Research Article Analysis of the Unsteady Flow Field in a ...downloads.hindawi.com/journals/ijrm/2014/729629.pdf · compressor stage composed of a splittered impeller and a vaned

Research ArticleAnalysis of the Unsteady Flow Field in a CentrifugalCompressor from Peak Efficiency to Near Stall withFull-Annulus Simulations

Yannick Bousquet12 Xavier Carbonneau2 Guillaume Dufour2

Nicolas Binder2 and Isabelle Trebinjac3

1 Liebherr-Aerospace Toulouse SAS 408 avenue des Etats Unis 31016 Toulouse France2Departement drsquoAerodynamique Energetique et Propulsion ISAE Universite de Toulouse BP 54032 31055 Toulouse Cedex 4 France3 Laboratoire de Mecanique des Fluides et drsquoAcoustique Ecole Centrale de Lyon UCB Lyon I INSA 36 avenue Guy de Collongue69134 Ecully Cedex France

Correspondence should be addressed to Xavier Carbonneau xaviercarbonneauisaefr

Received 10 September 2013 Accepted 15 November 2013 Published 16 January 2014

Academic Editor Farid Bakir

Copyright copy 2014 Yannick Bousquet et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This study concerns a 25 pressure ratio centrifugal compressor stage consisting of a splittered unshrouded impeller and a vaneddiffuser The aim of this paper is to investigate the modifications of the flow structure when the operating point moves from peakefficiency to near stall The 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 diffuser entry region throughtime-averaged and unsteady flow field In the impeller inducer this study demonstrates that the mass flow reduction from peakefficiency to near stall leads to intensification of the secondary flow effects The low momentum fluid accumulated near the shroudinteracts with the main flow through a shear layer zone At near stall condition the interface between the two flow structuresbecomes unstable leading to vortices development In the diffuser entry region by reducing the mass flow the high incidenceangle from the impeller exit induces a separation on the diffuser 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 field are expect-ed to achieve high pressure ratios and high efficiencies atdesign operating point while minimizing the element sizeIn this context typical centrifugal compressor stages arecomposed of high speed impellers with vaned diffusers 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 configurations the limitation at low massflow rates comes from the rotating stall andor 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 diffuser Surge is a system dependantphenomenon associated to large amplitude oscillations ofthe pressure through the compressor system [1] The worksof Galindo et al [2] show that the surge intensity can bemodified 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 Therefore a margin (surge margin) is takento keep away the operating point from these phenomenaleading to an operating range reduction

Backswept impellers are widely used to increase thestability of the impeller and finally the stability of the stage[3] Efforts have also been dedicated to identify flow control

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2014 Article ID 729629 11 pageshttpdxdoiorg1011552014729629

2 International Journal of Rotating Machinery

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 of flowmechanisms occurring before the stallinception

Stall phenomenon in compression systems has beenstudied for almost sixty years The experimental works ofEmmons et al [5] and Mizuky and Oosawa [6] in a lowpressure ratio centrifugal impeller with a vaneless diffusershow that rotating stall occurs in the inducer and leads tosurge In a high pressure ratio centrifugal compressor withvaned diffuser Wernet et al [7] and Trebinjac et al [8]observed separation of the boundary layer on the diffuservane before the surge inception

Before the onset of these developed instabilities twofamilies of precursors have been observed firstly in axialconfiguration [9] and then in centrifugal configuration [10]The first 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 (gt5) transonic compressors using vaned dif-fuser or low pressure ratio (lt2) compressors using vanelessdiffuser For the first category there is evidence that thediffuser entry region is often responsible for the surge onsetwhile for the second impeller inducer seems to be the weakestzone in terms of flow instability The present study concernsa subsonic and moderate pressure ratio (25) centrifugalcompressor stage composed of a splittered impeller and avaned diffuser

In addition work on the topic comes generally fromexperimental investigations where the flow description istherefore partial at best In this study investigations areperformed through a computational fluid analysis Near thesurge line unsteady phenomena uncorrelated to the bladepassing frequency may appear Therefore 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 diffuser entry zone effortsare concentrated at these locations

The two main objectives of this paper are to (i) numeri-cally analyze the modifications of the flow structure inducedby themass flow reduction from peak efficiency to a near stallcondition and (ii) investigate in depth through unsteady flowdata sets the near stall operating point in order to proposedifferent scenarios which may lead to flow breakdown In thefirst part of the paper the study case and the numerical pro-cedure are presentedThen the numerical model is validatedthanks to experimental measurements Afterwards detailedanalysis of the unsteady flow features in the impeller inducerand finally in the diffuser entry zone is given depending onthe operating pointThe last two parts constitute the scope ofthe paper

2 Test Case Presentation

The centrifugal compressor stage considered for this studyhas been designed by Liebherr-Aerospace Toulouse SAS andis integrated in an air-conditioning system The stage iscomposed of a backswept splittered unshrouded impeller avaned diffuser and a voluteThe design specification is basedon a stage static-to-total pressure ratio of 25 with a designrotation speed of 38000 rpm The impeller contains 8 mainblades and 8 splitter blades with a backsweep angle of 32∘The impeller exit radius is about 100mm The vaned diffuserconsists of 21 wedge blades (see Figure 1)

3 Numerical Procedure

31 Flow Solver Computations are performed using the 119890119897119904119860solver developed by ONERA and CERFACS [11] It solvesthe three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations based on a cell-centeredfinite volume approach on multiblock structured gridsThe turbulent viscosity is computed with the one-equationSpalart-Allmaras model [12] The convective fluxes are com-puted with the centered second-order scheme with artificialdissipation of Jameson and diffusive fluxes with a second-order centered schemeThe 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] This time-marching scheme is coupled witha second-order dual time stepping method proposed byJameson [14]The 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) This discretization value permits a correctdescription of the impeller-diffuser 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 reachedThis condition is satisfied in less than 10 subiterations Toreach the periodic state at least 12 impeller rotations areneeded equivalent to approximately 20000 physical timesteps They are performed using 512 computing cores andrequire 200000 CPU hours for a single operating point

32 Boundary Conditions The computational domain con-tains the centrifugal impeller with the inlet bulb the vanelessspace and the vaned diffuser and ends with a 90∘ turningpipe used as a computational buffer zone to damp possiblereflections from the exit boundary condition (Figure 2)The computational domain extends 15 impeller inlet tipradius upstream and downstream of the blade rows As themeshing of the complete annulus requires significant CPUcost the volute is not taken into consideration Consideringthe inlet boundary conditions the total pressure the totaltemperature and the flow angles (axial flow) are prescribedWhen the operating point moves toward the surge line theslope of the stage pressure ratio characteristic may reachzero or even positive values Therefore a static pressureexit condition is not adapted because two solutions may be

International Journal of Rotating Machinery 3

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 (different mass flow rates) for a same outlet pressurewhile a fixed mass flow condition may lead to numericalproblemTherefore in the present study the outlet ismodeledusing a throttle condition coupled with a simplified radialequilibrium law The outlet static pressure 119901out is set by thefollowing relation

119901out (119899 + 1) = 1198751198940 + 120582( (119899)

119898ref)

2

(1)

where 1198751198940is the inlet total pressure (119899) is the mass flow rate

at iteration 119899 through the exit section and 120582 is the throttleparameter The simulated operating point can move fromchoked point to surge line by simply increasing the value ofthe throttle parameter The rotor-stator interface is treatedwith a sliding mesh method In elsA the communicationthrough the sliding surface is performed using a distributionof fluxes This 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

33 Mesh Parameters The structured mesh grid was gener-ated with Autogrid V5 using classical H O and C topologiesIn order to obtain mesh independent results the parametersto generate the mesh result from a previous study [18]performed in the same configurationThe size of the first cellis set to 3 120583m corresponding to a normalized wall distance 119910+well below 3 at the walls The impeller main blade passagegrid and splitter blade passage grid consist of 89 points inthe spanwise direction including 29 points in the gap region92 points in the pitchwise direction and 161 points in thestreamwise direction The diffuser blade passage contains 57points in the spanwise direction 119 points in the pitchwisedirection and 141 points in the streamwise direction Theimpeller blade passage and the diffuser blade passage includerespectively 26lowast106 and 17lowast106 cell gridThe single passageis repeated to obtain the full annulus and the calculationdomain reaches a total of approximately 60 million points

34 Data Extraction Unsteady computations are performedfor three operating points OP1 (peak efficiency) OP2 andNS(near stall) As will be illustrated later unsteady fluctuationsfor the OP1 and OP2 are only generated by impeller-diffuserinteractions In other terms for these two operating pointsthe flow is time periodic in the frame of reference of each rowAfter reaching the unsteady periodic state a full rotation ofthe rotor is performed to extract data (unsteady and time-averaged) The time-averaging period is equal to one rotorrotation

For the NS operating point unsteady effects are notonly limited to rotor-stator interactions and the naturalperiodicity of the flow is no longer valuable Therefore afterreaching the stable state the simulation has been extendedduring six rotor rotations to validate the stability of theoperating point and to extract data The time-averagingperiod is therefore equal to 6 rotor rotations

Because of the domain size the data extraction of thecomplete flow field is hardly affordable with a correct tem-poral resolution Therefore data extraction is segregatedinto local information recorded at each time step two-dimensional planes extracted every 10 time steps and thecomplete three-dimensional field saved three times perimpeller rotation

4 Numerical Model Validation

Figure 3 depicts the total-to-static pressure ratio defined as120587 = 119901

411990101

as a function of the corrected mass flow fromnumerical simulations results and measurements for thedesign speed line The corrected mass flow is defined as

cor =radic11987901119879ref

11990101119901ref (2)

The experimental value of 1199014is the mean value of three static

pressure probes located on the hub surface at diffuser exitradius (plane 4 see Figure 2)The static pressure fromnumer-ical results is extracted at the same location All the computedoperating points show good agreement with experimentaldataThemain objective of the measurements was to validate


27

26

25

24

23

22

21

211 12 13 14 15 16 17 18 19

Pres

sure

ratio

U-RANSExperimental

NSOP2

OP1

Corrected mass flow (kgs)

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 shroudThe unsteady numerical resultsat this specific location are now presented

51 Secondary Flow Effects The centrifugal impeller flowstructure has been studied continually since the 1970s Thework of Eckardt [19 20] shows that the main flow isaffected by secondary flows responsible of the jet-wakestructure classically observed in centrifugal impellers Theyare produced by reorientation of transverse vorticity (in theboundary layers) into longitudinal vorticity under the effectsof curvature and rotation [21]Themeridional curvature parteffect drives the lowmomentumfluid in the boundary layer ofthe blades (radial migration from hub to shroud) while therotation effects act mainly on the fluid particles in the huband shroud boundary layer (migration from PS to SS) Thesecondary flow effects 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 impellerflow structure depending on the operating points analysis ofthe inlet flow field conditions is first conducted

The operating point displacement from peak efficiency 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 casethe mass flow 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 flow rateand 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

NSOP2OP1

100

80

60

40

20

2000

5 10 15

Span

()

998779120573 = 120573 minus 120573blade

Figure 4 Time-averaged axisymmetric profile from hub to shroudof the incidence angle at the impeller inlet

the reduced axial velocity profile in the suction side boundarylayer at 50 of the span near the leading edge for the threeoperating points At high mass flow 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 significantly increases

For OP1 the boundary layer thickness represents 1of the pitchwise By moving to OP2 the boundary layerthickness is twice larger while at NS it is four times largerAs a consequence of the boundary layer thickening at lowmass flow rate the secondary flow effects become strongerand are noticeable from the leading edge of the impeller bladeFigure 5(b) plots the reduced radial velocity profile 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 Therefore an increaseof radial velocity near the suction side of the impeller blade isnot observed At lowmass flow rates due to the thickening ofthe boundary layer the secondary flow effects can clearly beobserved by the significant rise of the radial velocity near thesuction side of the impeller blade Moving from OP2 to NSleads to intensification of this mechanism and the increase ofthe radial velocity is larger

The low momentum fluid 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 flow 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 flow rates a velocity deficit region(wake) can be noticed in the right channel close to the shroudThis region results from the combination of secondary andleakage flows By reducing the mass flow along the speed linefromOP2 toNS the wake region significantly enlarges In the


OP1OP2

NS

10

8

6

4

2

00

01 02 03 04 05minus01

Pitc

h (

)

VxU2

(a)

10

8

6

4

2

0

Pitc

h (

)

OP1OP2

NS

0 005 01 015 02

VrU2

(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

055

VmU

2

0

Figure 6 Time-averaged reduced meridional velocity contours forthe near stall operating point

left channel the mass flow reduction does not affect the flowstructure which is principally composed of the core flow

52 Unsteady Flow Analysis To investigate the unsteady flowpattern for the simulated operating points a spectral analysisis performed from a local extraction recorded at each timestep leading to an approximate sample frequency of 1MhzIn normal operating conditions (stable conditions constantrotation speed ) unsteady phenomena are mainly inducedby the blade passing effects Therefore in the impeller theflow is time periodic with a period of 119879

119877= 2120587Ω

119877119873119878

while in the diffuser the period is 119879119878= 2120587Ω

119877119873119877 This

specificity is often used to reduce the calculation domainto one single blade passage Afterwards 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 119891lowast = 21 (diffuser has 21 vanes) Since the compressoroperates in subsonic conditions potential effects from thevaned diffuser can propagate upstream and reach the impellerinletThese 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 at119891lowast

= 6 This occurrence shows clearly the need of meshingall the blade passages to the analyzed near stall operatingpoint The following part focusses on a detail analysis of thisfrequency emergence occurring at NS

As discussed in the previous section the impeller flowstructure is composed of the main flow and of the secondaryand leakage flows leading to high and low meridionalvelocity zones (see Figure 7)The interface between these twoflow structures is a region of significant shear By reducingthe mass flow the meridional velocity deficit due to leakageand secondary flows 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 flow downstream Figure 9 depictsthe instantaneous meridional velocity and instantaneousstreamlines at 90 span in the relative frame The incomingflow region can be identified as the high velocity zone (blueregion) while secondary and leakage flows are marked witha significant low velocity zone (white region) At 119905 = 91119879

119877

a vortex is seen near the splitter blade leading edge while theblack point represents the location of the vortex formationThe vortex is then transported by the main flow and growsAt 119905 = 10119879

119877the vortex is generated and two vortices

can be noticed During one rotor rotation six vortices are


OP1

MBSBMB

OP2

MBSBMB

NS

MBSBMB

ΩRΩRΩR

055

VmU

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

plitu

de

OP1OP2

NS

BPF

flowast

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 frequency119891lowast

= 6 seen in the frequency spectra (Figure 8) All theblade channels create the same phenomenon but the vorticeslocation varies slightly between the different passages

53 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 reverseflow near the trailing edge the tip clearance flow and theincoming flow The vortices move from the suction side tothe pressure side and are referenced as rotating instabilityDue to the reverse flow near the trailing edge the vorticesdo not move downstream and travel circumferentially Thecompressor operates in a stable mode even with this rotatinginstability In the present case as there is no reverse flowclose to the shroud the vortices are formed and convecteddownstream

According to Duc Vo et al [23] there are two necessaryconditions for the spike disturbance formation in axialcompressor The first one is that the interface between theincoming flow and the tip clearance flow becomes parallelto the leading edge plane permitting the tip clearance flowto spill into the following blade passage The second is theinitiation of reverse flow at the trailing edgeThefirst 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 The interface position dependson the flow momentum balance between the incoming flowand the leakage flow The mass flow reduction induces adecrease of the incoming flow momentum and an increaseof the leakage flow momentum due to the blade loadingincrease As a consequence when the mass flow is reducedthe interface between the two flow 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 significantly displaced but does not reach the leading edgeof the adjacent blade

Therefore we hypothesize that if the mass flow is furtherreduced the interface between the incoming and leakageflows will become parallel to the leading edge plane permit-ting the leakage flow to spill into the following passage andleading to impeller rotating stall

6 Diffuser Inlet Flow Structure Analysis

For the present compressor stage the diffusion process isaccentuated through a vaned diffuser As already mentionedin the literature concerning configurations with vaned dif-fusers there is evidence that surge is often triggered in thevaneless space or in the semivaneless space This part focuseson the description of the flow at this location

61 Mass Flow Reduction Effects 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 decreasesTherefore the vanes of the diffuser have to operate with ahigher incidence angle In addition all along the meridionalcurvature secondary and leakage flows continue to interactwith themain flow inducing a highly distorted pattern in boththe spanwise and the pitchwise directions The present partinvestigates the impeller exit flow conditions depending onthe three operating points

Since the work of Dean and Senoo [24] the impellerexit flow structure is described in the pitchwise directionby considering the jet-wake model The wake zone containslow radial velocity and high absolute tangential velocity flowsinducing high absolute flow angle values Figure 11(a) showsthe time-averaged pitchwise distribution of the flow angle


Vortexformation

05

0

ΩR ΩR

NS t = 91TR NS t = 10TR

VmU

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

profile at 90 span Considering the three operating pointsmajor differences occur in the right channel (from 50 to100 of the pitch) The increase of flow angle values at OP2and NS is linked to the low meridional velocity zone extentat low mass flow rate noticed in the impeller inducer nearthe shroud (see Figure 7) Due to the impeller rotation thispitchwise distortion induces temporal fluctuations of the flowangle at the diffuser inlet which play a role in the unsteadyflow structure described in the following

Besides this pitchwise distortion the study of Deniz et al[25] leads to the conclusion that the diffuser performanceis mainly determined by the axisymmetric time-averagedinlet flow angle Figure 11(b) shows this quantity for thethree operating points Diffuser vane angle (metal angle)is constant from hub to shroud Due to shroud and hubcurvatures the flow is decelerated and the boundary layerthickness increases on the convex shroud surface althougha transfer of flow toward the concave hub side induces aradial velocity increase Therefore from hub to 85 spanand for the three operating points the flow angle naturallyrises while above 85 span it rudely increases until theshroud due again to secondary flows and leakage flowseffects The compressor stability may be affected whenthe incidence angle becomes positive (120572 minus 120572Blade gt 0)leading to the possibility of boundary layer separation onthe diffuser vane suction side As the mass flow is re-duced the part of the span in that situation significantly

extends from 70ndash100 of the span to 40ndash100 of the span(see Figure 11(b))

In addition to the high incidence angle value near theshroud the pressure gradient in the semivaneless spaceincreases by reducing the mass flow Therefore 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 The red zone showsnegative radial velocity (reverse flow) while the blue zoneshows positive radial velocity As the flow is subsonic inthe vaneless space the separation bubble yields to a flowdeviation to a rise of flow angle and finally to a negativeradial velocity zone The mass flow 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 flow

62 Near Stall Condition Analysis The unsteady flow struc-ture in the boundary layer separation shown previously hasbeen analyzed with the 120582

2vortex criterion [26] The velocity

gradient tensor J is decomposed into its symmetric part S andantisymmetric partΩ and the eigenvalues of J2+Ω2 are deter-mined If the second eigenvalue 120582

2is negative in a region

it belongs to a vortex core This criterion is applied in thevaned diffuser considering the three-dimensional unsteadydata Figure 13 shows the instantaneous negative isosurface of


0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)

Figure 11 Time-averaged pitchwise distribution at 90 span (a) and axisymmetric profile (b) of the incidence angle 1mm after the impellerexit

OP1 OP2 NS

05

0

VrU

2

minus05

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 1205822

vortex criterion

the second eigenvalue coloured by the normalized span Theseparation due the high incidence angle allows the vorticityfrom the leading edge to be shed to form a vortex-tube Itspans from the diffuser vane suction side (60 span) to theshroudDue to the large increase of incidence angle from80

span to the shroud the upper end (near shroud) of the vortex-tube tends to move away from the diffuser vane suction sideThe recent works of Pullan et al [27] on axial configurationdemonstrate that the process of spike formation is linked toa suction side boundary layer separation resulting from high


Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts


vortex criterion representing the vortex formation

Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts


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 flow angle on theadjacent blade The boundary layer on the adjacent bladeseparates and the structure can propagate according to theEmmons theory [5] The onset of spike instability has alsobeen studied numerically by Everitt and Spakovszky [28]in an isolated vaned diffuser The works show that flowseparation at the diffuser vane leading edge associated toradial reverse flow near the shroud allows the vorticity fromthe leading edge to be convected into the vaneless space Thediffuser inlet blockage rises leading to diffuser instabilityThisstudy shows that the high tangential flow at the impeller exitis a key feature for spike onset

In the study configuration due to the blade passing effectsassociated to the high flow angle fluctuations the vortexcore behavior is highly unsteady and time periodic with theblade passing frequency (a blade passage is composed of twochannels) Therefore during one channel passing period thevortex forms and expands (Figure 14) During the secondchannel passing period (Figure 15) at 119905 = 00523119879

119878the vortex

core 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 thecircumferential direction but downstream along the suctionside Therefore the scenario described for the spike onsetin the literature is not observed for the simulated operatingpoints However further mass flow reduction may lead to amore tangential flow (increase of flow angle) near the shroudinducing a vortex displacement toward the circumferentialdirection and initiating the spike inception process in thevaned diffuser

7 Conclusion

Unsteady numerical simulations have been performed in a25 pressure ratio centrifugal compressor stage to achievea comprehensive description of the flow field from peakefficiency to near stallThe calculation domain extended to allthe blade passages has permitted to observe a new unsteadyflow pattern with a phenomenon decorrelated to the bladepassing frequency when the compressor operates near stallThe conclusions are summarized as follows

(i) In the impeller inducer reducing the mass flow indu-ces a rise of the secondary flow effects leading to asignificant enlargement of the low momentum fluidregion accumulated near the shroud At near stallcondition the interface between the secondary andleakage flows with the main flow becomes unstableleading to a vortex formation

(ii) At the blade tip and at near stall conditions the inter-face line that demarcates the oncoming flow from theleakage flow is almost aligned with the leading edgeplane suspecting that further mass flow reductionwill drive the compressor into stall as observed inaxial configurations

(iii) In the diffuser entry region the decrease of mass flowrate induces an increase of flow angle leading to aseparation on the diffuser 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 flow reduction may change the vortextrajectory to a more tangential direction leading toa propagation of the structure in the circumferentialdirection and inducing diffuser rotating stall


(v) Given theses conditions the prediction of the stallonset region and a priori scenario appear difficultHowever recent investigations presume that the flowbreakdown occurs in the impeller inducer due to thealignment of the interface line with the leading edge

Nomenclature

Latin Letters

ent Entropy (j(kgK))119891 IF BPF Frequency (Hz) impeller frequency (Hz)

and blade passing frequency (Hz) Mass flow rate (kgs)MB SB Main blade splitter blade119873 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 (ms) absolute velocity (ms)

Superscripts and Subscripts

0 Total variable1 Impeller inlet2 Impeller exit4 Diffuser exitlowast Reduced variable119887 Blade119898 119903 119905 Meridional radial and tangentialout Domain outletR S Rotor statorRef Reference condition119891 Time-averaged value of 119891

Greek Letters

120572 120573 Absolute flow angle (∘) relative flow angle (∘)Ω Rotational speed (rads)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The 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 simulationsThe authors are also grateful to GENCI-CINES for providingcomputational resources

References

[1] E M Greitzer ldquoSurge and rotating stall in axial flow com-pressors part I theoretical compression system modelrdquo ASMEJournal of Engineering and Power vol 98 no 2 pp 190ndash1981976

[2] J Galindo J R Serrano H Climent and A Tiseira ldquoExperi-ments and modelling of surge in small centrifugal compressorfor automotive enginesrdquo Experimental Thermal and Fluid Sci-ence vol 32 no 3 pp 818ndash826 2008

[3] N Cumpsty Compressor Aerodynamics Pearson Education2004

[4] G J Skoch ldquoExperimental investigation of centrifugal compres-sor stabilization techniquesrdquo Journal of Turbomachinery vol125 no 4 pp 704ndash713 2003

[5] H W Emmons C E Pearson and H P Grant ldquoCompressorsurge and stall propagationrdquo Transaction of the ASME vol 77pp 455ndash469 1955

[6] S Mizuki and Y Oosawa ldquoUnsteady flow within centrifugalcompressor channels under rotating stall and surgerdquo Journal ofTurbomachinery vol 114 no 2 pp 312ndash320 1992

[7] M PWernetMM Bright andG J Skoch ldquoAn investigation ofsurge in a high-speed centrifugal compressor using digital PIVrdquoJournal of Turbomachinery vol 123 no 2 pp 418ndash428 2001

[8] I Trebinjac N Bulot X Ottavy andN Buffaz ldquoSurge inceptionin a transonic centrifugal compressor stagerdquo in Proceedings ofthe ASME Turbo Expo pp GT2011ndashG45116 June 2011

[9] T R Camp and I J Day ldquoA study of spike and modalstall phenomena in a low-speed axial compressorrdquo Journal ofTurbomachinery vol 120 no 3 pp 393ndash401 1998

[10] Z S Spakovszky and C H Roduner ldquoSpike and modal stallinception in an advanced turbocharger centrifugal compressorrdquoJournal of Turbomachinery vol 131 no 3 pp 1ndash9 2009

[11] L Cambier and M Gazaix ldquoelsA an efficient object-orientedsolution to CFD complexityrdquo in Proceedings of the 40thAerospace Science Meeting and Exhibit Reno Nev USA 2002

[12] P R Spalart and S R Allmaras ldquoOne-equation turbulencemodel for aerodynamic flowsrdquo Recherche Aerospatiale no 1 pp5ndash21 1994

[13] S Yoon and A Jameson ldquoAn LU-SSOR scheme for the Eulerand Navier-Stokes equationrdquo in Proceedings of the AIAA 25thAerospace ScienceMeeting Paper No 87-0600 Reno Nev USA2002

[14] A Jameson ldquoTime dependent calculations using multigridwith applications to unsteady flows airfoils and wingsrdquo inProceedings of the 10th AIAA Computational Fluid DynamicsConference Paper No 91-1596 Reno Nev USA 1991

[15] F Sicot GDufour andNGourdain ldquoA time-domain harmonicbalance method for rotorstator interactionsrdquo Journal of Turbo-machinery vol 134 no 1 Article ID 011001 13 pages 2012

[16] G Filola M C Le Pape and M Montagnac ldquoNumericalsimulations around wing control surfacesrdquo in Proceedings of theInternational Conference on Agricultural Statistics (ICAS rsquo04)2004

[17] N Gourdain M Montagnac F Wlassow and M GazaixldquoHigh-performance computing to simulate large-scale indus-trial flows in multistage compressorsrdquo International Journal ofHigh Performance Computing Applications vol 24 no 4 pp429ndash443 2010

[18] G Dufour X Carbonneau P Arbez J Cazalbou and P Chas-saing ldquoMesh-generation parameters influence on centrifugal


compressor simulation for design optimizationrdquo in Proceedingsof the ASME Heat TransferFluids Engineering Summer Confer-ence (HTFED rsquo04) Paper No 8004-56314 pp 609ndash617 July2004

[19] D Eckardt ldquoInstantaneous measurements in the jet wakedischarge flow of a centrifugal compressor impellerrdquo ASMEJournal of Engineering for Power vol 97 pp 337ndash346 1975

[20] D Eckardt ldquoDetailed flow investigations within a high-speedcentrifugal compressor impellerrdquo Journal of Fluids Engineeringvol 98 no 3 pp 390ndash402 1976

[21] W R Hawthorne ldquoSecondary vorticity in stratified com-pressible fluids in rotating systemsrdquo CUEDA-TurboTR 63University of Cambridge Cambridge UK 1974

[22] J Marz C Hah andW Neise ldquoAn experimental and numericalinvestigation into the mechanisms of rotating instabilityrdquo Jour-nal of Turbomachinery vol 124 no 3 pp 367ndash374 2002

[23] H Duc Vo C S Tan and E M Greitzer ldquoCriteria for spikeinitiated rotating stallrdquo Journal of Turbomachinery vol 130 no1 Article ID 011023 5 pages 2008

[24] R C Dean and Y Senoo ldquoRotating wakes in vaneless diffusersrdquoJournal of Basic Engineering vol 82 pp 573ndash574 1960

[25] S Deniz E M Greitzer and N A Cumpsty ldquoEffects ofinlet flow field conditions on the performance of centrifugalcompressor diffusers part 2 straight-channel diffuserrdquo Journalof Turbomachinery vol 122 no 1 pp 11ndash21 2000

[26] J J Jinhee Jeong and F Hussain ldquoOn the identification of avortexrdquo Journal of Fluid Mechanics vol 285 pp 69ndash94 1995

[27] G Pullan A M Young I J Day E M Greitzer and Z SSpakovszky ldquoOrigins and structure of spike-type rotating stallrdquoin Proceedings of the ASME Turbo Expo pp GT2012ndashG68707June 2012

[28] J N Everitt and Z S Spakovszky ldquoAn investigation of stallinception in centrifugal ompressor vaned diffusersrdquo in Proceed-ings of the ASME Turbo Expo pp GT2011ndashG46332 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



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 of flowmechanisms occurring before the stallinception

Stall phenomenon in compression systems has beenstudied for almost sixty years The experimental works ofEmmons et al [5] and Mizuky and Oosawa [6] in a lowpressure ratio centrifugal impeller with a vaneless diffusershow that rotating stall occurs in the inducer and leads tosurge In a high pressure ratio centrifugal compressor withvaned diffuser Wernet et al [7] and Trebinjac et al [8]observed separation of the boundary layer on the diffuservane before the surge inception

Before the onset of these developed instabilities twofamilies of precursors have been observed firstly in axialconfiguration [9] and then in centrifugal configuration [10]The first 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 (gt5) transonic compressors using vaned dif-fuser or low pressure ratio (lt2) compressors using vanelessdiffuser For the first category there is evidence that thediffuser entry region is often responsible for the surge onsetwhile for the second impeller inducer seems to be the weakestzone in terms of flow instability The present study concernsa subsonic and moderate pressure ratio (25) centrifugalcompressor stage composed of a splittered impeller and avaned diffuser

In addition work on the topic comes generally fromexperimental investigations where the flow description istherefore partial at best In this study investigations areperformed through a computational fluid analysis Near thesurge line unsteady phenomena uncorrelated to the bladepassing frequency may appear Therefore 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 diffuser entry zone effortsare concentrated at these locations

The two main objectives of this paper are to (i) numeri-cally analyze the modifications of the flow structure inducedby themass flow reduction from peak efficiency to a near stallcondition and (ii) investigate in depth through unsteady flowdata sets the near stall operating point in order to proposedifferent scenarios which may lead to flow breakdown In thefirst part of the paper the study case and the numerical pro-cedure are presentedThen the numerical model is validatedthanks to experimental measurements Afterwards detailedanalysis of the unsteady flow features in the impeller inducerand finally in the diffuser entry zone is given depending onthe operating pointThe last two parts constitute the scope ofthe paper

2 Test Case Presentation

The centrifugal compressor stage considered for this studyhas been designed by Liebherr-Aerospace Toulouse SAS andis integrated in an air-conditioning system The stage iscomposed of a backswept splittered unshrouded impeller avaned diffuser and a voluteThe design specification is basedon a stage static-to-total pressure ratio of 25 with a designrotation speed of 38000 rpm The impeller contains 8 mainblades and 8 splitter blades with a backsweep angle of 32∘The impeller exit radius is about 100mm The vaned diffuserconsists of 21 wedge blades (see Figure 1)

3 Numerical Procedure

31 Flow Solver Computations are performed using the 119890119897119904119860solver developed by ONERA and CERFACS [11] It solvesthe three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations based on a cell-centeredfinite volume approach on multiblock structured gridsThe turbulent viscosity is computed with the one-equationSpalart-Allmaras model [12] The convective fluxes are com-puted with the centered second-order scheme with artificialdissipation of Jameson and diffusive fluxes with a second-order centered schemeThe 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] This time-marching scheme is coupled witha second-order dual time stepping method proposed byJameson [14]The 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) This discretization value permits a correctdescription of the impeller-diffuser 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 reachedThis condition is satisfied in less than 10 subiterations Toreach the periodic state at least 12 impeller rotations areneeded equivalent to approximately 20000 physical timesteps They are performed using 512 computing cores andrequire 200000 CPU hours for a single operating point

32 Boundary Conditions The computational domain con-tains the centrifugal impeller with the inlet bulb the vanelessspace and the vaned diffuser and ends with a 90∘ turningpipe used as a computational buffer zone to damp possiblereflections from the exit boundary condition (Figure 2)The computational domain extends 15 impeller inlet tipradius upstream and downstream of the blade rows As themeshing of the complete annulus requires significant CPUcost the volute is not taken into consideration Consideringthe inlet boundary conditions the total pressure the totaltemperature and the flow angles (axial flow) are prescribedWhen the operating point moves toward the surge line theslope of the stage pressure ratio characteristic may reachzero or even positive values Therefore a static pressureexit condition is not adapted because two solutions may be



1

4

B



119901out (119899 + 1) = 1198751198940 + 120582( (119899)

119898ref)

2

(1)









411990101



11990101119901ref (2)




27

26

25

24

23

22

21

211 12 13 14 15 16 17 18 19

Pres

sure

ratio

U-RANSExperimental

NSOP2

OP1









NSOP2OP1

100

80

60

40

20

2000

5 10 15

Span

()

998779120573 = 120573 minus 120573blade






OP1OP2

NS

10

8

6

4

2

00

01 02 03 04 05minus01

Pitc

h (

)

VxU2

(a)

10

8

6

4

2

0

Pitc

h (

)

OP1OP2

NS

0 005 01 015 02

VrU2

(b)


Separationzone

Hub

PS SS

055

VmU

2

0




119877= 2120587Ω

119877119873119878


119877119873119877 This





119877





OP1

MBSBMB

OP2

MBSBMB

NS

MBSBMB

ΩRΩRΩR

055

VmU

2

0


0

50

100

150

200

250

300

350

5 10 15 20 25

Am

plitu

de

OP1OP2

NS

BPF

flowast













Vortexformation

05

0

ΩR ΩR


VmU

2


OP1 OP2 NS

ΩRΩRΩR

ent












0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)


OP1 OP2 NS

05

0

VrU

2

minus05


Span

()

100

50

0

Shro

ud

Flow

Suction sideHub


vortex criterion




Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1

4

B



119901out (119899 + 1) = 1198751198940 + 120582( (119899)

119898ref)

2

(1)









411990101



11990101119901ref (2)




27

26

25

24

23

22

21

211 12 13 14 15 16 17 18 19

Pres

sure

ratio

U-RANSExperimental

NSOP2

OP1









NSOP2OP1

100

80

60

40

20

2000

5 10 15

Span

()

998779120573 = 120573 minus 120573blade






OP1OP2

NS

10

8

6

4

2

00

01 02 03 04 05minus01

Pitc

h (

)

VxU2

(a)

10

8

6

4

2

0

Pitc

h (

)

OP1OP2

NS

0 005 01 015 02

VrU2

(b)


Separationzone

Hub

PS SS

055

VmU

2

0




119877= 2120587Ω

119877119873119878


119877119873119877 This





119877





OP1

MBSBMB

OP2

MBSBMB

NS

MBSBMB

ΩRΩRΩR

055

VmU

2

0


0

50

100

150

200

250

300

350

5 10 15 20 25

Am

plitu

de

OP1OP2

NS

BPF

flowast













Vortexformation

05

0

ΩR ΩR


VmU

2


OP1 OP2 NS

ΩRΩRΩR

ent












0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)


OP1 OP2 NS

05

0

VrU

2

minus05


Span

()

100

50

0

Shro

ud

Flow

Suction sideHub


vortex criterion




Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










27

26

25

24

23

22

21

211 12 13 14 15 16 17 18 19

Pres

sure

ratio

U-RANSExperimental

NSOP2

OP1









NSOP2OP1

100

80

60

40

20

2000

5 10 15

Span

()

998779120573 = 120573 minus 120573blade






OP1OP2

NS

10

8

6

4

2

00

01 02 03 04 05minus01

Pitc

h (

)

VxU2

(a)

10

8

6

4

2

0

Pitc

h (

)

OP1OP2

NS

0 005 01 015 02

VrU2

(b)


Separationzone

Hub

PS SS

055

VmU

2

0




119877= 2120587Ω

119877119873119878


119877119873119877 This





119877





OP1

MBSBMB

OP2

MBSBMB

NS

MBSBMB

ΩRΩRΩR

055

VmU

2

0


0

50

100

150

200

250

300

350

5 10 15 20 25

Am

plitu

de

OP1OP2

NS

BPF

flowast













Vortexformation

05

0

ΩR ΩR


VmU

2


OP1 OP2 NS

ΩRΩRΩR

ent












0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)


OP1 OP2 NS

05

0

VrU

2

minus05


Span

()

100

50

0

Shro

ud

Flow

Suction sideHub


vortex criterion




Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










OP1OP2

NS

10

8

6

4

2

00

01 02 03 04 05minus01

Pitc

h (

)

VxU2

(a)

10

8

6

4

2

0

Pitc

h (

)

OP1OP2

NS

0 005 01 015 02

VrU2

(b)


Separationzone

Hub

PS SS

055

VmU

2

0




119877= 2120587Ω

119877119873119878


119877119873119877 This





119877





OP1

MBSBMB

OP2

MBSBMB

NS

MBSBMB

ΩRΩRΩR

055

VmU

2

0


0

50

100

150

200

250

300

350

5 10 15 20 25

Am

plitu

de

OP1OP2

NS

BPF

flowast













Vortexformation

05

0

ΩR ΩR


VmU

2


OP1 OP2 NS

ΩRΩRΩR

ent












0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)


OP1 OP2 NS

05

0

VrU

2

minus05


Span

()

100

50

0

Shro

ud

Flow

Suction sideHub


vortex criterion




Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










OP1

MBSBMB

OP2

MBSBMB

NS

MBSBMB

ΩRΩRΩR

055

VmU

2

0


0

50

100

150

200

250

300

350

5 10 15 20 25

Am

plitu

de

OP1OP2

NS

BPF

flowast













Vortexformation

05

0

ΩR ΩR


VmU

2


OP1 OP2 NS

ΩRΩRΩR

ent












0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)


OP1 OP2 NS

05

0

VrU

2

minus05


Span

()

100

50

0

Shro

ud

Flow

Suction sideHub


vortex criterion




Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Vortexformation

05

0

ΩR ΩR


VmU

2


OP1 OP2 NS

ΩRΩRΩR

ent












0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)


OP1 OP2 NS

05

0

VrU

2

minus05


Span

()

100

50

0

Shro

ud

Flow

Suction sideHub


vortex criterion




Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

10

20

30

40

50

0 20 40 60 80 100Pitch ()

OP1OP2

NS

minus10

Δ120572=120572minus120572

blad

e

(a)

0 20 40 60 80 100

Span ()

OP1OP2

NS

0

10

20

30

40

50

minus10

Δ120572=120572minus120572

blad

e

(b)


OP1 OP2 NS

05

0

VrU

2

minus05


Span

()

100

50

0

Shro

ud

Flow

Suction sideHub


vortex criterion




Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Span

()

100

50

0

t = 0047Ts t = 028Ts t = 0476Ts



Span

()

100

50

0

Vortex legbreakdown

t = 0523Tst = 08Ts

t = 1Ts





119878the vortex



7 Conclusion








Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Nomenclature

Latin Letters





Greek Letters




Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Analysis of the Unsteady Flow Field in a ...downloads.hindawi.com/journals/ijrm/2014/729629.pdf · compressor stage composed of a splittered impeller and a vaned