Performance Analysis of Centrifugal Compressor Stage, By Means of Numerical and Experimental...

8/12/2019 Performance Analysis of Centrifugal Compressor Stage, By Means of Numerical and Experimental Investigation

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PERFORMANCE ANALYSIS OF CENTRIFUGAL COMPRESSOR STAGE, BYMEANS OF NUMERICAL AND EXPERIMENTAL INVESTIGATION OFROTOR-STATOR INTERACTIONS.O.DOMERCQCIFRE Engineer,Centrifugal compressorsdesign,Aerothermodynamic department,Turbomeca - Boite 1765411 Bordes, FRANCE.

R. THOMASHead of the turbine design eam,Aerothermodynamicdepartment,Turbomeca, Boite 1765411 Bordes, FRANCE.

A. CARREREProfessor at SUPAERO,(Ecole Nationale Superieure de1ACronautiqueet de 1Espace)Thesis director,3 1400 Toulouse, France.

1. ABSTRACTThis paper deals with numerical and experimentalinvestigations of rotor-stator interactions between abackswept centrifugal impeller and its associatedvaned diffuser. Experimental data were obtained bylaser two focus velocimetry and fast responseKulite transducers. Computations were carried outthanks to a three-dimensionalNavier-Stokes solver,customisedby the authors, for the current purpose.Time-resolved simulations of the full stage withpassages number reduction but respect to realgeometry of components are then presented.Comparisonswith experimental data lead to a codevalidation phase and critic investigations of rotor-stator interaction phenomena. Evidence of theexistence of a strong interaction between the rotorand the stator flow fields are pointed out. Inparticular, an intense upstream influence of thevaned diffuser was observed. Finally, steady stagecalculations, coupling the components by a meaninterfacial treatment, are examined. The reasonablecomputational cost of this method now allows suchnumerical simulations of centrifugal stages o bepart of design cycles.The numerical part of the study was performed atTurbomeca, using the local software and hardwarefacilities, whereas the experimental campaign tookplace in the Propulsion Laboratory of SUPAERO,part of the LAMEP (Laboratoire Mixte enEnergetique et Propulsion), which recentlydesigneda test rig devoted to compressors.Nomenclature :CP Diffuser static pressure ecoverycoefficientQ,E,F,G Elements of Navier-Stokesequations n vectors formG Corrected mass lowJ JacobianM Mach numberu,v,w Contravariant velocity componentsPYPs Static pressurePi Total pressure

u, v, w Absolute velocity Cartesiancoordinatesx, YI z CartesiancoordinatesGreek symbols :rl EfficiencyP DensityT Shearstress ensorSuperscripts :T Transposedmatrix or vectorSubscripts :a Absolute frame of referencei Total conditionsr Relative frameS Static conditionsV Viscous terms

2. INTRODUCTIONAdvances made in the design of centrifugalcompressors n the past thirty years, elevated thatdevice to a key position in small and medium gasturbine engines. Besides,aeroenginesare requiredto be lighter and to involve reduced cost ofownership and maintenance. Consideringcompressors, hose trends lead to more compactcomponents with high level of aerodynamicloading, particularly for military applications. Then,the aim of first-attempt design with adequateperformance and stability margin, becomes ofrough achievement.In the last decade, thanks to detailed flowinvestigations, the extensive use of 3D steady(Euler or Navier-Stokes) solvers and experience ofdesigners gave birth to a high performancegeneration of centrifugal impellers. But, howeverefficient may be the rotor, the matching with itsassociated vaned diffuser remains a hard task,almost always obtained through mono-dimensionalconsiderations.The flow generatedby the impeller,entering the vaneless space and later the radial

Paper presented at the RTO AVT Symposium on Design Principles and Methods for Aircraji Gas Turbine Engines,held in Toulouse, France, 11-15 May 1998, and published in RTO MP-8.


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diffuser appears highly distorted in bothcircumferentia l and spanwise directions and subjectto severe unsteady conditions. Among manyaerodynamic causes, we can put emphasis oncurvature, viscosity and compressibility effects aswell as Coriolis force influence. Then the vaneddiffuser aimed at static pressure recovery from theflow kinetic energy, receives strongly time-dependant inle t conditions, whose influence on itsperformances and stability is not yet accuratelyknown but undoubtedly has undesirable adverseeffects. Those assertions are indeed derived fromexperimental studies and industrial experience23456.Therefore future design methods will need to takeinto account aspects of the flow fie ld currentlyignored. In particular, the previously mentionedeffects of the blade row proximity andunsteadiness. Some 3D Navier-Stokes codes, eitherin the form of commercial packages or researchderived software, are now avai lable to model thosefeatures. But the designer needs an estimation ofthe relevance of numer ical results. Then, eachconstructor must assess his numerical design toolson unsteady data, obtained by detailedinvestigations on engine representative machines,by carrying out a code validation phase.TURBOMECA ini tia ted such actions several yearsago and recently enhanced its data bases within ajoint research program with the LAMEP (Toulouse,France) among others.The present article is intended to give an outline ofthis process from the experimental work to the codevalidation phase and the modifications of thenumerical package necessary to allow a designrelevant use of such tools, regarding currenthardware capab ilities . The first part of the text willbriefly describe the test compressor and the test rig,before examining the experimental data acquisitioncarried out by means of a Laser Two Focusvelocimeter and fast responsepressure ransducers.In a secondpart, after a brief numerical backgroundexplanation, we will focus our attention on fullunsteady simulations of the centrifugal stage flowfield. Then, a steady mode of stage calculation,involving Riemann invariant theory, will bepresented and assessed s an available design tool,already in useat TURBOMECA.

3. TEST STAGE AND MEANS OFINVESTIGATION.3.1 Compressor and test rig.The centrifugal compressor stage investigated inthe present work is composed of a transonicbackswept impeller matched with a vaned diffuser.

The rotor has an equal number of full blades andsplitter blades.Close to the maximum efficiency point on thedesign speed curve, the impeller blade passingfrequency is superior to 5000 Hz. The compressorstage pressure ratio and the mass flow rate arerespectively around 4.0 and 2.0 kg/s. The impellerisentropic efficiency is then over 90 . Thiscompressor and its experimental mounting weredesignedby Turbomeca company. In particular, theoptical access is provided by a shroud insertedwindow allowing measurements situated in thevaneless diffuser and in the captation area (i.e.semi-vaneless pace).Experimental studies were performed in thePropulsion laboratory of the SLJPAERO (part of theLAMEP, Toulouse, France). The compressorsdevoted test rig used is powered by an electricmotor delivering 400kW. The air intake wasprecalibrated to ensure accurate mass flowmeasurement. The outflow enters a plenumchamber and the desired pressure atio is reachedby means of a butterfly valve motion. Theoperating point of the compressor s controlled with42 pressure probes, inlet and outlet temperatureprobes. A computer linked to the rig allows on-the-fly storageof those data with a view to taking intoaccount small operating point disturbances inexperimental post-processing ( for instance massflow recovery calculation). Figure 1, shows theSUPAERO facility.

Figure l- SUPAERO compressor test rig.3.2 Laser Two Focus velocimeter.3.2. I General description.The experimental approach had been carried outwith a Laser Two Focus velocimeter. The presentdevice is derived from DLR works and its maincharacteristics were given by Schold*. Briefly, theprinciple of L2F velocimetry consists in themeasurement of the transit time of seedingparticles, included in the flow, between two highly


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focused laser spots. Histograms of partic lesdetection as a function of spot alignment directionand time of flight ( i.e. transit time) lead to flowvelocity determination. The projection of thevelocity vector on the plane perpendicular to thelaser beams is obtained through its modulus, angleand turbulent rates by statistical calculations asdescribed by Schold. The measurement accuracydepends on the flow turbulence intensity.Considering our experimental facilities, theprecision can be evaluated to +I- 1% on theabsolute velocity and +I- 1 on the absolute flowangle, when turbulent rates are less than 5%.Those measurements are intended to provide datafor rotor-stator interaction mechanismscomprehension. Then, they have to be taken forvarious relative locations of the impelle r main bladein front of the diffuser passage. A magnetic pick-upsituated on the machine rotation axis allow thenecessary data storage triggering.The choice of L2F velocimeter instead of LDV (Laser Doppler) device was linked to the narrownessof the flow path and the restriction of flowaccessibility to a single window. The need of highsignal to noise ratio necessary for wall approachinginvestigations claimed in favour of the time offlight solution. Discussions on the technical aspectsof this choice, as well as interesting developmentson advantages and disadvantages of both devicesapplied to small high speed turbomachinery shouldbe found in Fagan and Fleeter and Elder, Forsterand Gill publications.3.2.2 Measurement positions.Rotor-stator interaction influence on flow evolutionhas been investigated in three main test sections:. the mean radius of the vaneless diffuser.. the vaned diffuser leading edge.l the throat of the vaned diffuser.Each of the three main sections contains tenmeasurement locations. Several relative depthswere investigated.NB: Some results taken from a previousexperimental campaign from the ONERA andconducted by Fradin are added to our currentlyperformed measurements with a view to increasingour validation data base.3.2.3 Data analysis.The flow in the mean vaneless space sectionappears to be dominated by a high level of timedependant heterogeneities. More precisely, a strongwake influence of the impelle r passing blades isclearly observed. The wakes take the form of a high

absolute speed and over-deflected flow feature.Velocity fluctuations up to 20% and flow anglevariations of 15 to 20 are measured. However, theflow delivered by the rotor exhib its a relativesmoothness, i.e. no jet/wake pattern in the sense ofDean and Krain* is observed. Turbulent rates reach10 to 15% within the wake regions and are lower to5% elsewhere.The question then arise, to know to which extendthese flow heterogeneities mix out before the radialdiffuser lead ing edge as currently always assumedin design process. Considering the secondmeasurement section, in terms of velocitymagnitude, both the peak induced by the bladewake passing and the outer gradients have beenreduced. However, large leve l of fluctuations,around 15% remain. The mixing hypothesis is thencontradicted in our particular case. Similarobservations can be drawn from the flow anglefluctuations remaining around 10 to 15. Besidesthe discrepancies between turbulent rates obviouslysuggest that the mix ing process is far to becompleted at the radial diffuser leading edge.At the throat section, the flow is still highly time-dependant and spatial ly heterogeneous. However,due to the differences in streampathes, adversepressure gradients and in the influence of theleading edge stagnation area across the diffuserpitch, the time-organized blade passing feature hasvanished.3.3 Unsteady pressure measurement.3.3.1 Transducers and measurements locations.The transducers used for this app licat ion wereKul ite pressure probes of the XCQ-093 serie. Theyfit the temperature and pressure conditionsencountered in that flow region and present abandwidth suitable for high frequencymeasurements. Each probe was calibrated in termsof transient response in a shock tube with its ownprotection screen, flush mounting device andacquisit ion faci lity used during later compressorruns. The measurement configuration is presentedon Figure 2.

Figure 2 - Kulite flush mounting facility.


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Sixteen measurement positions were distributed onthe external wall of the radia l diffuser (see laterfigures 5) :

l Four positions at the mean radiusbetween impeller trailing edge andvaned diffuser leading edge at thereduced pitch ratios of O., 0.25, 0.5 and0.75.

l Three positions at the vaned diffuserleading edge, at reduced pitch ratios of0.25, 0.5 and 0.75.

l Three positions in the captation area.l Three positions at the diffuser throat

section.l Two positions downstream the diffuserthroat situated on a mid-pitch line.

3.3.2 Data acquisition and processing.The transducer signal is ampli fied via 4 channels ofANS-E300F4 and converted from analogic todigi tal through an OX2000 Metrix Oscilloscope at a5OOkHz rate. A pent ium 90MHz PC is used tocommand the A/D converter and store the files viaan RS232 serial link.The acquired data consists in the raw signalobtained during five to ten impeller rotations. Thesynchronisation signal is given by a one per bladeimpulse allowing the ini tial time to be converted ina reduced time of the impeller blade passing infront of the diffuser pitch but preventing distinctionbetween impeller passages. Then manufacturingdifferences between rotor passages will not betaken into account in our current study.Those data are processed by a phase-lockedaveraging process, as described by Ainsworth orCicatelli and Sieverding13. Figure 3 represents theraw data obtained from position 1 for instance. Theaveraging consists in the following :a) Ensemble averaged signal :

P(t) = P(n,t)n-lb) Average random unsteadiness :P(n, t) = P(t) + p(n, t)

where P(n,t) is the raw signal, N is the number oicycles acquired, t is the time, n is the index withirthe N cycles. A cycle corresponds to the rotation 01an imueller passage in front of the probing position.

sufficient number of cycles is described. Inparticular, no difference is observed between a fiverotor rotations or ten rotor rotations acquis ition.The accuracy in terms of reduced time dependencyon synchronisation device can be evaluated to 2%of the cycle duration.

Nota : The unsteady pressures on the meanvaneless space radius and the throat section weretreated to extract the time mean pressure(p,(t) = -&)dd which can be compared to static0pressure tappings originally implemented on thetest compressor. The comparisons showed somediscrepancies between pressure probes. Correctingfactors correlatedfor difSerent operating points andassessed by swapping probe positions were thentaken into account.

Figure 3 - Raw Data

Figure 4 - Phase-meaned data3.3.3 Data presentation.Figure 5 represents the phase averaged period forthe 4 experimental positions. The x-coordinatecorresponds to the reduced period of rotor bladepassing in front of the diffuser pitch, where 0.corresponds to a situation where the impellertrailing edge and the stator leading edge stands atthe same azimuth.

Figure 4 give the results of this procedure forposition 1 for two different numbers of cycles, thusshowing the independence of the solution when a


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Figure 5 - Pressure evolutions (1).

4. THREE DIMENSIONAL NAVIER-STOKESSOLVER.4.1 Foreword.The NREC commercial software packageVISIUNTM constituted the basis of this numericalstudy. This code, written for turbomachinerypurpose solves the three-dimensional Navier-Stokessystem of equations4567. Pul liam and Stegerworks give an overview of the implementedmethod. Developments were carried out by theauthors wishing to closely examine rotor-statorinteraction features. In particular, the treatment ofinterfacial areas and multi-channels domains hadbeen customised, as well as the possibility toperform steady stage calculations.4.2 Numerical background.4.2. I System of Equations.The numerical approach of VISIUNTM is basedupon a three dimensional Navier-Stokes code,

written for turbomachinery purpose. The ful lsystem of equations expressed in strongconservation form is used herein . Its compact formcan be expressed as follows in Cartesiancoordinates.Q-+ d(E-EJ + W-GJ +W-Fv) -oat ax ay az -where vectors are given by :

Q=(P.P.P.PW.)7E=(pu,pu* +p,puv,puw,~(e+/7))~I;=(pv,puv,Pv2+p,PVW,V(e+P))lG=(pu,puw,pvw,pw+p,w(e+/~))~

E,, = (0. r, r,r,ur,+vr,iwr, 1I;, = (0 7 rw.~,.r, TX+ +vryxT + wr,, 1

equations can be transformed to an arbitrarycurvilinear space &q,


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4.2.3 Two frames of referenceThe main difference between single blade rowcomputations and stage simulations lies in theexistence of two frames of reference, one for eachcomponent, separated by an interfacial area,through which numerical information has to betransferred in order to predict rotoristatorinteract ion effects. Several different approaches,either conservative or non conservative, have beenused. The matching of the two frames reta ined inVISIUNTh is based on M. M. Rai 22 method. Thegrid is split into a rotating zone and a non-rotatingzone with an inter facia l overlay. Flux vectors areinterpolated from one grid to the other in thisoverlaid area to obtain boundary conditions relatedto each component sub-domain. H-type meshes areused to mode l the geometry. Two overlaid grids aregenerated, one for each component. The interfacearea consists in a cylindr ical surface situated at themean radius between the impeller trailing edge andthe vaned diffuser leading edge.4.2.4 Unsteady stage calculations : a reduction ofthe computational domain.Cpu time and memory necessary for unsteady stagenumerical simulations make the use of acomputational domain reduction unavoidable. Acommon approach consists in geometrymodifications in order to obtain the same azimuthalextension in the rotor and in the stator modelledpassages. This was basically used by VISIUNTM,but also by Rai22 and Dawes6 among others.In fact, geometr ical transformations are, in the caseof centrifugal compressors, mainly applied to thevaned diffuser considered passages. Therefore, thehub and/or shroud countours have to be ajusted toensure the tota l design throat section conservation ifan accurate simulation of stage performance isawaited. Then, in a code assessment contex,interpolations in the numerical flow field to probethe solution at the exact measurement locationshave to bear reduced space considerationsMoreover, some cases lead to a slightly divergingvaneless space which may adversly affect acommonly observed shroud recirculat ing region.Therefore, an alternative method was preferred bythe authors with a view to computing the flow inthe actual geometry thanks to minor numericalmodifications. This reduction technique, developedby the ONERA (see for instance Fourmaux23), maybe summarised as follows : let Nl and N2 be thereal blade numbers of the rows to study, le t Kl andK2 the number of passages considered in each stage

component so that Kl and K2 are small but Kl/K2stays as close as possible to Nl/N2. A periodicazimuthal condition is implemented in each row(Iper ad Iper. lines for the impeller and Dper and DperYlines for the diffuser on Figure 6). This results in atime lag cancelling at the extreme azimuthalboundaries of each group of passages. Theinformation transferred through the inter facia l areafrom one grid to the opposite must be compatiblewith those spatial ly periodic condit ions. Then wehave to use an expansion/contraction step at theinterface. Let e,=2ITK,/N,, e,=2HK,/N, be therespective azimuthal extension of each componentgrid on Figure 6 and ec= (e,+e,)/2. Fl is thedownstream boundary of the first sub-domainrelated to el, F2 is the upstream boundary of thesecond sub-domain related to e2. Fc is then avirtual frontier related to ec through which data aretransferred by interpolation on an equal azimuthalextension ec thanks to previousexpansion/contraction of the azimuthal gradientbetween Fl and Fc or between F2 and Fc asrepresented on Figure 6.ec=1/2(el+e2)

Periodic boundaries

Figure 6 - Reduction of the computationaldomain.

The comparison between numerical results andexperimental data presented in the following partswill give an outline of the level of descriptionobtained with this method.4.2.5 Steady stage calculations : an industrialnecessity.The previously described unsteady calculationsinvolved a fu ll time resolved interpolat ion processat the rotor-stator interface and a slow convergencetowards a periodic numerical solution. Consideringcurrent hardware capabilities avai lable toaeronautical design engineers, a time meaninterfacial treatment becomes an industrialnecessity. Such a calculation tool , taking intoaccount rotor-stator coupl ing mainly in terms ofhub to shroud distortions, is already in use duringdesign cycles. For instance, three dimensionalgeometries of components, fitt ing intra-stageinteractions, can be studied within short termdevelopment cycles.


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22-lThe method implemented in VISIUNTM by theauthors and presented herein is based on Riemanninvariants theory and the derived compatibilityrelations. This approach comes from twoconsiderations :

l Compatibi lity relations are a way to takeinto account the transport of flowproperties by wave frontsZ4.

l A grid point, steady in its own frame,receives informations from opposite pointsin the other frame points in the other framerotating in front o f him.

Then, the approach chosen consists in imposinginterfacial boundary conditions through azimuthalymeaned compatibility relations. The FrenchONERA, first described this technique5.26.Let D be the computational domain and n an inwarddirected vector. The five compatibility relationsobtained from the five eigenvalues(V . n - a, V . n, V . n + a) of the hyperbolicEuler system are :

iii:;:~

where P is the static pressure, p the density, a thesound speed, V the speed vector, V,, = V. n andV, = V - (V . n) . n . The superscript * indicates ascheme value and indicates the flow properties atthe position receiving the correspondingcharacteristic.The implementation for the interface meantreatment can be summarised as follows. Thenormal Mach number is supposed to be less thanunity, inward and outward flow are distinguished.For exiting flow, V on < 0, four compatibilityrelations are applied (four negative eigenvalues)and one boundary condition is necessary. Thiscondition is similar to a non-reflection boundarycondition. Then we have :P - (pa) Vi, = P* - (pa)V,tP -(a) Vi, = P* - (a*)V,:v; = VTP + (pa) Vl, = (P* + (pa)V,:), = I,

where I1 is an azimuthaly averaged valuecalculated on the opposite domain. The averagingprocess is surface weighted and results in hub toshroud profile of I,.

For inlet flows, V. n > 0, one compatibil ityrelation is applied (one negative eigenvalue) andfour boundary conditions are necessary. Then therelations are :IP - (pa) Vi, = P* - (pa)V,:I II - (a)V;, = P* - (a2)V,: = I,P + (pa) Vi, = (P* + (pa)V,:), = I,

where 12,13,14 and 15 are averaged by the sameprevious process and result in hub to shroudvarying boundary conditions.

Numerical flow fields obtained through thisapproach will be compared to experiments in thesixth part.5. UNSTEADY FLOW CALCULATIONS ANDASSESMENT.5.1 Numerical simulations conducted.The real ratio of blade numbers between the wheeland the stator is surrounded by I and l/2. Then,two basic mesh configurations were built : the firstone contained one blade passage of eachcomponent and will be named case A, the secondone matched one blade passage of the impel ler withtwo passages of the vaned diffuser, named case B.In both casesan approximate number of 125000nodes for each passagemeshedwas chosen whichis quite low but planned to give an interestingcompromise between accuracy and solution time.As will be stated ater some luctuations induced byimpeller wakes were partly damped in those firstcases,a third configuration was then meshedwithan increased node number in the azimuthaldirection. This casewill be referred as caseC.

I I Impeller82;61x24 1Diffuser 1CaseA 74x69~24CaseB 82x61~24 2*(74x69x24)-1CaseC 82x82~24 2*(74x81x24)-1

Table I- Node distribution.For each configuration, the flow field of the peakefficiency point on the design speedcurve hasbeencomputed. A time-periodic solution was obtained inall cases. Convergence was monitored byexamining static pressure evolution in the mostsensitive parts of the flow field i.e. the impellertrailing edge and the diffuser leading edge. An


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approximate number of 10 to 15 blade passingperiod were necessary to obtain a periodic solution.5.2 Mono-dimensional results.From the designer poin t of view, the overallperformance rendering capability of a code is ofmajor importance, allowing him to evaluate a newdesigned release numerically without requiringintensive test rig campaign. The comparisonsmade on one-dimensional mean values can besummarised in the following chart. The valuesgiven are differences between experimental andnumer ical results expressed in percent.

Tab le 2- Mono-dimensionnal results.The operating point is then quite accuratelydescribed in al l cases. The efficiency lack generallyobserved is similar to the difference experienced inisolated wheel simulations. Moreover, it should benoted that previous simulations obtained by thesliding of impelle r outflow conditions at the inlet ofan isolated diffuser grid did not allow to reach sucha level of description of the diffuser operatingpoint. For instance the static pressure recoverycoeff icient was underestimated by more than 20%,thus suggesting, the importance of fu ll stagecoupling in a transonic configuration.

5.3 Two-dimensional results.The first validation step consists in comparisons

between measured and time averaged calculatedspanwise evolu tion of the absolute flow angle andthe absolute flow velocity . This phase will allowthe evalution of the code capability to reproduce thehub-to-shroud distortions which, according toDawes6 are a key factor of rotoristator interactioninfluence on stage performance. On Figure 7, the y-axis coordinate represents the hub-to-shroudreduced distance, where 0. corresponds to the hub.Either the absolute flow angle (counted between thevelocity direction and the circumferentialdirection) , to which a reference angle is substractedor the absolute velocity modulus (reduced by therotor tip speed) are given on the x-axis. Thoseevolutions are extracted at the mean vaneless spaceradius and here are given at a reduced pitch

position of 0.3. More details are given by Domercqand Thomas*.

Figure 7 - Time averaged spanwise evolutions.The two calculations performed on the A and Bbasic grids, restitute the same spanwise variation interms of velocity and angle, thus illustrating theirclose one-dimensional behaviour. Besides, ratheraccurate descriptions of the hub to shroudexperimental evolution are obtained. In particular,the gradient of velocity is shown by both (A and B)calculated profiles. The mean level difference islinked to the slight mass-flow discrepancies incalculations, see Table 2. Similarly, the calculatedand measured flow angles denote an interestingagreement. The shroud area subdeflexion , knownto result from a complex interaction between tipleakage vortex, passage vortex and horseshoevortex (Kang and Hirsch) is precisely given byboth calculations. Concerning. Case C, similarprofiles are obtained with the increased nodedensity. In particular, flow angle evolutions areiden tica l to the previous (A and B) results5.4 Unsteady assessment and unsteady flowinvetsigation.5.4. I Unstea& assessmen t.

In the following part, we will focus our attention oncase C results which, regarding the higherazimuthal node density, gave suitable results to faceexperiments. Figure 8 and Figure 9 represent theabsolute flow angle and velocity at midspan forthree reduced pitch positions of 0.3, 0.5 and 0.7.The measurement section considered is still section1. i.e. the mean vaneless snace radius.

Rsduced pttch.0.5.

Figure 8 - Midspan unsteady evolu tion of theabsolute flow angle.


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Figure 9 - Midspan unsteady evolu tion of thereduced absolute velocity.

A strong blade wake influence characterises theexperimental results. This region is occupied by alow velocity fluid attached to the trailing edge inthe rotating frame of reference. A speed triangleanalysis shows that this results in a low, i.e. rathercircumferential, absolute flow angle and highspeed pattern in the absolute frame of reference.Those wakes are indeed larger near the hub, sincethe trai ling edge thickness increases from hub toshroud. Moreover, a steady point ( i.e . a L2Fmeasurement point i n the diffuser frame ofreference sees the pressure side of the backsweptblade before its suction side. The experimentalgradients observed thus suggest that the absolutespeed magnitude decreases from suction side topressure side while the absolute flow angleincreases. Then, in the relative frame, the impellerdelivers flu id of higher energy near the pressureside. Thus suggesting that the Coriolis effect thatgenerally drags low energy particles to the suctionside takes advantage, in our case, on the curvatureeffect, which on the contrary leads low energy fluidparticles to the centre of curvature, that in ourbackswept case corresponds to the pressure side.The comparison between experimental data andcomputational results shows that the wakesextensions are underestimated by the numericalsimulations. However, the magnitude of thefluctuations is quite well estimated. A 10 to 12angle fluctuation is obta ined numer ically whereasaround 15 were measured. In terms of velocity , thepredicted order of variation is situated between 17to 25% where the corresponding L2F results rangefrom 17 to 30 %. More precisely, despite the wakeextension reduction, the flow angle and speedmodulus blade-to-blade gradient, linked tosecondary flow behaviour, are accurately rendered.Moreover, the speed modulus fluctuations arereduced in the same way with increasing reducedpitch position. Nonetheless, the downstreampropagation of the numer ical wake, thinner than theexperimentally observed corresponding patternswill also be subject to faster mixing in the captat ionarea.Figure 10 presents the comparisons between case Cand unsteady pressure measurements obtained withKul ite transducers. A fair agreement is obtained.The shape of the fluctuation is rendered for each

position. Small structure of the pressure fie ld aredescribed with accuracy for locations 1 and 3. Theevolution of the signal between location 1 and 2,consisting in the separation of the flat profile in amain and secondary peak is also captured. Thedescription of this dual shape profi le is confirmedby locat ion 3 comparison. However, an inadequatenumerical damping appears at location 4, since onlyhalf of the signal amplitude has been simulatednumerically.

Figure 10 - Confrontat ion of pressure evolutions.

As a conclusion, the unsteady assessment reveals tobe quite satisfactory, since the global behaviour ofthe matching between the impeller and its vaneddiffuser is given by the code.5.4.2 Unsteady flow investigation from impelleroutlet to the captation area.Figure 11 and Figure 12 give the time-resolvedevolution of the unsteady flow field through itsstatic pressureand absolute Mach for six positionsacross he blade passingperiod.

Figure 11 - Unsteady flow field, static pressure.


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_.-._Figure 12 - Unsteady flow field, Mach number.Those representations are given at midspan whereexperiment versus simulation agreement wasinteresting. The rotor/stator interaction appears tobe reciprocal, the wheel indeed delivers pitchdependant flow conditions as discussed previouslybut the magnitude of stator vane counter effectreaches the same leve l. In fact, the pressure fieldrepresentation, for instance, underlines the diffuservane leading edge influence on the impelleroutflow pressure condi tion through the existence ofa high static pressure zone near the stagnation poin tsituated on the leading edge. This leads to anapproximate variation of 20 of static pressureonthe pressureside of the impeller blades.Moreover, the blade passingwakes have an obviousinfluence on the captation area flow field, inparticular in the vane suction side nearby. Theimpeller blade trailing edge imposesa high absoluteMach number and low absolute angle flow patternto the diffuser inlet. This zone has hardly no effecton the diffuser pressure side since its extend isreduced by the leading edge high pressure ield,when impeller and diffuser blades face each other(t/T=O.).Then, it affects the diffuser suction side bydragging a low Mach number fluid into the channel(t/T=0.2). The next step consists n the creation of ahigh Mach number flow region in the middle of thediffuser pitch (t/T=0.4), which stands n place of asimilar pattern appeared at t/T=0 and observedwhilst diffusing slightly downstreamat this reducedtime. Thus the captation area experiences asuccessionof high speedand low speedbulbs thatmix downstream. The blade-to-blade flowdependenceat the impeller outlet leads herefore toa fluctuation that follows the main flow direction.6. STEADY SIMULATIONS OF BLADE ROWINTERACTIONS.

The geometry of the compressor previouslyinvestigated in an unsteady mode was submitted toa steady calculation involving the coupling processdescribed n paragraph4.2.5.Table 3 sums up the discrepancies obtainedbetween the time averaged flow field of caseC andthe steady simulation name case D. They areexpressed n percent.

Table 3 - Mono-dimensionnal comparison ofcaseC (unsteady) and D (steady).Close performance description is given by the twocoupling techniques. An increased evel of loss ispredicted between he impeller trailing edge and theradial diffuser leading edge by the steady couplingcalculation. This mainly results from slightdiscontinuities generatedat the averaging plane.Finally, spanwiseevolutions of the absolute flowangle and absolute educed speedof casesC and Dare compared on Figure 13. The profiles areextracted at the leading ec

--

e radius of the stator.

Figure 13 - Comparisons of spanwiseevolutions.The two profiles exhibit a good agreement.The hubto shroud gradients are accurately rendered. Thediscrepancy in terms of absolute flow angle is lessthan 1. Thus a steady coupling calculation provesto be able to simulate the correct evolution ofincidence angle and speedon the span of the radialdiffuser. Then it can be consideredas an interestingtool to take into account the coupling between thecomponents of a centrifugal compressor stagethanks to calculations of a design affordable cost.

This part of the study will give an overview of thecode capability to describe blade row interactionwithin the frame of steady coupling.


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7. CONCLUSIONS.The flow patterns that govern the rotor/stator

interact ion in a centrifugal compresssor stage havebeen investigated by means of experimental andnumerical studies. The test stage representative ofhigh speed and high performance turbomachinerydevices, was known to be a rather severeaerodynamic case. The present paper yields to thefollowing conclusions concerning the unsteady partof the study :. An intense upstream influence of the vaned

diffuser on the impeller flow fie ld is observed.The performance of the compressor is thenproperly caculated by a ful l time-resolvedsimulation of the stage, whilst a methodconsisting in using impel ler outflow as upstreamboundary condi tion of the vaned diffuserreveals unsatisfactory.

l Unsteady variations measured thanks to a L2Fdevice were qual itat ively fairly described. Theagreement in terms of blade to blade gradients,for instance, put emphasis on the codecapab ility to reproduce secondary flowsinfluence on the stage flow fie ld. Moreover thisgave an outline of the computational domainreduction as an acceptable representation.

l The interaction of the impeller blade leadingedge and the vaned diffuser stagnation zone atmidspan appeared to drive both the impelleroutflow conditions and the unsteady flowpatterns in the captat ion area.

Moreover, a method allowing design time-affordable calculations, which couples componentsthanks to a mean treatment of the interfacial area,using Riemann invarian t theory, has beenimplemented in the Navier-Stokes code. Thecomparison made between the steady stage flowfield and the time-averaged flow field of unsteadycalculations underlines the capability of this tool tointegrate rotor-stator interaction features in thecalculations of the performance of a transoniccentrifugal stage.References : P.Belaygue, H.Vignau,Le compresseur centrifuge, composant essentieldes turbomoteurs de peti te et moyenne puissance.AGARD-CP-537.2 Krain H.,A study on centrifugal impe ller and diffuser flowASME paper 8 1 GT-9, 198 1.

3 Krain H., Experimental observations of the flowin impellers and diffusersVKI Lecture Series 1984-07, 1984.

4 Bois G., Duchemin J.M., Vouillarmet A.,Papaillou K.D.Analyse expCrimentale de ICcoulement dans unCtage de compresseur centrifuge.

AGARD-CP-282. 1980.5 Hus H., Fradin Ch.Influence de IhCt&o&nCitC de ICcoulement B lasortie du rotor sur les performances du diffuseurdun compresseur centrifuge.AGARD-CP-282, 1980.6 Dawes W.A simulation of the unsteady interaction of acentrifugal impeller with its vaned diffuser : flowanalysis.ASME paper 94-GT- 105. Bois G., Fradin Ch., Vignau H.Probl6mes de validation des codes Euler 3D pourcompresseurs centrifuges.Third European Propulsion Forum , November 13-15. 1991. AAAFIDGLRIRAeS.* Schold R..Laser Two Focus Velocimetry.AGARD-CP 399, 1986.9 Fagan J.R., Fleeter S.L2F & LDV velocimetry measurement and analysisof the 3D flow fie ld in a centrifugal compressor.AIAA-89-2572. Elder R.L., Forster C.P., Gill M.E.Appl ication of Doppler and Transit LaserAnemometry on small Turbomachines.AGARD-CP-399. Fradin Ch.Constitution dune base de donnCes relative a1Ccoulement du fluide dans un compresseur

centrifuge.ONERA Report.I2 R. W. AinsworthUnsteady Measurements Techniques.VKI Lecture Series. G. Cicatelli, C.H.SieverdingThe Effect of Vortex Shedding on the UnsteadyPressure Distribution Around the Trailing Edge of aTurbine Blade.


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Journal of Turbomachinery, Transaction of theASME, Vol. 119, October 1997.I4Users Guide VISIUN-2FRTM Version 3.0,Simultaneous three-dimensional CFD analysis ofrotating and stationary bladed passages inturbomachinery, a computational system.Northern Research and Engineering Corporation,Wobum, Massachusets, USA.SAnalysis of three-dimensional unsteady flow incentrifugal compressors.Final report, phase one : diffuser performance.Principal investigator : Oreper G.Northern Research and Engineering Corporation,Wobum, Massachusets, USA.I6 Analysis of three-dimensional unsteady flow incentrifugal compressors.Fina l report, phase two : impeller performance.Principal investigator : Oreper G.Northern Research and Engineering Corporation,Woburn, Massachusets, USA.Analysis of three-dimensional unsteady flow incentrifugal compressors.Fina l report, phase three : stage performance.Principal investigator : Oreper G.Northern Research and Engineering Corporation,Wobum, Massachusets, USA.* Pulliam T.H., Steger J.L.Implicit Finite-Difference Simulations of Three-Dimensional Compressible Flow.AIAA Journal, Vol. 18, February 1980.I9Anderson D.A., Tanneh ill J.C., Plechter R.H.Computational Fluid Mechanics and Heat

Transfer-t.2oBaldwin B.S., Lomax H.,Thin layer approximation and Algebraic Model forSeparated Turbulent Flows.AIAA paper 78-257, 1978.

Beam R.M., Warming R.F.An implic it factored scheme for the compressibleNavier-Stokes Equations.AIAA Journal, Vol. 16, April 1978.

23Fourmaux A.,Assessment of a Low storage Technique for Multi-Stage Turbomachinery Navier-StokesComputations.ASME Winter Annual Meeting, Chicago, USA,November 6- 11, 1994.24JP Veuillo t, G. MeauzeA 3D Euler Method for Internal Transonic FlowsComputation with a Multi-domain Approach.AGARD-LS- 140A. LEMEURCalculs stationnaires et instationnaires dans un&age de turbine transsoniqueAGARD - CP- 5 10.26C. Toussaint, A. Fourmaux, G. BillonnetComparison of Steady and Unsteady 3D ViscousFlows Computations through a transsonic turbinestage.ISABE, November 1997.270. Domercq, R. Thomas.Unsteady Flow Investigation in a TransonicCentrifugal Compressor Stage.AIAA-97-287728Hirsh Ch., Kang S., Poin tel G.A numerically supported investigation of the 3DFlow in Centrifugal Impellers, Part II : SecondaryFlow StructureASME paper 96-GT- 152

22Rai M.M.Navier-Stokes Simulations of Rotor-StatorInteraction using Patched and Overlaid Grids.AIAA paper 85-1519.

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