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This is an author-deposited version published in: http://oatao.univ-toulouse.fr/
Eprints ID: 11821
To link to this article: DOI: 10.1155/2014/729629
URL: http://dx.doi.org/10.1155/2014/729629
To cite this version: Bousquet, Yannick and Carbonneau, Xavier and Dufour,
Guillaume and Binder, Nicolas and Trébinjac, Isabelle Analysis of the Unsteady
Flow Field in a Centrifugal Compressor from Peak Efficiency to Near Stall
with Full-Annulus Simulations. (2014) International Journal of Rotating
Machinery. 11 p. ISSN 1023-621X
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Analysis of the Unsteady Flow Field in a CentrifugalCompressor from Peak Efficiency to Near Stall withFull-Annulus Simulations
Yannick Bousquet,1,2 Xavier Carbonneau,2 Guillaume Dufour,2
Nicolas Binder,2 and Isabelle Trebinjac3
1 Liebherr-Aerospace Toulouse SAS, 408 avenue des Etats Unis, 31016 Toulouse, France2 Departement d’Aerodynamique, Energetique et Propulsion, ISAE, Universite de Toulouse, BP 54032, 31055 Toulouse Cedex 4, France3 Laboratoire de Mecanique des Fluides et d’Acoustique, Ecole Centrale de Lyon, UCB Lyon I, INSA, 36 avenue Guy de Collongue,69134 Ecully Cedex, France
Correspondence should be addressed to Xavier Carbonneau; [email protected]
Uis study concerns a 2.5 pressure ratio centrifugal compressor stage consisting of a splittered unshrouded impeller and a vaneddiIuser.Ue aim of this paper is to investigate the modiVcations of the Jow structure when the operating point moves from peakeXciency to near stall. Ue investigations are based on the results of unsteady three-dimensional simulations, in a calculationdomain comprising all the blade. A detailed analysis is given in the impeller inducer and in the vaned diIuser entry region throughtime-averaged and unsteady Jow Veld. In the impeller inducer, this study demonstrates that the mass Jow reduction from peakeXciency to near stall leads to intensiVcation of the secondary Jow eIects.Ue low momentum Juid accumulated near the shroudinteracts with the main Jow through a shear layer zone. At near stall condition, the interface between the two Jow structuresbecomes unstable leading to vortices development. In the diIuser entry region, by reducing the mass Jow, the high incidenceangle from the impeller exit induces a separation on the diIuser vane suction side. At near stall operating point, vorticity from theseparation is shed into vortex cores which are periodically formed and convected downstream along the suction side.
1. Introduction
Centrifugal compressors for the aeronautical Veld are expect-ed to achieve high pressure ratios and high eXciencies atdesign operating point while minimizing the element size.In this context, typical centrifugal compressor stages arecomposed of high speed impellers with vaned diIusers toachieve the high pressure recovery in a reduced space. Onthe other hand, extending the operating range as much aspossible is also an important design constraint.As for axial conVgurations, the limitation at low mass
Jow rates comes from the rotating stall and/or surge phe-nomena. Rotating stall is characterized by the presence ofone or several cells rotating around the annulus, either in
the impeller or in the diIuser. Surge is a system dependantphenomenon associated to large amplitude oscillations ofthe pressure through the compressor system [1].Ue worksof Galindo et al. [2] show that the surge intensity can bemodiVed by changing the length of the duct downstream thecompressor. However, operating the system in these unstableconditions induces a dramatic drop of performance associ-ated with mechanical stresses that may cause the failure ofthe compressor.Uerefore, a margin (surge margin) is takento keep away the operating point from these phenomena,leading to an operating range reduction.Backswept impellers are widely used to increase the
stability of the impeller and Vnally the stability of the stage[3]. EIorts have also been dedicated to identify Jow control
strategies in order to delay the emergence of instability. Dif-ferent techniques are presented by Skoch [4] in a high speedcentrifugal compressor. However, the use of stabilizationtechniques to extend the operating range requires a goodcomprehension ofJowmechanisms occurring before the stallinception.
Stall phenomenon in compression systems has beenstudied for almost sixty years. Ue experimental works ofEmmons et al. [5] and Mizuky and Oosawa [6] in a lowpressure ratio centrifugal impeller with a vaneless diIusershow that rotating stall occurs in the inducer and leads tosurge. In a high pressure ratio centrifugal compressor withvaned diIuser, Wernet et al. [7] and Trebinjac et al. [8]observed separation of the boundary layer on the diIuservane before the surge inception.
Before the onset of these developed instabilities, twofamilies of precursors have been observed, Vrstly in axialconVguration [9] and then in centrifugal conVguration [10].Ue Vrst precursor signal is the growth of a small amplitudedisturbance with a long length scale referenced as modalstall, while the second concerns the growth of a higheramplitude disturbance but with smaller length scale (severalblade passages) termed spike.
Moreover, most of the past works deal either with highpressure ratio (>5) transonic compressors using vaned dif-fuser or low pressure ratio (<2) compressors using vanelessdiIuser. For the Vrst category, there is evidence that thediIuser entry region is oHen responsible for the surge onsetwhile for the second impeller inducer seems to be the weakestzone in terms of Jow instability.Ue present study concernsa subsonic and moderate pressure ratio (2.5) centrifugalcompressor stage composed of a splittered impeller and avaned diIuser.
In addition, work on the topic comes generally fromexperimental investigations where the Jow description istherefore partial at best. In this study, investigations areperformed through a computational Juid analysis. Near thesurge line, unsteady phenomena uncorrelated to the bladepassing frequency may appear. Uerefore, to capture all ofthe spatial and temporal content, the calculation domain hasbeen extended to all the blade passages leading to 60-million-pointmesh. Since, the surge onset is generally triggered in theimpeller inducer or in the vaned diIuser entry zone, eIortsare concentrated at these locations.
Ue two main objectives of this paper are to (i) numeri-cally analyze the modiVcations of the Jow structure inducedby themass Jow reduction from peak eXciency to a near stallcondition and (ii) investigate in depth through unsteady Jowdata sets the near stall operating point in order to proposediIerent scenarios which may lead to Jow breakdown. In theVrst part of the paper, the study case and the numerical pro-cedure are presented.Uen, the numerical model is validatedthanks to experimental measurements. AHerwards, detailedanalysis of the unsteady Jow features in the impeller inducerand Vnally in the diIuser entry zone is given depending onthe operating point.Ue last two parts constitute the scope ofthe paper.
2. Test Case Presentation
Ue centrifugal compressor stage considered for this studyhas been designed by Liebherr-Aerospace Toulouse SAS andis integrated in an air-conditioning system. Ue stage iscomposed of a backswept splittered unshrouded impeller, avaned diIuser, and a volute.Ue design speciVcation is basedon a stage static-to-total pressure ratio of 2.5 with a designrotation speed of 38000 rpm.Ue impeller contains 8 mainblades and 8 splitter blades with a backsweep angle of 32∘.Ue impeller exit radius is about 100mm.Ue vaned diIuserconsists of 21 wedge blades (see Figure 1).
3. Numerical Procedure
3.1. Flow Solver. Computations are performed using the !"#$solver developed by ONERA and CERFACS [11]. It solvesthe three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations, based on a cell-centeredVnite volume approach on multiblock structured grids.Ue turbulent viscosity is computed with the one-equationSpalart-Allmaras model [12].Ue convective Juxes are com-puted with the centered second-order scheme with artiVcialdissipation of Jameson and diIusive Juxes with a second-order centered scheme.Ue time-marching integration is per-formed with an implicit scheme composed of the backwardEuler scheme and a scalar lower-upper symmetric successiveoverrelaxation method (LUSSOR) proposed by Yoon andJameson [13]. Uis time-marching scheme is coupled witha second-order dual time stepping method proposed byJameson [14].Ue number of physical time steps to discretizea complete rotation is set to 1680, corresponding to 210time steps per impeller main blade passing (impeller has8 main blades). Uis discretization value permits a correctdescription of the impeller-diIuser interactions accordingto what is usually reported in the literature [15]. For eachphysical time step, iterations are performed in the inner loopuntil two orders of magnitude residual reduction are reached.Uis condition is satisVed in less than 10 subiterations. Toreach the periodic state, at least 12 impeller rotations areneeded, equivalent to approximately 20000 physical timesteps. Uey are performed using 512 computing cores andrequire 200000 CPU hours for a single operating point.
3.2. Boundary Conditions. Ue computational domain con-tains the centrifugal impeller with the inlet bulb, the vanelessspace, and the vaned diIuser and ends with a 90∘ turningpipe used as a computational buIer zone to damp possiblereJections from the exit boundary condition (Figure 2).Ue computational domain extends 1.5 impeller inlet tipradius upstream and downstream of the blade rows. As themeshing of the complete annulus requires signiVcant CPUcost, the volute is not taken into consideration. Consideringthe inlet boundary conditions, the total pressure, the totaltemperature, and the Jow angles (axial Jow) are prescribed.When the operating point moves toward the surge line, theslope of the stage pressure ratio characteristic may reachzero or even positive values. Uerefore, a static pressureexit condition is not adapted because two solutions may be
Figure 1: 3D sketch of the compressor stage hub with the returndownstream channel.
1
4
B
Figure 2: Meridional view of the calculation domain.
obtained (diIerent mass Jow rates) for a same outlet pressurewhile a Vxed mass Jow condition may lead to numericalproblem.Uerefore, in the present study, the outlet ismodeledusing a throttle condition, coupled with a simpliVed radialequilibrium law.Ue outlet static pressure %out is set by thefollowing relation:
%out (& + 1) = '"0 + ((+ (&)+ref )2, (1)
where '"0 is the inlet total pressure, +(&) is the mass Jow rateat iteration & through the exit, section and ( is the throttleparameter. Ue simulated operating point can move fromchoked point to surge line by simply increasing the value ofthe throttle parameter. Ue rotor-stator interface is treatedwith a sliding mesh method. In elsA, the communicationthrough the sliding surface is performed using a distributionof Juxes.Uis approach rigorously ensures conservativity forplanar interfaces, which is almost the case here. Details on theimplementation and use of the sliding mesh technique withthe elsA code can be found in the work of Filola et al. [16]and Gourdain et al. [17]. At the blade, hub and shroud wallsno-slip adiabatic conditions are prescribed.
3.3. Mesh Parameters. Ue structured mesh grid was gener-ated with Autogrid V5 using classical H, O, and C topologies.In order to obtain mesh independent results, the parametersto generate the mesh result from a previous study [18]performed in the same conVguration.Ue size of the Vrst cellis set to 3 -m corresponding to a normalized wall distance .+well below 3 at the walls. Ue impeller main blade passagegrid and splitter blade passage grid consist of 89 points inthe spanwise direction including 29 points in the gap region,92 points in the pitchwise direction, and 161 points in thestreamwise direction.Ue diIuser blade passage contains 57points in the spanwise direction, 119 points in the pitchwisedirection, and 141 points in the streamwise direction. Ueimpeller blade passage and the diIuser blade passage include,
respectively, 2.6∗106 and 1.7∗106 cell grid.Ue single passageis repeated to obtain the full annulus and the calculationdomain reaches a total of approximately 60million points.
3.4. Data Extraction. Unsteady computations are performedfor three operating points OP1 (peak eXciency), OP2, andNS(near stall). As will be illustrated later, unsteady Juctuationsfor the OP1 and OP2 are only generated by impeller-diIuserinteractions. In other terms, for these two operating points,the Jow is time periodic in the frame of reference of each row.AHer reaching the unsteady periodic state, a full rotation ofthe rotor is performed to extract data (unsteady and time-averaged). Ue time-averaging period is equal to one rotorrotation.For the NS operating point, unsteady eIects are not
only limited to rotor-stator interactions, and the naturalperiodicity of the Jow is no longer valuable.Uerefore, aHerreaching the stable state, the simulation has been extendedduring six rotor rotations to validate the stability of theoperating point and to extract data. Ue time-averagingperiod is therefore equal to 6 rotor rotations.Because of the domain size, the data extraction of the
complete Jow Veld is hardly aIordable with a correct tem-poral resolution. Uerefore, data extraction is segregatedinto local information recorded at each time step, two-dimensional planes extracted every 10 time steps, and thecomplete three-dimensional Veld saved three times perimpeller rotation.
4. Numerical Model Validation
Figure 3 depicts the total-to-static pressure ratio deVned as0 = %4/%01 as a function of the corrected mass Jow fromnumerical simulations results and measurements, for thedesign speed line.Ue corrected mass Jow is deVned as
+cor = +√201/2ref%01/%ref . (2)
Ue experimental value of %4 is the mean value of three staticpressure probes located on the hub surface at diIuser exitradius (plane 4, see Figure 2).Ue static pressure fromnumer-ical results is extracted at the same location. All the computedoperating points show good agreement with experimentaldata.Ue main objective of the measurements was to validate
2.7
2.6
2.5
2.4
2.3
2.2
2.1
21.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Pre
ssu
re r
atio
U-RANS
Experimental
NSOP2
OP1
Corrected mass flow (kg/s)
Figure 3: Pressure ratio of the compressor stage.
the numericalmodel. In the following sections, investigationswill only consider the numerical simulation results.
5. Impeller Flow Structure Analysis
When the centrifugal impeller is responsible for the surgeonset, the origin of the destabilization occurs generally in theinducer and near the shroud.Ue unsteady numerical resultsat this speciVc location are now presented.
5.1. Secondary Flow E5ects. Ue centrifugal impeller Jowstructure has been studied continually since the 1970s. Uework of Eckardt [19, 20] shows that the main Jow isaIected by secondary Jows, responsible of the jet-wakestructure classically observed in centrifugal impellers.Ueyare produced by reorientation of transverse vorticity (in theboundary layers) into longitudinal vorticity under the eIectsof curvature and rotation [21].Ue meridional curvature parteIect drives the lowmomentumJuid in the boundary layer ofthe blades (radial migration from hub to shroud), while therotation eIects act mainly on the Juid particles in the huband shroud boundary layer (migration from PS to SS).Uesecondary Jow eIects are generally noticeable from the axial-radial turn and intensify up to the impeller exit due to thethickening of the boundary layers. To investigate the impellerJow structure depending on the operating points, analysis ofthe inlet Jow Veld conditions is Vrst conducted.
Ue operating point displacement from peak eXciency tonear stall leads to a gradual decrease of the mean meridionalvelocity. Since the rotation speed is constant, the incidenceangle on the impeller main blades rises. In the study case,the mass Jow reduction induces an increase of the incidenceangle of approximately 4∘ fromOP1 to OP2 and 4∘ again fromOP2 to NS (Figure 4).Because of the high incidence at low mass Jow rate
and of the pressure rise occurring in the impeller (adversepressure gradient), the boundary layer thickens and separateson the impeller main blade suction side. Figure 5(a) shows
NS
OP2
OP1
100
80
60
40
20
2000
5 10 15
Span
(%
)
�� = � − �blade
Figure 4: Time-averaged axisymmetric proVle from hub to shroudof the incidence angle at the impeller inlet.
the reduced axial velocity proVle in the suction side boundarylayer, at 50% of the span near the leading edge for the threeoperating points. At high mass Jow rate (OP1), the incidenceangle does not exceed the critical value and no separation isobserved. By moving to OP2, the critical incidence angle isreached and a small separation occurs while at NS conditionit signiVcantly increases.For OP1, the boundary layer thickness represents 1%
of the pitchwise. By moving to OP2, the boundary layerthickness is twice larger while at NS it is four times larger.As a consequence of the boundary layer thickening at lowmass Jow rate, the secondary Jow eIects become strongerand are noticeable from the leading edge of the impeller blade.Figure 5(b) plots the reduced radial velocity proVle in thesuction side boundary layer, at 50% span near the leadingedge, for the three operating points. At design condition, theboundary layer is not enough developed (boundary layer istoo thin) to induce a radial migration.Uerefore, an increaseof radial velocity near the suction side of the impeller blade isnot observed. At lowmass Jow rates, due to the thickening ofthe boundary layer, the secondary Jow eIects can clearly beobserved by the signiVcant rise of the radial velocity near thesuction side of the impeller blade. Moving from OP2 to NSleads to intensiVcation of this mechanism and the increase ofthe radial velocity is larger.
Ue low momentum Juid near the main blade suctionside is then transported along the blade from hub to shroud(positive radial velocity). At the tip of the blade, it istransported and stretched by the leakage Jow of the mainblade in the middle of the channel (Figure 6). As a result, byobserving the time-averaged meridional velocity at sectionB (Figure 7), at low mass Jow rates, a velocity deVcit region(wake) can be noticed in the right channel close to the shroud.Uis region results from the combination of secondary andleakage Jows. By reducing the mass Jow along the speed linefromOP2 toNS, the wake region signiVcantly enlarges. In the
OP1
OP2NS
10
8
6
4
2
00
0.1 0.2 0.3 0.4 0.5−0.1
Pit
ch (
%)
Vx/U2
(a)
10
8
6
4
2
0
Pit
ch (
%)
OP1
OP2NS
0 0.05 0.1 0.15 0.2
Vr/U2
(b)
Figure 5: Time-averaged reduced axial velocity (a) and time-averaged reduced radial velocity (b), in the main blade suction side boundarylayer, at 50% span, 2mm downstream the leading edge.
Separationzone
Hub
PS SS
0.55
Vm/U
2
0
Figure 6: Time-averaged reduced meridional velocity contours forthe near stall operating point.
leH channel, the mass Jow reduction does not aIect the Jowstructure which is principally composed of the core Jow.
5.2. Unsteady Flow Analysis. To investigate the unsteady Jowpattern for the simulated operating points, a spectral analysisis performed from a local extraction, recorded at each timestep leading to an approximate sample frequency of 1Mhz.In normal operating conditions (stable conditions, constantrotation speed. . .), unsteady phenomena are mainly inducedby the blade passing eIects. Uerefore in the impeller, theJow is time periodic with a period of 2# = 20/Ω#4$while in the diIuser the period is 2$ = 20/Ω#4#. UisspeciVcity is oHen used to reduce the calculation domainto one single blade passage. AHerwards, the solution can beobtained with an unsteady calculation model using a spatial-temporal periodicity (chorochronic approach).
Figure 8 plots the frequency spectra of a static pressureprobe linked to the relative frame located at 90% span, at theimpeller inlet. It can be seen that the frequency content forOP1 andOP2 is limited to the blade passing frequency locatedat 5∗ = 21 (diIuser has 21 vanes). Since the compressoroperates in subsonic conditions, potential eIects from thevaned diIuser can propagate upstream and reach the impellerinlet.Uese operating points could have been simulated usinga spatial-temporal periodicity. However, at NS condition, thefrequency content is not only limited to the blade passingfrequency and a periodic unsteady phenomenon emerges at5∗ = 6.Uis occurrence shows clearly the need of meshingall the blade passages to the analyzed near stall operatingpoint.Ue following part focusses on a detail analysis of thisfrequency emergence occurring at NS.As discussed in the previous section, the impeller Jow
structure is composed of the main Jow and of the secondaryand leakage Jows, leading to high and low meridionalvelocity zones (see Figure 7).Ue interface between these twoJow structures is a region of signiVcant shear. By reducingthe mass Jow, the meridional velocity deVcit due to leakageand secondary Jows increases and at NS condition it is suchthat the velocity gradient is enough to create an interfaceinstability. Vortices are formed at the interface and aretransported with themain Jow downstream. Figure 9 depictsthe instantaneous meridional velocity and instantaneousstreamlines at 90% span, in the relative frame.Ue incomingJow region can be identiVed as the high velocity zone (blueregion) while secondary and leakage Jows are marked witha signiVcant low velocity zone (white region). At 6 = 9.12#,a vortex is seen near the splitter blade leading edge while theblack point represents the location of the vortex formation.Ue vortex is then transported by the main Jow and grows.At 6 = 102# the vortex is generated and two vorticescan be noticed. During one rotor rotation, six vortices are
OP1
MBSBMB
OP2
MBSBMB
NS
MBSBMB
ΩRΩRΩR
0.55
Vm/U
2
0
Figure 7: Time-averaged reduced meridional velocity contours at section B, for the three operating points.
0
50
100
150
200
250
300
350
5 10 15 20 25
Am
pli
tud
e
OP1
OP2NS
BPF
f∗
Figure 8: Frequency spectra of a pressure signal in the relativeframe, at 90% span, at the impeller inlet.
formed and shed, responsible of the fundamental frequency5∗ = 6 seen in the frequency spectra (Figure 8). All theblade channels create the same phenomenon, but the vorticeslocation varies slightly between the diIerent passages.
5.3. Similarities with Axial Compressors. In axial compres-sors, Marz et al. [22] have also observed vortices in the rotortip region, induced by the interaction between the reverseJow near the trailing edge, the tip clearance Jow, and theincoming Jow. Ue vortices move from the suction side tothe pressure side and are referenced as rotating instability.Due to the reverse Jow near the trailing edge, the vorticesdo not move downstream and travel circumferentially. Uecompressor operates in a stable mode even with this rotatinginstability. In the present case, as there is no reverse Jowclose to the shroud, the vortices are formed and convecteddownstream.According to Duc Vo et al. [23], there are two necessary
conditions for the spike disturbance formation in axialcompressor. Ue Vrst one is that the interface between theincoming Jow and the tip clearance Jow becomes parallelto the leading edge plane, permitting the tip clearance Jowto spill into the following blade passage. Ue second is theinitiation of reverseJow at the trailing edge.UeVrst criterion
has been investigated in our case by observing the interfaceposition. Figure 10 shows the time-averaged entropy contourmap at the tip of the blade.Ue interface position dependson the Jow momentum balance between the incoming Jowand the leakage Jow. Ue mass Jow reduction induces adecrease of the incoming Jow momentum and an increaseof the leakage Jow momentum due to the blade loadingincrease. As a consequence, when the mass Jow is reduced,the interface between the two Jow structures becomes moretangential. For OP1 and OP2, the interface line (red linein Figure 10) goes from the main blade leading edge to thesplitter blade leading edge. At NS condition, the interface lineis signiVcantly displaced but does not reach the leading edgeof the adjacent blade.
Uerefore, we hypothesize that if the mass Jow is furtherreduced, the interface between the incoming and leakageJows will become parallel to the leading edge plane, permit-ting the leakage Jow to spill into the following passage andleading to impeller rotating stall.
6. Diffuser Inlet Flow Structure Analysis
For the present compressor stage, the diIusion process isaccentuated through a vaned diIuser. As already mentioned,in the literature concerning conVgurations with vaned dif-fusers, there is evidence that surge is oHen triggered in thevaneless space or in the semivaneless space.Uis part focuseson the description of the Jow at this location.
6.1. Mass Flow Reduction E5ects. At the impeller exit, whenthe operating point is displaced to the surge region along thespeed line, the mean tangential velocity increases due to therise of work input while the mean radial velocity decreases.Uerefore, the vanes of the diIuser have to operate with ahigher incidence angle. In addition, all along the meridionalcurvature, secondary and leakage Jows continue to interactwith themainJow inducing a highly distorted pattern in boththe spanwise and the pitchwise directions.Ue present partinvestigates the impeller exit Jow conditions depending onthe three operating points.Since the work of Dean and Senoo [24], the impeller
exit Jow structure is described in the pitchwise directionby considering the jet-wake model.Ue wake zone containslow radial velocity and high absolute tangential velocity Jowsinducing high absolute Jow angle values. Figure 11(a) showsthe time-averaged pitchwise distribution of the Jow angle
Vortexformation
0.5
0
ΩR ΩR
NS, t = 9.1TR NS, t = 10TR
Vm/U
2
Figure 9: Instantaneous reduced meridional velocity contours and streamlines at 90% span in the inducer.
OP1 OP2 NS
ΩRΩRΩR
ent
Figure 10: Time-averaged entropy contours at the blade tip (98% span) in the inducer for the three operating points.
proVle at 90% span. Considering the three operating points,major diIerences occur in the right channel (from 50% to100% of the pitch).Ue increase of Jow angle values at OP2and NS is linked to the low meridional velocity zone extentat low mass Jow rate, noticed in the impeller inducer nearthe shroud (see Figure 7). Due to the impeller rotation, thispitchwise distortion induces temporal Juctuations of the Jowangle at the diIuser inlet, which play a role in the unsteadyJow structure described in the following.
Besides this pitchwise distortion, the study of Deniz et al.[25] leads to the conclusion that the diIuser performanceis mainly determined by the axisymmetric time-averagedinlet Jow angle. Figure 11(b) shows this quantity for thethree operating points. DiIuser vane angle (metal angle)is constant from hub to shroud. Due to shroud and hubcurvatures, the Jow is decelerated and the boundary layerthickness increases on the convex shroud surface althougha transfer of Jow toward the concave hub side induces aradial velocity increase. Uerefore, from hub to 85% spanand for the three operating points, the Jow angle naturallyrises while above 85% span it rudely increases until theshroud due again to secondary Jows and leakage JowseIects. Ue compressor stability may be aIected whenthe incidence angle becomes positive (7 − 7Blade > 0),leading to the possibility of boundary layer separation onthe diIuser vane suction side. As the mass Jow is re-duced, the part of the span in that situation signiVcantly
extends from 70–100% of the span to 40–100% of the span(see Figure 11(b)).In addition to the high incidence angle value near the
shroud, the pressure gradient in the semivaneless spaceincreases by reducing the mass Jow. Uerefore, given theseconditions, a boundary layer separation occurs on the dif-fuser vane suction side for OP2 and NS. Figure 12 illustratesthe separation zone by representing the time-averaged radialvelocity contour and the streamlines. Ue red zone showsnegative radial velocity (reverse Jow) while the blue zoneshows positive radial velocity. As the Jow is subsonic inthe vaneless space, the separation bubble yields to a Jowdeviation, to a rise of Jow angle, and Vnally to a negativeradial velocity zone. Ue mass Jow reduction from OP2to NS induces an enlargement and a displacement of theseparation bubble along the suction side toward the leadingedge, yielding to a more intense reverse radial Jow.
6.2. Near Stall Condition Analysis. Ue unsteady Jow struc-ture in the boundary layer separation shown previously hasbeen analyzed with the (2 vortex criterion [26].Ue velocitygradient tensor J is decomposed into its symmetric part S and
antisymmetric partΩ and the eigenvalues of J2+Ω2 are deter-mined. If the second eigenvalue (2 is negative in a region,it belongs to a vortex core. Uis criterion is applied in thevaned diIuser considering the three-dimensional unsteadydata. Figure 13 shows the instantaneous negative isosurface of
0
10
20
30
40
50
0 20 40 60 80 100
Pitch (%)
OP1
OP2
NS
−10
Δ�=�−�
bla
de
(a)
0 20 40 60 80 100
Span (%)
OP1
OP2
NS
0
10
20
30
40
50
−10
Δ�=�−�
bla
de
(b)
Figure 11: Time-averaged pitchwise distribution at 90% span (a) and axisymmetric proVle (b) of the incidence angle, 1mm aHer the impellerexit.
OP1 OP2 NS
0.5
0
Vr/U
2
−0.5
Figure 12: Time-averaged reduced radial velocity contours and streamlines, at 90% span and near the vane leading edge, for the threeoperating points.
Span
(%
)
100
50
0
Shro
ud
Flow
Suction sideHub
Figure 13: Instantaneous isosurface of the negative (2 vortex criterion.
the second eigenvalue coloured by the normalized span.Ueseparation due the high incidence angle allows the vorticityfrom the leading edge to be shed to form a vortex-tube. Itspans from the diIuser vane suction side (60% span) to theshroud.Due to the large increase of incidence angle from 80%
span to the shroud, the upper end (near shroud) of the vortex-tube tends to move away from the diIuser vane suction side.Ue recent works of Pullan et al. [27] on axial conVguration
demonstrate that the process of spike formation is linked toa suction side boundary layer separation resulting from high
Span
(%
)
100
50
0
t = 0.047Ts t = 0.28Ts t = 0.476Ts
Figure 14: Instantaneous isosurface of the negative (2 vortex criterion representing the vortex formation.
Span
(%
)
100
50
0
Vortex leg
breakdown
t = 0.523Tst = 0.8Ts
t = 1Ts
Figure 15: Instantaneous isosurface of the negative (2 vortex criterion representing the vortex displacement.
incidence angle. A vortex is also formed which starts at thesuction surface and terminates at the shroud. It is observedthat near the shroud the vortex moves in the circumferentialdirection along the shroud increasing the Jow angle on theadjacent blade. Ue boundary layer on the adjacent bladeseparates and the structure can propagate according to theEmmons theory [5]. Ue onset of spike instability has alsobeen studied numerically by Everitt and Spakovszky [28]in an isolated vaned diIuser. Ue works show that Jowseparation at the diIuser vane leading edge associated toradial reverse Jow near the shroud allows the vorticity fromthe leading edge to be convected into the vaneless space.UediIuser inlet blockage rises leading to diIuser instability.Uisstudy shows that the high tangential Jow at the impeller exitis a key feature for spike onset.In the study conVguration, due to the blade passing eIects
associated to the high Jow angle Juctuations, the vortexcore behavior is highly unsteady and time periodic with theblade passing frequency (a blade passage is composed of twochannels).Uerefore during one channel passing period thevortex forms and expands (Figure 14). During the secondchannel passing period (Figure 15), at 6 = 0.05232$ the vortexcore is detached from the suction side, and the lower endseparates from the upper end. As the radial velocity is higherat midspan compared to near the shroud, the lower end of thevortex is convected at higher velocity.It is found that the vortex-tube does not move in the
circumferential direction but downstream along the suctionside. Uerefore, the scenario described for the spike onsetin the literature is not observed for the simulated operatingpoints. However, further mass Jow reduction may lead to amore tangential Jow (increase of Jow angle) near the shroudinducing a vortex displacement toward the circumferentialdirection and initiating the spike inception process in thevaned diIuser.
7. Conclusion
Unsteady numerical simulations have been performed in a2.5 pressure ratio centrifugal compressor stage to achievea comprehensive description of the Jow Veld from peakeXciency to near stall.Ue calculation domain extended to allthe blade passages has permitted to observe a new unsteadyJow pattern with a phenomenon decorrelated to the bladepassing frequency when the compressor operates near stall.Ue conclusions are summarized as follows.
(i) In the impeller inducer, reducing the mass Jow indu-ces a rise of the secondary Jow eIects leading to asigniVcant enlargement of the low momentum Juidregion accumulated near the shroud. At near stallcondition, the interface between the secondary andleakage Jows with the main Jow becomes unstableleading to a vortex formation.
(ii) At the blade tip and at near stall conditions, the inter-face line that demarcates the oncoming Jow from theleakage Jow is almost aligned with the leading edgeplane, suspecting that further mass Jow reductionwill drive the compressor into stall as observed inaxial conVgurations.
(iii) In the diIuser entry region, the decrease of mass Jowrate induces an increase of Jow angle leading to aseparation on the diIuser vane suction side near theshroud. At near stall condition, the vorticity from theseparation is shed and leads to a periodic formationof vortex-tube which travels along the suction side.
(iv) Further mass Jow reduction may change the vortextrajectory to a more tangential direction, leading toa propagation of the structure in the circumferentialdirection and inducing diIuser rotating stall.
(v) Given theses conditions, the prediction of the stallonset region and a priori scenario appear diXcult.However, recent investigations presume that the Jowbreakdown occurs in the impeller inducer due to thealignment of the interface line with the leading edge.
Nomenclature
Latin Letters
ent: Entropy (j/(kgK))5, IF, BPF: Frequency (Hz), impeller frequency (Hz),
and blade passing frequency (Hz)+: Mass Jow rate (kg/s)MB, SB: Main blade, splitter blade4: Number of bladesPS, SS: Pressure side, suction sidep: Pressure (Pa)T: Time period (s), temperature (K)t: Time (s)NS: Near stallOP: Operating pointU, V : Blade speed (m/s), absolute velocity (m/s).
Superscripts and Subscripts
0: Total variable1: Impeller inlet2: Impeller exit4: DiIuser exit∗: Reduced variable9: Blade+, :, 6: Meridional, radial, and tangentialout: Domain outletR, S: Rotor, statorRef: Reference condition
5: Time-averaged value of 5.
Greek Letters
7, ;: Absolute Jow angle (∘), relative Jow angle (∘)Ω: Rotational speed (rad/s).
Conflict of Interests
Ue authors declare that there is no conJict of interestsregarding the publication of this paper.
Acknowledgments
Ue authors would like to express their thanks to Liebherr-Aerospace Toulouse SAS for supporting the present researchprogram and to the CFD team of CERFACS for its helpand support in the achievement of numerical simulations.Ue authors are also grateful to GENCI-CINES for providingcomputational resources.
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