the passwake. On the other side, the fluctuations prior to the laminar seration bubble propagate upstream with the speed of sound antherefore triggered by an acoustic mechanism.

Large amplitude pressure fluctuations due to coherent structare observed by Stieger@19# performing unsteady pressure mesurements on the suction surface of a turbine blade. He shothat the coherent structures are rollup vortices formed inboundary layer as the wake passes and occur by an inviKelvin–Helmholtz mechanism, therefore the fluctuations doevolve purely from the periodic turbulent disturbances linked wthe wake.

Figure 9 displays the pressure fluctuations obtained forsame inflow conditions but with half the bar speed ofubar520 m/s and bar pitches of 120 mm (tbar/t51) and 40 mm

Fig. 8 Ensemble averaged pressure traces, bar pitch Ä120mm, bar speed Ä40 mÕs „t bar ÕtÄ1, Sr1Ä0.44…

Fig. 9 Ensemble averaged pressure traces, bar speed Ä20 mÕs



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(tbar/t51/3). The pattern of the pressure fluctuations in the serated flow region in case of the bar pitch 120 mm is comparablthe latter case but the amplitudes are increased. Different osction patterns arise in the front part of the suction side, wherecharacteristic high frequency fluctuations as seen, e.g., in Fiare detectable. The oscillations are nearly sinusoidal with simnegative and positive amplitudes. The period corresponds tobar passing period. The appearance of these oscillations inensemble averaged values points again at the existence of cent structures in the boundary layer. In case of the lower bar p40 mm, large sinusoidal oscillations with nearly same amplitustart at aboutxax/ l ax50.42 up to the last Kulite sensor positioThe pattern of the pressure oscillations in the separated flowgion strongly depends on the frequency of the bars in terms ofbar pitch and bar speed.

Changing the inlet Mach or Reynolds number results in a silar oscillation pattern as could be seen in Fig. 10 for an increaReynolds number of Re15700,000~left side, constant inlet Machnumber Ma150.67) and for a decreased Mach number of M150.40 ~right side, constant inlet Reynolds number R15450,000). However, the amplitudes of the fluctuations areduced in case of the lower Mach number and only small presvariations are observable prior to the separation.

Surface-Mounted Hot-Film Measurements. The effects ofthe wake passing on the boundary layer transition on the sucside will be considered in the following section. The state ofboundary layer will be identified using the parameters quasi wshear stress~QWSS! and the root mean square~RMS!. The resultsof the hot-film measurements in terms of space–time diagramensemble averaged normalized RMS values and ensembleaged QWSS are shown in the following figures. The datamapped only qualitatively; dark regions indicate maximum alight areas minimum values. To identify the movement of ttransition point, the dash–dotted white lines within the RMS dgrams, representing zero skewness, are used. The transitionunder steady inflow conditions is shown as a dotted vertical lTo illustrate the wake-induced transition process, different regirepresentative for various boundary layer states are marked infigures similar to Halstead et al.@6#.

The flow development takes place along a wake-induced pand a path between two wakes. Following the wake path in11, a wake-induced transitional flow regime~B! emerges, whereearly transition is forced as can be seen in the RMS values andwhite zero skewness line. The migration of the transition pocovers about 27% of the surface length. The path betweenwakes remains still laminar~A!. The transitional region~B! isfollowed in time by a stable calmed region~D! with decreasingRMS values. The calmed region is able to delay the onsetransition in the path between two wakes~E!. The transition point

Fig. 10 Ensemble averaged pressure traces, bar pitch Ä120mm „t bar ÕtÄ1…, bar speed Ä20 mÕs



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moves periodically downstream in the region influenced by caing effects~D! as compared with steady inflow conditions. Thregions~C! and ~F! are turbulent up to the trailing edge, but thboundary layer properties change in time as could be seen innext chapter.

The wake-induced transitional region~B! exhibits a doublepeak of high RMS values. Mailach and Vogeler@8# pointed outthat this double peak is a response of the boundary layer duthe increased turbulence of the incoming wake. The wake geated by the bars can generally be described as a von Karvortex street with shedded vortices. Due to the short axialbetween the bar plane and the cascade inlet plane, the vorticenot mixed out as they enter the cascade inlet plane as shown isingle hot-wire measurements of Teusch et al.@10#. As a possibleconsequence of the larger measuring volume of the current utriple hot-wire probe, the present measurements~Fig. 4! do notshow any double peaks in the turbulence distribution upstreamcascade inlet. However, the wake width in the RMS diagracorresponds to the results of the triple hot-wire measuremdisplayed in Fig. 4.

Closer insight can be obtained by looking at one single senduring wake passing, as shown, for example, in Fig. 12the axial locationxax/ l ax50.40. Note that the origin of thenondimensional time on the abscissa represents the start omeasurement and do not necessarily coincide with the wakepact on the boundary layer at this specific sensor location. Duthe high reduced frequency in case of the bar pitch of 40 m

Fig. 11 Ensemble averaged RMS values, Ma 1Ä0.67, Re1Ä450,000, t barÄ40 mm, u barÄ20 mÕs „t bar ÕtÄ1Õ3, Sr1Ä0.66…

Fig. 12 Ensemble averaged values at single sensor locationx ax Õ l axÄ0.40, Ma1Ä0.67, Re1Ä450,000, t barÄ40 mm, u barÄ20 mÕs „t bar ÕtÄ1Õ3, Sr1Ä0.66…

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(Sr150.66), no distinct regions of undisturbed laminar boundlayer flow exist. The wall shear stress increases after the impathe wake due to the increased turbulence inside the wake.maximum fluctuations marked as M1 and M2 occur at temporuniformly distributed parts of the laminar and turbulent boundlayer with an intermittency ofg50.5. Between the points M1 anM2, the turbulent part in the boundary layer outweighs withintermittency of 0.5,g,1, indicated by the minimum RMS valuand the maximum of the QWSS value at the center of the waThen the wall shear stress decreases. Subsequent to the wafluence, the wall shear stress is still decreasing for a short twhile the fluctuations remain at a low level. This is accordingHalstead et al.@6# the indication of the calmed region. The calmeregion is interrupted by the appearance of the next wake.

The space–time diagram of quasi wall shear stress on thetion side surface~Fig. 13! allows identifying the location andextent of the laminar separation bubble characterized by minimvalues in the QWSS distribution. Every wake passing, the trational flow regime ~B! prevents the formation of a separatiobubble and transition takes place via bypass mode. The calregion also suppresses the laminar separation.

In case of the high bar pitch 120 mm (tbar/t51) shown in Fig.14, a region of undisturbed transition similar to the steady cexists, where a laminar separation bubble develops betweenwakes. The migration of the transition point covers about 27%the surface length. There is only a small delay of the transitonset downstream due to the calming effects of the calmed regThe influence of the Reynolds number to the transition proces

Fig. 13 Ensemble averaged QWSS values, Ma 1Ä0.67, Re1Ä450,000, t barÄ40 mm, u barÄ20 mÕs „t bar ÕtÄ1Õ3, Sr1Ä0.66…

Fig. 14 Ensemble averaged RMS values, Ma 1Ä0.67, Re1Ä450,000, t barÄ120 mm, u barÄ20 mÕs „t bar ÕtÄ1, Sr1Ä0.22…

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displayed in Fig. 15 for an inlet Reynolds number R15700,000. The bar pitch is still 120 mm. Following the wakinduced path, the downstream migration of the transition poinmore obvious. The periodical migration process covers about 3of the surface length. With increasing Reynolds number, the efof the calmed region is therefore amplified.

Boundary Layer Traverses. To get detailed information onthe change of characteristic boundary layer parameters duringwake passing, single hot-wire traverses have been performethe turbulent part of the boundary layer. All the traverses habeen performed at a bar speed of 20 m/s. Figure 16 showsensemble averaged normalized velocities across the bounlayer at design inlet conditions and a bar pitch of 40 mm for oaxial positionxax/ l ax50.65. The wall–normal distanceh/ l alongthe ordinate is plotted over a nondimensionalized bar passingriod t/T. The wake path can be identified in the freestream dueits velocity deficit.

The large velocity oscillations inside the boundary layer exha pattern similar to the pressure traces in Fig. 9~right side!. Theoscillations are amplified across the boundary layer, but slighdamped when approaching the blade surface. Similar resultsthe velocity distribution can be found in Chakka and Schob@20#. In case of the higher bar pitch 120 mm (tbar/t51). which isshown in Fig. 17, the typical pattern of the large amplitude a

Fig. 15 Ensemble averaged RMS values, Ma 1Ä0.67, Re1Ä700,000, t barÄ120 mm, u barÄ20 mÕs „t bar ÕtÄ1, Sr1Ä0.22…

Fig. 16 Ensemble averaged velocity, Ma 1Ä0.67, Re1Ä450,000,t barÄ40 mm, u barÄ20 mÕs „t bar ÕtÄ1Õ3, Sr1Ä0.66…



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Fig. 17 Ensemble averaged velocity, Ma 1Ä0.67, Re1Ä450,000,t barÄ120 mm, u barÄ20 mÕs „t bar ÕtÄ1, Sr1Ä0.22…

Fig. 18 Momentum thickness and shape factor at x ax Õ l axÄ0.97, Ma1Ä0.67, Re1Ä450,000, t barÄ40 mm, u barÄ20 mÕs„t bar ÕtÄ1Õ3, Sr1Ä0.66…

Fig. 19 Momentum thickness and shape factor at x ax Õ l axÄ0.75, Ma1Ä0.67, Re1Ä450,000, t barÄ120 mm, u barÄ20 mÕs„t bar ÕtÄ1, Sr1Ä0.22…



high frequency oscillations already identified in the Kulite sign~see, e.g., Fig. 7! are obvious. The period of this fluctuationabout 40% of the bar passing period. These patterns, and therthe underlying coherent structures, emerge within the boundlayer, whereas in the freestream and near the wall only the watypical velocity deficit appears.

Figures 18 and 19 display the corresponding integral boundlayer parameters momentum thicknessd2 and shape factor H12obtained near the trailing edge atxax/ l ax50.97 and xax/ l ax50.75,2 respectively, both normalized with their values frosteady inflow conditions. In case of the low bar pitch 40 mm,oscillations about the mean values are again sinusoidal. Duone wake passing, the momentum thickness varies between5% and minus 45% compared to the steady case, while the timmean momentum thickness shows a decrease of about 20%the momentum thickness at the trailing edge is regarded as asure for the profile losses, a substantial loss reduction comparethe steady case is estimated. The time–mean shape factorshows an increase of about 11%.

There is only a moderate increase of the time-mean shape faof about 3% in case of the bar pitch 120 mm (tbar/t51). Thetime–mean momentum thickness is reduced at about 11% cpared to the steady inflow case. In contrast to the case at lowpitch, the momentum thickness temporarily increases up to 2during the high peak fluctuations.

The space–time diagram of the ensemble averaged shapetors is given in Fig. 20 for the low bar pitch of 40 mm (tbar/t51/3). The alternation of high shape factors in the regionabout xax/ l ax50.50 representing separated flow and low valurepresenting attached flow is clearly visible.

ConclusionsDetailed experimental investigations were performed on

highly loaded linear compressor cascade focusing on unsteboundary layer development due to wake passing effects. Cydrical bars moving parallel to the cascade inlet plane simulateperiodically unsteady flow caused by the relative motion of roand stator rows. The experimental data were acquired usingferent measurement techniques, such as fast-response Kulitesors, hot-film array and hot-wire measurements. The experimwere carried out using two different bar pitches of the wake gerator. In case of the high bar pitch of 120 mm (tbar/t51), thepassing wakes lead to a periodical change of the blade loadLarge amplitude pressure oscillations with high frequency duedeterministic coherent structures in the boundary layer start inregion of the separated flow. They trigger the upstream presfluctuations by an acoustic mechanism as they propagate upstwith the local speed of sound. The reduction in flow velocity aaffects the velocity triangle and results in a periodic increase

2At the present, no data are available for the high bar pitch of 120 mm beyxax / l ax50.75.

Fig. 20 Ensemble averaged shape factors, Ma 1Ä0.67, Re1Ä450,000, t barÄ40 mm, u barÄ20 mÕs „t bar ÕtÄ1Õ3, Sr1Ä0.44…

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the inflow angle of aboutDb52 deg during every wake passingThe overall background turbulence level is significant larger copared to steady inflow conditions. Surface mounted hot-film ssors are used to measure the qualitative distribution of unsteness and the quasi wall shear stress along the suction sidetime. For both bar pitches, the separation bubble is periodicreduced, but still existent. The migration of the transition pocovers up to one third of the surface length. The RMS valuethe wake-induced transitional region exhibit a double peak aresponse of the boundary layer to the structure of the incomwakes. To get detailed information on the change of characterboundary layer parameters during wake passing, single hot-traverses have been performed in the turbulent part of the boary layer. Large velocity oscillations inside the boundary layoccur, which are amplified across the boundary layer. The timean momentum thickness values at unsteady inflow conditare significantly reduced compared to the steady ones and thfore clarify the potential for a loss reduction due to wake passeffects.

The measurements are also intended as a contribution tovalidation process of unsteady Navier–Stokes codes.

AcknowledgmentsThe authors wish to acknowledge the support of the Deuts

Forschungsgemeinschaft~DFG! for the research program partlreported in this paper. The work was performed within the joproject ‘‘Periodical Unsteady Flow in Turbomachines.’’

Nomenclature

E @V# 5 anemometer output voltageM1, M2 @-# 5 RMS maxima within the wake-induced path

Ma @-# 5 Mach numberN @-# 5 number of ensembles

QWSS@-# 5 quasi wall shear stressRe @-# 5 Reynolds number

RMS @-# 5 root mean squareSr @-# 5 Strouhal numberT @s# 5 bar passing period

Tu @%# 5 turbulence intensityb @V# 5 general time-dependent signalb8 @-# 5 turbulent component of signalb̃ @-# 5 period component of signal

dbar@m] 5 bar diameterl @m# 5 blade chord lengtht @s# 5 time

t @m# 5 blade pitchtbar@m] 5 bar spacingu @m/s# 5 velocity

x @m# 5 chordwise positionb @°# 5 flow angleg @-# 5 intermittency

tw @N/m2# 5 wall shear stress

500 Õ Vol. 126, OCTOBER 2004


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Subscripts

0 5 zero flow conditions1 5 cascade inlet plane2 5 cascade exit plane

ax 5 axial distancei 5 time index

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