an experimental study of the unsteady characteristics of the turbulent

8/14/2019 An Experimental Study of the Unsteady Characteristics of the Turbulent

1/11

An experimental study of the unsteady characteristics of the turbulentnear wake of a turbine blade

Marina Ubaldi, Pietro Zunino *

Dipartimento di Macchine, Sistemi Energetici e Trasporti, Universita di Genova, Via Montallegro 1, I-16145 Genova, Italy

Received 24 January 2000; accepted 24 July 2000

Abstract

The paper reports the results of an experimental investigation of the time-varying characteristics of the ow in the turbulent near

wake behind the central blade of a large-scale turbine cascade. The blade wake has been surveyed by means of a two-component

laser Doppler velocimeter (LDV) over a close experimental grid extending from the blade trailing edge to six trailing edge diameters

downstream. A phase-locked ensemble averaging technique has been applied to the LDV instantaneous data in order to separate

coherent contributions due to large-scale organised structures from random contributions due to turbulence. A reference signal

generated by a hot-wire probe, located at a xed position within the ow, is utilised to associate each LDV velocity realisation with

the phase of the vortex shedding. The hot-wire signal provides also an univocal time reference suitable for correlating all single-point

measurements, allowing to construct sequences of images which show the time evolution of the organised structures embedded in the

ow. In the discussion, the mean ow properties, the periodic structure of the unsteady ow and the vortex shedding mechanism are

analysed. Similarities and dierences between the present results for a turbine blade wake and those for wakes of circular cylinders

are highlighted. Normal stresses due to the periodic motion and those due to turbulence uctuations are resolved separately. Both

contributions have the same order of magnitude in the region close to the trailing edge, where the vortices are forming, but the

normal stresses associated with the periodic uctuations decay more rapidly in streamwise direction. 2000 Elsevier Science Inc.

All rights reserved.

Keywords: Turbine blade wake; Unsteady ow; Coherent structures; Laser doppler velocimeter

1. Introduction

Wakes from turbine blades are unsteady in characterbecause of the presence of large-scale organised struc-tures, known as von Karman vortex streets. Vortexshedding represents an important cause of energy losses,blade dynamic loadings, mechanical vibrations andnoise.

In spite of the importance of this phenomenon, theow in the wake behind turbine blades is generallyviewed as the superposition on a time-averaged ow ofan unresolved unsteadiness comprehensive of all theuctuations regardless of their scale. Only few examplesof detailed studies concerning the time-varying charac-teristics of blade wakes [1] are available in the technical

literature, because of the experimental diculties asso-ciated with the large gas velocities and the small bladetrailing edge dimension, resulting in very large sheddingfrequencies and scarce spatial resolution of the mea-surement. Therefore, our present knowledge on themechanism of vortex shedding from blade trailing edgesis still mainly based on the results of detailed experi-mental investigations behind cylinders (e.g., [2,3]).

The present contribution is part of a research ac-tivity carried out within the framework of a Brite Eu-ram project and aimed at the improvement of theknowledge on the time-varying turbine wake charac-teristics. The program included systematic investiga-tions on large-scale models carried out in dierentlaboratories making use of complementary experimen-tal techniques. Results concerning the eect of vortexshedding on the unsteady pressure distribution aroundthe blade trailing edge and the details of the unsteadyow in the base region have been previously published[4,5]. The present paper concerns a LDV systematic

Experimental Thermal and Fluid Science 23 (2000) 2333

www.elsevier.nl/locate/etfs

* Corresponding author. Tel.: +39-010-353-2448; fax: +39-010-353-

2566.

E-mail address: [email protected] (P. Zunino).

0894-1777/00/$ - see front matter 2000 Elsevier Science Inc. All rights reserved.

PII: S 0 8 9 4 - 1 7 7 7 ( 0 0 ) 0 0 0 3 0 - 3


2/11

investigation in the turbulent near wake of a turbineblade in cascade. A phase-locked ensemble averagetechnique suitable for LDV measurements has beendeveloped and used together with the triple decompo-sition scheme for the instantaneous velocity in order to

identify the periodic organised structures embedded inthe turbulent wake ow.

A key point to the present investigation is the highspatial resolution obtained, thanks to the adoption of alarge-scale three-blade cascade, a probe volume of smalldimensions and a high precision probe traversingsystem. Tests were run at a Reynolds number Rec 1X6 106, which is representative of gas turbine highpressure stages. The resulting test outlet Mach numberM2is 0X24 is low compared with the modern gasturbine Mach number range which extends in the me-diumhigh subsonic and transonic regimes. The presentresults still can be considered representative for subsonicgas turbines, because, according to the review paper ofCicatelli and Sieverding [1], the vortex shedding Strou-hal number in the subsonic regime depends mainly onthe boundary layer state at the trailing edge, which isstrongly inuenced by the Reynolds number, the free-stream turbulence and the streamwise velocity gradients,rather than by the compressibility eects associated withthe Mach number variations. In the transonic regime, onthe contrary, the shedding mechanism is strongly mod-ied by the formation of the trailing edge shock system[1,6]. The result is an increase of the Strouhal numberand the breakdown of the stable von Karman vortexstreet with the occurrence of highly transient vortexshedding patterns.

2. Experimental details

2.1. Test facility and instrumentation

The experiment was conducted in the DIMSET low

speed wind tunnel. The facility is a blow-down contin-uously operating variable speed tunnel with an open testsection of 500 300 mm2.

The ow was surveyed downstream of the centralblade of a three-blade large-scale turbine linear cascade.The blade prole, designed at VKI [4], is representativeof a coolable hp gas turbine nozzle blade. A three-bladeconguration has been selected in order to have largerblade dimensions within the given test section with thepurpose of lowering the vortex shedding frequency andincreasing the spatial resolution of the measurements. Aschematic of linear cascade and experimental traverses isshown in Fig. 1. The main geometrical parameters of thecascade and the test conditions are summarised in Table1. The coordinates of the blade are given in [4].

The three blades are instrumented at mid-span with atotal of 110 pressure tappings. Periodicity condition wasmonitored by comparing the pressure distributions onthe central blade and the two adjacent ones andachieved by modifying the curvature of the adjustabletailboards and throttling two lateral apertures at thecascade inlet [5].

In the present experiment, a four-beam two-colourlaser Doppler velocimeter (LDV) with back-scattercollection optics (Dantec Fiber Flow) has been used.The light source is a 300 mW argon ion laser tuned to488 nm (blue) and 514.5 nm (green).

Nomenclaturec blade chord (m)D trailing edge diameter (m)f vortex shedding frequency (Hz)H12 boundary layer shape factor, dimensionless

M2is Mach number based on outlet isoentropicconditions, dimensionless

n normal distance from the blade surface (m)Rec Reynolds number based on blade chord

and ascade outlet velocity Rec qcU2al,dimensionless

ReD Reynolds number based on trailing edgethickness and cascade outlet velocity

ReD qD U2al, dimensionlessReh Reynolds number based on the boundary layer

momentum thickness and free-stream velocityReh q uehal, dimensionless

s streamwise coordinate along the blade surface(m)

St Strouhal number St fDaU2, dimensionlesst time (s)T period of one vortex shedding cycle (s)uY v boundary layer velocity components in

streamwise and cross-stream directions (m/s)

uHY vH boundary layer velocity uctuations instreamwise and cross-streamdirections (m/s)

U velocity (m/s)x streamwise direction at the cascade outlet (m)

y cross-stream direction at the cascade outlet (m)

Greeksd boundary layer displacement thickness (m)h boundary layer momentum thickness (m)l dynamic viscosity (kg/m s)q uid density (kg/m3)x vorticity (s1)

Subscriptse free-stream values in the streamwise directionn in the cross-stream direction1 at the cascade inlet

2 at the cascade outletSuperscripts and overbars uctuating component time averaged$ ensemble average

24 M. Ubaldi, P. Zunino / Experimental Thermal and Fluid Science 23 (2000) 2333


3/11

The probe consists of an optical transducer head of60 mm diameter connected to the emitting optics and tothe photomultipliers by means of optic bres. With afront lens of 400 mm focal length and a beam separa-tion of 38 mm, the optical probe volume is 0.12 mm ofdiameter and 2.4 mm of length. The probe volume wasoriented with the larger dimension along the spanwisedirection, in order to have better spatial resolution inthe blade-to-blade plane. A Bragg cell is used to applya frequency shift (40 MHz) to one of each pair ofbeams, allowing to solve directional ambiguity and toreduce angle bias. The signals from the photomultipli-ers were processed by two burst spectrum analysers(BSA).

The ow was seeded with a 0X52 lm atomised sprayof mineral oil injected in the ow at about 2 chord up-stream of the cascade leading edge.

The probe was traversed using a three-axis computercontrolled probe traversing system with a minimumlinear translation step of 8 lm.

2.2. Measuring procedure

According to the triple decomposition scheme pro-posed by Reynolds and Hussain [7] for the study ofcoherent structures in shear ows, a generic velocitycomponent v in a generic position P can be represented

as the sum of the time-averaged contribution "v, theuctuating component due to the periodic motion~v "v and the random uctuation vH

v "v ~v "v vHX 1

The time-varying mean velocity component ~v can beobtained by ensemble averaging the samples.

~vi 1

Ki

Kik1

viY kY 2

where i 1Y F F F YI is the index of the phases into which avortex shedding period is subdivided and k 1Y F F F YKi isthe index of the samples for each window associated

with a particular phase i.The time-averaged velocity component "v can be

simply determined as

"v 1

I

Ii1

~viX 3

Ensemble averaged variances, which are proportional tothe Reynolds stress normal components, are obtained as

fvH2i

1

Ki 1

Kik1

viY k ~vi2

vuut X 4

In the present experiment, an ensemble averaging tech-nique suitable for LDV data processing has been im-plemented. The technique makes use of a single-sensorhot-wire probe which is sensitive to the passage of theorganised structures in order to generate a referencesignal. The hot-wire output is band-pass ltered, am-plied and processed by means of an electronic devicecapable of producing a suitable TTL signal of 5 ls du-ration in correspondence of the maximum of the hot-wire signal. This phase information is provided to thesynchronisation input port of the BSA processors op-erating in ``encoder enabled mode''. The arrival time ofeach LDV velocity realisation is recorded together withthe phase reference signal.

To allow the ensemble average, the data are sortedinto 50 phase bins each representing a particular phaseof the vortex shedding cycle. To obtain statistically ac-curate ensemble averages of the LDV velocities, 50,000validated data for each component have been sampledat each measuring point. For a vortex shedding fre-quency of about 1300 Hz the bin width is 15 ls and themean number of samples for each bin is 1000.

2.3. Measurement accuracy

A comprehensive review of errors in LDV measure-ments and guidelines to evaluate them are given by

Fig. 1. Schematic of turbine blade cascade and measuring traverses.

Table 1

Cascade geometry and test conditions

Cascade geometry

Chord length c 300 mmPitch-to-chord ratio gac 0X7Aspect ratio hac 1X0Inlet blade angle bH1 0Gauging angle bH2 19X1

Test conditions

Relative inlet total pressure pt1 3060 PaInlet total temperature Tt1 293 KInlet turbulence intensity Tu 1%Outlet isoentropic Mach number M2is 0X24Outlet Reynolds number Rec 1X6 106

M. Ubaldi, P. Zunino / Experimental Thermal and Fluid Science 23 (2000) 2333 25


4/11

Boutier [8] and, in the case of turbomachinery applica-tions, by Strazisar [9]. A specic evaluation of the errorsfor frequency domain processors is given by Modarresset al. [10].

The error on the instantaneous velocity due to ran-dom noise from the photomultiplier tube depends on the

background scattered light and on the processing tech-nique. BSA can measure with a signal to noise ratio aslow as 5 dB, without apparent increase of the S.D.[10]. The resolution of the BSA processor depends onthe record length of the FFT and on the backgroundnoise. For the present experiment, even in the worstcases, it was below 1% of the mean velocity.

A statistical bias can occur because the arrival timesof the measurable particles are not statistically inde-pendent on the ow velocity which brings them into theprobe volume. If the velocity is not constant in time, theresulting non-uniform data sampling causes an errorwhen simple arithmetic averages are performed. Themagnitude of the bias is of the order of the square of theturbulence intensity based on the local mean velocity.The ensemble averaging procedure that has beenadopted in the present experiment, where the samples ineach bin are statistically independent because they werecollected during dierent cycles, avoids statistical bias,as observed by Lyn et al. [3].

Angle bias occurs when the particle trajectories arenot normal to fringe orientation. Moving the fringepattern in the probe volume by means of the Bragg cellallows to minimise this error. For the present experi-ment, the angle bias was kept lower than 1% of the meanvelocity.

Statistical uncertainty in mean and rms velocities

depends on the number of sampled data, turbulenceintensity and condence level [8]. For the present ex-

periment, considering a typical value of 1000 sampleddata, a condence level of 95% and a local turbulenceintensity of 30%, uncertainties of 2% and 5% areexpected for the mean and rms velocities, respectively.

3. Results and discussion

The time-varying characteristics of the blade wakeow is strongly inuenced by the boundary layer state atthe blade trailing edge [11]. The blade boundary layerdevelopment mainly depends on the surface velocitydistribution, the Reynolds number and the free-streamturbulence.

In the present experiment, the mid-span surface ve-locity distribution along the turbine blade is typical of afront-loaded prole with a moderate suction side diu-sion rate [12]. The chord based Reynolds number isrepresentative of high pressure stages of gas turbines.Boundary layer measurements along the blade prole,described in details in [12], show that, in case of naturaldevelopment, the boundary layer at the trailing edge isturbulent on the suction side and laminar-transitionalon the pressure side. The mixed boundary layer condi-tion at the trailing edge increases the Strouhal numberand results in a broader vortex shedding frequencyspectrum [11]. The necessity to have well-dened andreproducible boundary layer conditions at the trailingedge has led to the decision to enforce turbulent con-ditions also on the pressure side by installing a 0.4 mmdiameter trip wire. Due to the large turbulence intensityof turbomachinery ows, the condition of turbulentboundary layer at the blade trailing edge on both pres-

sure and suction sides is expected to be the most rep-resentative of real ow conditions.

Fig. 2. Boundary layer velocity, turbulence proles and integral parameters at the blade trailing edge.



5/11

Boundary layer velocity and turbulent proles mea-sured just upstream of the trailing edge are shown inFig. 2. In the same gure, the integral parameters of theboundary layers are also summarised. Proles are typi-cal of turbulent boundary layers, but on the suction sidethe boundary layer thickness is approximately twice that

on the pressure side.In order to get a preliminary overview of the time-

varying characteristics of the ow, instantaneous ve-locities were measured in selected points in the wake bymeans of a single-sensor hot-wire probe [5]. Time tracesand power density spectra of the velocity measured at

xaD 2X0 and yaD 1X0 are given in Fig. 3. Details ofthese measurements and data processing are given in[13]. The ow in the wake is highly unsteady because ofboth turbulent and organised uctuations. A peak ofenergy corresponding to the vortex shedding frequency,can be easily detected at about 1300 Hz. The corre-sponding Strouhal number St f DaU2 is 0.26, in closeagreement with the value measured at VKI on a cascadewith the same blade prole and very similar ow con-ditions [4].

The systematic investigation of the near wake owhas been performed measuring the velocity componentsat the nodes of a close experimental grid made of 23cross-stream traverses ranging from xaD 0X0625 to

xaD 5X625. Each traverse consisted of 27 pointsranging from yaD 1X875 to yaD 1X875. The originof the coordinate system is the extremity of the bladetrailing edge. The experimental grid is shown in Fig. 1.

3.1. Mean ow properties

Before analysing the periodic structure of the un-steady ow in the wake, a survey of the mean ow eld(Fig. 4) can be appropriate, as it is an important term ofcomparison with numerical predictions and represents

Fig. 3. Instantaneous velocity and power density spectrum of the

unsteady ow in the wake: xaD 2X0Y yaD 1X0.

Fig. 4. Time-averaged ow eld.



6/11

the base ow upon which the motion of organisedstructures is superimposed.

Streamwise velocity distribution "UsaU2 shows theextension and the rapid decay of the wake velocity de-fect. Because of the continuity condition, large trans-verse mean velocity components "UnaU2 of opposite sign

are present on the two sides of the wake. This eectextends in cross-stream direction well beyond the wakedefect region and free-stream ow is drawn towards thewake centre.

Both streamwise velocity distribution and vector plotshow the extension of the mean separated ow. Themean closure point is about 0.7 D. For circular cylin-ders this quantity is sensitive to the Reynolds numberbased on diameter and free-stream velocity ReD. Cant-well and Coles [2] estimated xaD 1 for ReD 140Y 000, Mc Killop and Durst [14] xaD 1X65 for

ReD 15Y 000. Both experiments were performed in theso-called ``shear layer transition regime'' [15], charac-terised by laminar separation from the surface and

turbulent transition in the shear layer. In the presentinvestigation, the ReD value ReD 85Y 000 is inter-mediate. In spite of that, the boundary layer state at thetrailing edge is turbulent on both sides, because of thelarge-blade chord Reynolds number Rec 1X6 10

6,the moderate suction side rearward deceleration and the

presence of the trip wire on the pressure side. Boundarylayer conditions at the separation points explain thereduced length of the mean recirculating region foundin the present investigation as well as the large value ofthe Strouhal number St 0X26 which is characteristicof the so called ``boundary layer transition or super-critical regime'' of circular cylinders with ReD b 10

6

[16].

3.2. Ensemble averaged velocity components

Figs. 57 show the temporal sequence of the periodiccharacteristics of the wake ow for four instants in avortex shedding period

ta

T

0Y

0X25Y

0X50Y

0X75

.

Fig. 5. Contours of the periodic velocity components at successive phases.



7/11

The streamwise periodic velocity component ~Us "Us (left of Fig. 5) shows an anti-symmetricperiodic structure with peaks and valleys whichalternate on the pressure and the suction side ofthe wake proceeding in streamwise direction. Thecross-stream periodic component ~Un "Un (right ofFig. 5) is structured in cores of positive and negativevalues, approximately centred in the wake, which al-ternate along the wake centreline. The nuclei of ~Un "Un appear displaced in respect of those of ~Us "Us of about half wavelength in streamwise di-rection.

The kinematic structure of the periodic ow, ascomes out from the present results, looks qualitativelysimilar to that presented by Cantwell and Coles [2] forthe wake downstream of a cylinder, but the magnitudeof the periodic velocity components, made non-di-mensional with the cascade outlet velocity U2, is muchlower. This dierence may be attributed to variousfactors, like a less-dened vortex shedding frequency,the boundary layer state at separation, the ratio of theboundary layer thickness to the distance between theseparation points and the ow acceleration in the cas-cade.

Fig. 6. Vector plots and vorticity contours of the periodic ow at successive phases.



8/11

The combination of the two velocity patterns ~Us "Us and ~Un "Un gives rise to the rolling up ofthe periodic ow in a row of vortices as shown by thevector plots of Fig. 6.

Vortices of opposite circulation are shed alternativelyfrom both the trailing edge sides. The magnitude of theperiodic velocity vectors attains values as large as 1520% of the cascade outlet velocity U2 in the near wakeregion with xaD ` 3. Due to their periodic advectionaction, such large vortices are expected to play a sig-nicant role in the mixing out process of the near wake.From xaD 3 onwards the magnitude of the velocityvectors is strongly reduced indicating a surprisingly fastdissipation of the kinetic energy of the periodic motionwithin few trailing edge diameters.

3.3. Vorticity

Identication of coherent structures and analysis oftheir evolution in time have been carried out with the aidof the periodic ow vorticity ~x "x. In Fig. 6, thevortices are highlighted by zones of positive and nega-tive intense vorticity alternating in streamwise direction.The vorticity patterns are structured into individualnuclei of opposite vorticity located on opposite sides.The vortex centres lie very close to the wake centreline,in agreement with the ndings of Cantwell and Colesinvestigation [2]. These nuclei extend backward bymeans of ribs embracing on the two sides the incomingnucleus of opposite vorticity. The ribs on the two sidesof each vortex are characterised by a dierent level of

vorticity with larger values on the side from which thevortex has been shed o. Local peaks of vorticity inthe region xaD6 3 are very high. The peak values for thequantity ~x "x caU2 are of the order of 20, indicating

that the local periodic vorticity is as large as 20 times themean streamwise acceleration U2ac that the ow un-dergoes through the cascade.

Concerning the mechanism of vortex shedding, twodierent modes are recognised [17]: a low speed modeand a high speed mode. The low speed mode describedby Kovasznay [18] applies for cylinders with ReD ` 400.In this mode, the eddy street starts as trail instability andthe eddies grow along the wake, while carried down-stream. The high speed mode presents two distinctstages: formation and shedding. The eddies are formedbehind the cylinder by the rolling up of the free-shearlayer at a xed location, and the eddy growth ceaseswhen the feeding shear layer is cut o. This hypothesis isput forward by Gerrard [19], who postulates that at theend of the formation process of one vortex, uid fromthe opposite side bearing vorticity of opposite sign isdrawn across the axis. When this vorticity equals andcancels out the local vorticity, the vortex is shed o.

Gerrard's high speed eddy shedding model is helpfulfor interpreting the instantaneous pictures of the un-steady ow in the vortex formation region. In Fig. 6, thevortices shed from the suction side are clockwise and theassociated vorticity is negative (black). At taT 0X25(second frames from the top), a clockwise vortex ex-tending from xaD 0 on the suction side to xaD 1X7on the centreline, characterised by negative vorticity, is

Fig. 7. Contours of the normal Reynolds stresses at successive phases.



9/11

shown just at the shedding instant. Fluid entrained fromthe pressure side is rolling up in a counterclockwise looplling the base region. The positive (white) vorticity ofthis uid tends to cancel out the local negative vorticityon the suction side at xaD 0X0, causing the clockwisesuction side vortex shedding.

At taT 0X50 (third frames), the clockwise suctionside vortex has been shed o, while the core of positivevorticity associated with the pressure side vortex information is growing, being fed by the ow from thepressure side.

At taT 0X75 (fourth frames), half period after thesuction side vortex shedding taT 0X25, the periodicow is in opposition of phase, the counterclockwisepressure side vortex, just before the shedding instant,possesses the maximum of positive vorticity. Negativevorticity is now entering in the base region from thesuction side and the clockwise suction side vortex beginsto form.

3.4. Reynolds stresses

The evaluation of Reynolds stress components dueonly to random uctuations is made possible by thedecomposition technique, which allows separating therandom uctuations from the periodic part of the signal.Fig. 7 shows the normal Reynolds stresses at four suc-cessive phases in a period taT 0Y 0X25Y 0X50Y 0X75.Streamwise and cross-stream normal Reynolds stressesare large in the wake region, with maxima of turbulenceintensity larger than 25% and 30%, respectively. Thesevalues are comparable, but slighly lower than thosefound by Cantwell and Coles [2] in the wake of a circular

cylinder. Dierent patterns for the two components,with a double-peak structure for the streamwise normalcomponent and a single-maximum centred in the wakefor the cross-stream normal component, result in largeturbulence local anisotropy. A feature of the turbulentstress pattern is the low turbulence intensity of bothcomponents in a narrow zone in proximity of the trail-ing edge surface.

A certain degree of periodicity interests the turbu-lence quantities, as shown by the periodic change ofcurvature of the normal stress contours. Local contourline curvatures depend on the convective transport ofthe contra-rotating vortices, as can be inferred bycomparing the contours of Fig. 7 with the vector plots of

Fig. 6. Superposing the distribution of the cross-streamnormal stress gUH2n (Fig. 7, right side) and the vorticitydistribution of Fig. 6 right side, it can be veried that theisocontours of relatively large values of normal stresscorrespond with the cores of periodic vorticity.

Considering the momentum equations for the phase-averaged ow [2], only the Reynolds stress terms due torandom uctuations appear, since the large-scale motionis accounted in the non-steady term. On the contrary, ifglobal (time-averaged) equations are considered, addi-tional terms due to the correlation of the large-scaleperiodic uctuations have to be evaluated and intro-duced into the momentum balance [2]. Fig. 8 shows the

distributions of these terms obtained from the experi-mental data.

The normal components ~Us "Us2

and ~Un "Un2

reect the distribution of the corresponding velocityuctuations with a couple of peaks of dierent magni-tude on the two sides of the wake for the streamwisecomponent and a centred core of larger values for thecross-stream component. The normal stresses due to theperiodic motion are appreciably lower, but of the sameorder of magnitude of the turbulent stresses. The rate ofdecay in streamwise direction is more rapid for thestresses associated with the periodic motion, because themechanisms of production and dissipation are dierentfor the two types of stresses. After the vortices areformed with accumulation of opposite vorticity from thetwo shear layers, the kinetic energy of the organisedstructures is dissipated by the deformation work [20]performed by the turbulent stresses on the strain eldassociated with the periodic motion and this dissipationis not compensated by production mechanisms. On the

Fig. 8. Time-averaged stresses due to the periodic velocity uctua-

tions.



10/11

other hand, the deformation work, appearing as a pro-duction term in the turbulence kinetic energy equation,acts to transfer energy from the large structures to therandom turbulence uctuations. As a consequence, vis-cous dissipation is partially balanced by production andthe turbulent stresses decay at a slower rate.

The shear stress Us 9 "UsUn 9 "Un associatedwith the large-scale periodic motion exhibits character-istic anti-symmetry with change of sign through thewake centreline. This shear stress, in accordance with

that due to random uctuations fUHs UHn acts to accel-erate the ow in the wake central region decelerating thewake periphery. The von Karman vortex pattern is suchthat the periodic cross-stream velocities convey positiveperiodic streamwise momentum from the free-streamtowards the interior of the wake.

4. Practical signicance/usefulness

The results of the present work show that the wakesof turbine blades, similar to those of cylinders, are af-fected by von Karman vortex shedding. In the presentexperiment carried out at operating conditions repre-sentative of real gas turbines, the Strouhal number as-sociated with the shedding frequency is higher than thatof circular cylinders. Knowledge of the shedding fre-quency during the blade design phase is important inorder to prevent blade resonance operating conditions.

Moreover, the present experiment provides details ofthe physics of the vortex shedding phenomenon fromturbomachinery blades, which contribute to improve its

understanding. The results constitute a comprehensivedatabase suitable for validation of unsteady codes to beused for turbomachinery numerical simulations.

5. Conclusions

Time-varying properties of the ow in the near wakeof a large-scale turbine blade have been experimentallyinvestigated in detail by means of a two-componentLDV and analysed by using a phase-locked ensembleaveraging technique allowing the decomposition of theow into mean, periodic and random contributions.

Due to the turbulent state of the boundary layers atthe separation points, the time-mean recirculating owzone at the trailing edge is appreciably shorter comparedwith the ones found in previous investigations on cir-cular cylinders in the ``shear layer transition regime''.The rather high value for the Strouhal numberSt 0X26 of the present experiment, typical of cylin-ders with larger value of ReDb10

6, is consistent withthe short separation bubble found behind the bladetrailing edge. The structure of the periodic ow isqualitatively in agreement with that described by Cant-well and Coles in the near wake of a cylinder at

ReD 140Y 000, but the amplitudes of the periodicuctuations in the present case are weaker.

Reconstruction of the time evolution of the periodicvector eld and the associated periodic vorticity revealsthe existence of a regular vortex street with peaks ofopposite vorticity located very close to the wake centre-line. These results support entirely the model of vortexformation proposed by Gerrard.

The shear stress associated with the large-scale peri-odic motion produce a ux of positive streamwise mo-mentum from the periphery toward the interior of thewake.

Normal Reynolds stresses associated with the ran-dom uctuations are larger and decay more slowly instreamwise direction compared with the normal stressesassociated with the large-scale periodic motion. How-ever, in the near wake region the two contributions arecomparable and, therefore, stresses due to periodic ve-locity uctuations cannot be neglected in the time-averaged momentum balance.

Acknowledgements

This work was performed under the BRITE-EU-RAM Contract AER2-92-0048, endorsed by MTUMunich and SNECMA Paris. These supports aregratefully acknowledged.

References

[1] G. Cicatelli, C.H. Sieverding, A Review of the Research on

Unsteady Turbine Blade Wake Characteristics, AGARD PEP

85th Symposium on Loss Mechanisms and Unsteady Flows in

Turbomachines, Derby, 1995.

[2] B. Cantwell, D. Coles, An experimental study of entrainment and

transport in the turbulent near wake of a circular cylinder, J. Fluid

Mech. 136 (1983) 321374.

[3] D.A. Lyn, S. Einav, W. Rodi, J.-H. Park, A laser Doppler

velocimetry study of ensemble-averaged characteristics of the

turbulent near wake of a square cylinder, J. Fluid Mech. 304

(1995) 285319.

[4] G. Cicatelli, C.H. Sieverding, The Eect of Vortex Shedding on

the Unsteady Pressure Distribution Around the Trailing Edge of

a Turbine Blade, ASME Paper No. 96-GT-359, 1996.

[5] P. Zunino, M. Ubaldi, U. Campora, A. Ghiglione, An experi-

mental investigation of the ow in the trailing edge region of a

turbine cascade, in: Proceedings of the Second European Con-ference on Turbomachinery Fluid Dynamics and Thermodynam-

ics, Antwerpen, March 1997.

[6] W.E. Carscallen, H.U. Fleige, J.P. Gostelow, Transonic Turbine

Vane Wake Flows, ASME Paper No. 96-GT-419, 1996.

[7] W.C. Reynolds, A.K. Hussain, The mechanics of an organized

wave in turbulent shear ow. Part 3. Theoretical models and

comparisons with experiments, J. Fluid Mech. 54 (2) (1972)

263288.

[8] A. Boutier, Accuracy of Laser Velocimetry, Lecture Series 1991-

05, VKI, Brussels, 1991.

[9] T. Strazisar, Laser Anemometry in Compressors and Turbines,

ASME Lecture on Fluid Dynamics of Turbomachinery, 1986.

[10] D. Modarress, H. Tan, A. Nakayama, Evaluation of signal

processing techniques in laser anemometry, in: Proceedings of the



11/11

Fourth International Symposium on Application of Laser Ane-

mometry to Fluid Dynamics, Lisbon, July 1988.

[11] C.H. Sieverding, H. Heinemann, The inuence of boundary layer

state on vortex shedding from at plates and turbine cascades,

ASME J. Turbomachinery 112 (1990) 181187.

[12] M. Ubaldi, P. Zunino, U. Campora, A. Ghiglione, Detailed

velocity and turbulence measurements of the prole boundary

layer in a large scale turbine cascade, ASME Paper No. 96-GT-

42, 1996.

[13] BRITE EURAM AER2-92-0048, Time varying ow character-

istics behind at plates and turbine cascades, Final Technical

Report, 1996.

[14] A.A. McKillop, F. Durst, A laser anemometry study of separated

ow behind a circular cylinder, in: Proceedings of the Second

International Symposium on Application of Laser Anemometry

to Fluid Dynamics, Lisbon, July 1984.

[15] C. Williamson, Vortex dynamics in the wake of a cylinder, in: S.I.

Green (Ed.), Fluid Vortices, Kluwer Academic Publishers,

Dordrecht, 1995, pp. 155234.

[16] R.D. Blevins, Vortex-structure interaction, in: S.I. Green (Ed.),

Fluid Vortices, Kluwer Academic Publishers, Dordrecht, 1995,

pp. 533574.

[17] M.M. Zdravkovich, Flow Around Circular Cylinders, Oxford

University Press, Oxford, 1997.

[18] L.S.G. Kovasznay, Hot wire investigations of the wake behind

cylinders at low Reynolds numbers, Proc. Roy. Soc. A 198 (1949)

174190.

[19] J.H. Gerrard, The mechanics of the formation region of

vortices behind blu bodies, J. Fluid Mech. 25 (2) (1966)

401413.

[20] H. Tennekes, J.L. Lumley, A First Course in Turbulence, MIT

Press, Cambridge, MA, 1978.


an experimental study of the unsteady characteristics of the turbulent

Documents