Influence of Blade Vibration onPart-Span Rotating Stall

Fanzhou Zhao1, John Dodds2 and Mehdi Vahdati1

1Mechanical Engineering Department, Imperial College London, UK2Rolls-Royce plc, Derby, UK

AbstractThis paper presents the interaction between blade vibration and

part-span rotating stall in a multi-stage high speed compressor. Un-steady aerodynamic and aeroelastic simulations were conducted us-ing URANS CFD. Steady state computations showed short lengthscale disturbances formed local to the tip of a front stage rotor. Us-ing a full annulus model, these disturbances were shown to coalesceinto flow structures rotating around the annulus at approximately76% of the shaft rotational speed. Natural evolution of the rotatingstall did not result in a coherent spatial pattern. Subsequent analy-ses carried out with prescribed rotor blade vibration showed a spa-tial ‘lock-in’ event where the circumferential order of the part-spanrotating stall shifted to match that induced by the vibration mode.Moreover, in contrast to its natural form in the absence of vibration,the fully developed rotating stall showed a coherent stall signal.

INTRODUCTIONThis paper presents the work on part-span rotating stall in a high-

speed compressor. Part-span rotating stall usually occurs at part-speed as the stability limit of one or more blade rows is reached [1].In this state the compressor is operating in stable rotating stall andthe flow structure is believed to follow the form described by Em-mons, Pearson and Grant [2]. This behaviour is typical of part-span‘progressive’ stall, whereby multiple stall cells are present local tothe hub or, more commonly, the tip region, and can be confined to alimited number of blade rows. The remainder of the span operatesnormally.

The majority of published research on rotating stall is based uponlow-speed compressor testing where the phenomena can be stud-ied in a controlled manner. Such testing on high-speed machinesis considerably more complex. Day and Freeman [3] presented asystematic comparison between behaviour at low and high-speeds,using a three stage compressor at the Whittle Laboratory and aRolls-Royce Viper engine, with an 8 stage 5:1 compressor. Thiscomparison demonstrated similarities between both machines andconfirmed that rotating stall always precedes surge even at high-speed conditions. It was also reported that low-speed operation ofthe engine resulted in multi-cell part-span stall local to the frontstages (referred to as ‘front-end stall’[3]). This was shown to arisedue to the matching effects for multi-stage compressor, which causethe front to become stalled at part-speed at working line conditionswhilst the compressor as a whole remains stable. For this reason,the presence of rotating stall in the front stages did not impair theoperation of the engine during starting. Although this type of ro-tating stall may not result in surge or massive loss of power, it cancause excessive vibration and noise. From an industrial perspec-tive, it is important to understand the factors that influence changesin stall characteristics as it may result in moving from a safe operat-ing regime to one that causes rotor blade failure. These effects are

normally assessed by engine strain gauge tests, which are used tomap out stall boundaries.

Fig.1 Example of an experimentally measured lock-in event. Con-tour: rotor strain gauge. [4]

Despite its benign effects on aerodynamic stability, part-span ro-tating stall (especially at front stages) is typically higher risk froman aeroelastic vibration point of view, as the phenomenon generallyoccurs at higher frequencies than full-span stall and has greater po-tential to interact with the resonant modes of the compressor blades[5]. When the frequency of rotating stall is close to the natural fre-quency of a blade vibration mode, the two frequencies can ‘lock-in’giving rise to high vibration levels, which may result in high cyclefatigue failures [6]. This type of event is generally categorised as amain subset of non-synchronous vibration (NSV), which can occurduring compressor operation driven by aerodynamic flow unsteadi-ness such as rotating stall or vortex shedding.

Figure 1 shows an experimentally measured lock-in event re-ported in [4]. Between 77-83% speed a multiple mode pattern of25-30 lobes1, driven by rotating stall near blade tip, can be identi-fied in the strain gauge spectrum. Above 83% speed, the stall activ-ity ‘jumps’ to become dominant at a higher frequency, interactingwith the second torsion vibration mode. In total 4 ‘streaks’ can beobserved to cross this mode, corresponding to a 35 cell patten fol-lowed by 34, 33 and 32 cells. A key point here is that below 83%speed the stall phenomenon occupies a wide frequency range and isincoherent in the sense that multiple modes appear to coexist. Athigher speeds, the stall phenomenon appears to become constrainedto a fixed frequency in the rotating frame aligned exactly with the

1Cell count can be calculated by observing the different frequencies seenon static (casing pressure transducers) and rotating (strain gauge) instrumen-tations.

International Journal of Gas Turbine, Propulsion and Power Systems April, Volume 12, Number 2

Presented at International Gas Turbine Congress 2019 Tokyo, November 17-22, Tokyo, Japan Review Completed on , September 17, 2020

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Copyright ©2021 Rolls-Royce.

torsional mode. In this strongly coupled condition the near-fixedfrequency of the blade vibration mode is thus ‘driving’ the aerody-namics such that the stall cell count is forced to ‘adjust’ naturally tomaintain this coupling as the shaft speed changes.

This type of interaction has been reported in recent experimentaland computational investigations [4, 6, 7]. With the increased ap-plication of highly loaded multi-stage compressors, the occurrenceof such events is expected to be frequent. As turbomachinery bladeaerofoils are thinned to improve performance and reduce weight,aeroelastic challenges become more crucial which highlights theimportance of accurate prediction of transient flow behaviour insuch conditions. Moreover, the use of titanium blade-integrated-disks, i.e. blisks, is becoming more common. Such structures havevery low mechanical damping in contrast to traditional bladed-diskassemblies and will be more prone to high amplitude vibrations insuch situations.

The objective of this paper is to computationally investigate theinteraction between part-span rotating stall and vibration of a frontstage rotor in a multi-stage high speed compressor. The paperdemonstrates the capability of CFD in modelling part-span rotat-ing stall events at off-design conditions and the coupling betweenstall and blade vibration through aeroelastic calculations. The oc-currence of a spatial ‘lock-in’ event will be presented, where thepresence of blade vibration modifies the circumferential cell countof part-span rotating stall in a manner similar to the experimentalcase shown in Figure 1.

COMPUTATION MODEL AND THE FLOW SOLVERThe research rig compressor was designed by Rolls-Royce and

is representative of a modern high speed machine. Experimental in-vestigations have been carried out on the test rig to study stall andsurge in a high speed compressor [8]. The compressor has eightstages with an inlet guide vane (IGV) upstream of the first rotor. TheIGV and the first two stator rows (Stators 1 and 2) are of the variablestagger type (VSVs[9]). Tip clearances and stator shroud clearancesare representative of a modern high speed compressor and the Ro-tor 1 (R1) relative inlet flow is supersonic at design conditions. Ameridian schematic view of the compressor is shown in Figure 2.A choked nozzle was used at the domain outlet which allows atmo-spheric conditions to be used at both inlet and exit. Constant speedcharacteristics were obtained by adjusting the throat area of the noz-zle. The stagger of the three VSVs (IGV, S1 and S2) were held atfixed positions throughout this investigation.

Fig.2 Meridian view of the compressor.

The grids used for the blading are semi-structured, with hexahe-dral elements around the aerofoil in the boundary layer region, andprismatic elements in the passage. The end-wall boundary layersare resolved by refining the grid radially towards the hub and cas-ing [10]. A typical passage mesh contains approximately 300,000grid points, 44 mesh layers on the blade, 6 layers in the tip gapand approximately 800 points in the circumferential direction. Theclearances between the rotor blades and the casing were set at alevel consistent with the experimental test. Fillets at the blade endsand leakage flows through the shroud cavities beneath the statorvanes were not included since the stall cells investigated in thiswork are located at R1 blade tip. Steady analyses with these fea-tures included showed their relative importance to be very limitedcompared to other effects such as VSV stagger angles. In the steadycomputations, the interface boundaries between stationary domains

and rotating domains are modelled as mixing planes. In total, thesingle passage computation domain consisted of approximately 5million nodes.

All the computations are performed using AU3D, which is a 3D,time-accurate, viscous, finite-volume compressible flow solver [10].The unsteady flow cases are computed as URANS, with the basicassumption that the frequencies of interest are sufficiently far awayfrom the frequencies of turbulent flow structures. In the currentwork, the source term of the standard Spalart-Allmaras is scaled,based on the local pressure gradient and the velocity helicity ofthe flow, to enhance the capability of CFD in conditions near tostall [11]. The parameters of the turbulence model are held con-stant in the present work. Furthermore, a generalised wall function[11] valid for non-zero wall pressure gradient is also used to im-prove the accuracy of boundary conditions at the wall. The resultingCFD code has been used over the past 20 years for flows at off de-sign conditions with a good degree of success [12–14]. Moreover,the methodology used in this work has been applied in part-spanrotating stall modelling of multi-stage high speed compressor andshowed a good degree of success compared with experimental mea-surements [8, 15].

INVESTIGATION STRATEGY AND POST-PROCESSINGTECHNIQUES

All computations were undertaken at 85% of compressor designspeed, which showed significant interesting activity in the experi-ment when the compressor was mis-matched [8]. Part-span rotatingstall was observed in the front stages which persists indefinitely asa stable phenomenon, as the downstream stages operate sufficientlystable to prevent stall/surge of the whole compressor. It was also ob-served that the frequency of R1 tip rotating stall is in close proxim-ity with that of a blade natural mode. Therefore, the main objectiveof this work is to investigate the development of part-span rotatingstall in the tip region of R1 and its interaction with the vibration ofR1 blades.

Fig.3 The unsteady computation domain.

The investigation was carried out in 4 steps:

1. In the first step, steady state operating conditions of the com-pressor were obtained based on single passage model bymeans of constant speed throttling. Validation of the steadystate model was achieved through comparison with data ac-quired from rig tests.

2. A single passage steady state solution, obtained in Step 1, wasexpanded to obtain a full-annulus geometry of R1 (Figure 3).Based on the expanded initial solution, unsteady computationswere carried out using mixing planes between blade rows. Thejustification for the choice of model is based on the assump-tion that the part-span rotating stall is limited to the nearfieldof R1, which has been shown in an earlier work carried out byDodds and Vahdati [15].

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3. Unsteady aerodynamic computations were performed withoutphysical vibration of R1 blades. This allows investigation ofthe natural formation and development of stall cells.

4. Unsteady aeroelastic computations were carried out by pre-scribing R1 blades with a fixed amplitude vibration in themode of interest. Using this partially coupled approach, in-fluence of blade vibration on the development of rotating stallcan be studied.

In order to gain some physical understanding of the transient be-haviour, for instance the onset and development of stall cells, thetemporal and spatial evolution of flow field was interrogated bymeans of ‘numerical probes’. In this investigation, transient datawas collected at 5%, 50% and 95% radial height upstream of R1.The collected data has a circumferential resolution of 1440 probesand a temporal resolution of 300 samples per shaft revolution. Theevolution of rotating stall can be examined, as illustrated schemati-cally in Figure 4a, by constructing contour plot of flow variables asa function of time (shaft revolution) and space (circumferential po-sition). Spatial discrete Fourier transform was subsequently carriedout on the acquired data to obtain instantaneous modal content inthe unsteady flow field, which led to the contour plot of circumfer-ential modal content as a function of time and mode order, as shownin Figure 4b. The construction of these plots enables one to exam-ine the transient behaviour at various circumferential positions andradial heights.

(a) (b)

Fig.4 Schematic example showing visualisation of post-processedresults for an evolving 3 cell rotating stall solution.

For the results presented in this paper, all the numerical probesare locked in positions stationary with respect to R1, i.e. recordingin rotor frame of reference. Consider a pattern of m stall cells prop-agating around the circumference at a speed Ωstall, which (typicalof rotating stall) is a fraction of rotor shaft speed Ωshaft but in thesame direction. It follows that stationary and rotating instrumen-tation will detect this spinning pattern as a waveform at differentfundamental frequencies given by Equations 1 and 2 respectively

nstat =mΩstall

Ωsha f t(1)

nrot = m(1− Ωstall

Ωsha f t) (2)

where n denotes the frequency of rotating stall with units in EngineOrder (EO)2.

A temporal discretisation level of approximately 200 time stepsper rotor blade vibration cycle was used throughout this investi-gation, which results in approximately 180 time steps for the fre-quency of rotating stall. Convergence studies were undertaken andconfirmed that the results were insensitive to further discretisationin time.

21EO is the frequency of shaft revolution.

STEADY STATETo gain some confidence in the model, single-passage steady

analyses with mixing planes were performed at several inlet massflows conditions and the results were compared with experimen-tal measurements for the same VSV configuration and compressorspeed.

0.6

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ratio [−

]

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S6I−S8I

(a) (b)

(c) (d)

Fig.5 Normalised steady state overall and block performance.

Figure 5a shows the overall performance of the com-pressor in terms of total pressure ratio as a functionof corrected inlet mass flow, referred to as ‘MRTP-IN’((min

√T0/P0)/(mre f

√T0re f /P0re f )), calculated from the in-

let of IGV to the exit of Stator 8. A comparison with theexperimental data is also shown in this figure. All the values inthese plots were normalised by the experimental measurement ata chosen reference condition. The model shows an approximately1% over-prediction in mass flow, which are attributed to theabsence of secondary geometry features in the calculations. Theoverall trend of the characteristic is in good agreement with theexperiment. An operating point with higher pressure ratio wasrecorded in the experimental data (at MRTP-IN=0.98), which wasnot achieved in the steady state computations. To investigate thecause of pre-mature numerical stall, characteristics are plotted fordifferent blocks of blade rows in the compressor. Figure 5b to 5dshows a comparison of compressor block performance betweenthe model and the experiment. In this figure characteristics areshown for 3 axially-divided blocks, namely the front stages IGVto R3, the middle stages S3 to R6 and the back stages S6 to R8. Itis noted that characteristics are calculated based on values at theinlet to stator rows, e.g. Stator 3 inlet (S3I) to Stator 6 inlet (S6I)for the middle block. The overall agreement with the experiment issatisfactory, with only slight deviation in the predicted mass flowin the front stages. The matching of the compressor is adequatelyrepresented by the model. As the compressor is throttled up,stall initiates in the middle stages as shown by the ‘roll-over’ ofits block characteristic. This behaviour is successfully capturedby the model. The operating point on the positive slope of thecharacteristic showed asymmetric unsteadiness in the experiment,which is not possible to be captured with the single passagesteady state CFD model. Full annulus unsteady simulation ofthe compressor confirmed the surge trigger to be stalling of S3[16]. An overall good agreement is nevertheless seen between themodel and the experiment. It is noted again that for the purposeof this investigation the compressor is intentionally mis-matched,by setting the stagger of the VSVs to extreme conditions, so as to

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provoke stall. The block performance shown in Figure 5 does notrepresent the design intent of this compressor.

R1

S1

S3R7

Fig.6 Mid-passage entropy function.

Fig.7 Q criterion in R1 domain.

Fig.8 Rotor 1 1T mode shape.

Further flow separations in the compressor can be seen in themid-passage entropy contours shown in Figure 6, where separationsare local to R1 tip, S1/R2 hub and the tip of back stage rotors. Thefindings show similar trend with the experimental measurements in[8] and the numerical calculations in [15] where short length scalerotating disturbances were observed at the tip of R1 and hub of S1.The steady state solution for R1 is shown in Figure 7, displaying anisosurface of the Q criterion parameter for R1. Vortex like structurescan be observed in the passage near blade tip, with flow ‘spillingforward’ of the leading edge. Using a full annulus model of R1,it will be shown that flow structures arisen from these disturbances

propagate relative to the rotors and can couple with tip-dominatedblade vibration modes (e.g the 1T mode for R1 shown Figure 8).

UNSTEADY WITHOUT BLADE VIBRATIONIn the first step, unsteady computations were performed without

blade vibration, so that the natural formation and development ofstall cells can be investigated.

Fig.9 Evolution of circumferential profile and modal content of ax-ial velocity at R1 inlet, 95% span. (Rotor frame of reference)

Figure 9 shows the evolution of solution at 95% radial height ofR1 inlet, in terms of the circumferential profile and modal contentof unsteady axial velocity. The plots are constructed from data ac-quired by numerical probes as illustrated in Figure 4. It should benoted that data presented here is in rotor frame of reference. In Fig-ure 9, and figures of the same type that follow, the unsteady axialvelocity (contour in the top plot) and its modal amplitude (contourin the bottom plot) are normalised by the circumferential mean axialvelocity in the steady solution. Variation in axial velocity indicatesthe presence of flow distortion or unsteadiness. These signals canthen be further identified based on the circumferential mode spec-tra. Circumferential disturbances such as potential and wakes ap-pear on a single mode order equaling blade counts, whereas stallcan manifest as signals spread across multiple mode orders for non-axisymmetric type, or as a single dominant mode for fully devel-oped axisymmetric rotating stall.

It can be seen from Figure 9a that travelling flow disturbancesemerge after approximately 4 revolutions due to flow separation atR1 tip. The axial velocity disturbances have an amplitude close to10% of the mean flow, and are seen to travel circumferentially rel-ative to R1 blades. The travelling path of these disturbances can beidentified by tracing the peak (or trough) of axial velocity contour.For the case studied, disturbances are seen to travel with a circum-ferential speed of approximately 26% of the the shaft speed, in thedirection opposite to rotor rotation, i.e. rotating 26% slower thanthe rotor. In the absolute frame of reference, the observed resultscorrespond to disturbances travelling at approximately 74% of theshaft speed in the same direction as R1.

The spatial structure of the rotating disturbances is revealed bythe circumferential modal spectra shown in Figure 9b. Starting fromrevolution 4, a group of broadband-like signals appear in the vicin-ity of circumferential mode orders m = 20 to 28 (labeled as ‘RS’

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Fig.10 Contour of normalised unsteady axial velocity at inlet to R1,rev 14.

0 %

0.5 %

1 %

1.5 %

2 %

2.5 %

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64

R1

RS

R1−RS

|∆u

x|/u

x0

Circumferential mode order [−]

Fig.11 Circumferential spectra of unsteady axial velocity at 95%radial height, rev 14.

which denotes rotating stall). This corresponds to the developmentof rotating stall identified in Figure 9a. The fully developed flowsolution at the inlet to R1 is shown in Figure 10, where stall cellscan be identified in the top 15% of the blade span with circumfer-ential length scale slightly larger than one blade passage. Fourierdecomposition of unsteady axial velocity at 95% blade span shows,as presented in Figure 11, a band of signals centred around a domi-nant mode of m = 23. It was found that the dominant mode m = 23corresponds to a frequency of approximately 6.05EO. The aliasedsignal between the rotating stall and R1 potential (labeled as ‘R1-RS’) is also observed spatially at lower span of R1 (shown in Fig-ure 10) and modally around m = 11 (shown in Figure 11)3.

The development of rotating stall near the tip results in unsteadyloading applied on the blades, which can potentially force or inter-act with blade vibration modes. For the case studied, the mode ofinterest is the first torsion (1T) mode of R1 (mode shape shown inFigure 8), due to the proximity of its natural frequency (5.7EO) tothe dominant stall frequency (6.05EO). Time history of unsteadyforcing on the Rotor 1 1T mode was recorded in the computationsand those results are examined next.

Figure 12 shows the time history and temporal spectra of modalforce for R1 1T mode. Modal force is calculated by integratingunsteady forces on blade surface and the mode shape of the 1Tmode. In this figure positive nodal diameter denotes forward trav-elling modes and negative nodal diameter denotes backward travel-ling modes. The highest amplitude nodal diameter modes, namely-9ND to -13ND, are displayed in Figure 12. Unsteady forcing isrecorded on several NDs due to the lack of coherent structure inthe rotating stall, among which -11ND shows the highest ampli-

3R1 has 34 blades.

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−9ND−10ND−11ND−12ND−13ND

0

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ed m

odal fo

rce [−

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EO [−]

−9ND−10ND−11ND−12ND−13ND

9

1011

11

11

12

12

13

Fig.12 (a) Time histories of blade modal force for 1T mode; (b)Temporal spectra of modal force for 1T mode.

tude. The forcing results are in agreement with the axial velocitymeasurements at R1 inlet (Figure 11), where 23-cell rotating stallaliases to -11ND unsteady loading on 34 rotor blades. Negativenodal diameter modes, i.e. backward travelling waves, are excitedsince the rotating stall spins slower than the rotor. Moreover, resultsshown in Figure 12 indicate that significant energy transfer can po-tentially occur due to the close proximity between the frequency ofrotating stall and the natural frequency of the 1T mode.

Table 1 Dominant modes of R1 tip rotating stall

ND [-] m [-] nrot [-] ΩstallΩsha f t

[-]-9 25 6.52EO 0.74EO

-10 24 6.24EO 0.74EO-11 23 6.05EO 0.74EO-12 22 5.86EO 0.73EO-13 21 5.58EO 0.73EO

Table 1 summarises the dominant modal signals detected in therotating stall in R1 tip region and the corresponding nodal diam-eters excited by these flow disturbances. In this table, the domi-nant frequency for each circumferential mode is displayed based onwhich the angular speed of stall cell is calculated. Results in thetable show that the disturbances as a whole travel circumferentiallyat a speed approximately 74% of R1 shaft speed. However due toits non-axisymmetric structure, the spectra of perturbation spreadsinto several consecutive circumferential modes which excites mul-tiple blade nodal diameters.

UNSTEADY WITH PRESCRIBED BLADE VIBRATIONIn the next step, unsteady computations were carried out by pre-

scribing R1 with a fixed amplitude vibration in the 1T mode. Theoverall system is partially coupled, based on which influence ofblade vibration on the unsteady flow field and development of ro-tating stall can be studied. For the work presented here, R1 bladesare excited in the 1T/-10ND mode with a fixed amplitude vibration.

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The vibration nodal diameter (-10ND) and frequency (5.7 EO) wereintentionally chosen to be different from the dominant mode of therotating stall (23-cell which forces -11ND in 6.24 EO as shown Fig-ures 11 and Figure 12), so that the impact of vibration on stall celldevelopment can be assessed. The amplitude of blade vibration iskept constant at a level at which the maximum peak-to-peak dis-placement at blade tip leading edge is approximately 0.33% of R1tip chord.

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Fig.13 Time history of modal displacement and modal force for R11T mode. (Dashed grey line indicates blade forcing level in a de-throttled condition without rotating stall.)

Figure 13 shows the time history of modal displacement andforce for R1 1T mode. Results for nodal diamters 9 to 13 are dis-played (no response recorded for other NDs). It is seen from themodal force plot that, unlike results obtained without blade vibra-tion, unsteady loading is only recorded in -10ND. The results indi-cate that, instead of a non-axisymmetric 23-cell dominant mode pat-tern, the rotating stall locks in (spatially) with blade vibration whichresults in a coherent 24-cell structure. This is further confirmed bythe plot of axial velocity modal content at 95% radial height of R1inlet shown in Figure 14, where a single mode m = 24 is observedduring the development of rotating stall. The influence of vibrationon rotating stall is clearly demonstrated in these figures, where asmall amplitude motion (max pk-pk displacement about 0.33% tipchord) can vary the circumferential structure of rotating stall.

It is also noted that the -10ND modal force shown in Figure 13band the m = 24 signal shown in Figure 14 contain contributionsfrom both the vibration and the rotating stall due to aliasing. Never-theless, it is seen from Figure 13b that the amplitude of blade -10NDforcing sees a significant increase (about 600%) due to the presenceand lock-in of rotating stall (the forcing level in the absence of ro-tating stall was obtained by opening Stator 1 which unloads Rotor1 and removes flow separation at the tip). It should be noted the in-crease in blade forcing occurs even though the frequency of rotatingstall (6.2 EO) remains different from that of the vibration (5.7 EO),indicating a strong non-linear interaction between stall and vibra-tion.

Figure 15 shows the circumferential spectra of unsteady axialvelocity and the comparison with the case without blade vibration.The plot clearly shows that -10ND blade vibration in the 1T mode

Fig.14 Evolution of circumferential profile and modal content ofaxial velocity at R1 inlet, 95% span.

Fig.15 Circumferential spectra of unsteady axial velocity.

results in a coherent axisymmetric signal at m = 24 (stall cells). Thefully developed solution at R1 inlet is shown in Figure 16 in termsof unsteady axial velocity contour, where 24-cells can be identifiedin the tip region and a m = 10 (stall/rotor interaction) pattern is seenat lower span.

Fig.16 Contour of unsteady axial velocity contour at inlet to R1.

Table 2 Dominant mode of rotating stall, with and without bladevibration

fvib. [-] ND [-] m [-] nrot [-] ΩstallΩsha f t

[-]fixed -11 23 6.05EO 0.74EO

5.7EO -10 24 6.20EO 0.74EO

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Table 2 summarises the dominant modal signals observed in thecase without and with blade vibration. Results in the table showthat, irrespective of the presence of blade vibration, the flow distur-bances travel circumferentially at a constant speed approximately74% of R1 shaft speed, however, the number of stall cells change tomatch the (aliased) nodal diameter of the vibration. Similar studiesat vibration frequencies and nodal diameter modes away from thiscondition did not show lock-in events. Those cases are not reportedin this paper.

CONCLUSIONSIn this paper the part-span rotating stall and blade vibration of a

multi-stage high speed compressor was investigated numerically atoff-design conditions. Steady state computations showed that flowseparation and recirculation formed local to the tip of Rotor 1. Us-ing a full annulus model of R1 in unsteady calculations, these dis-turbances coalesce into flow structures rotating around the annulusat approximately 76% of the shaft rotational speed. Natural evolu-tion of the rotating stall did not result in a coherent spatial pattern.The dominant mode of response was shown to be m = 23 whichtravels at frequency 6.05EO. Subsequent analyses were carried outwith prescribed R1 vibration in the 1T/-10ND mode at the modalnatural frequency 5.7EO. Despite a small vibration amplitude (maxpk-pk displacement of 0.33% R1 tip chord), a spatial ‘lock-in’ eventwas observed where the circumferential order of the part-span ro-tating stall shifted to match that induced by the vibration mode, i.e.from m = 23 to 24. Moreover, in contrast to its natural form with-out vibration, the fully developed rotating stall showed a coherentaxisymmetric stall signal m = 24 travelling at frequency 6.20EO.

Overall, the URANS CFD model is shown to be capable of pre-dicting detailed flow features at conditions which can be challeng-ing for numerical simulations. The effect of blade vibration on thedevelopment of part-span rotating stall is clearly demonstrated inthis paper. It is also shown that the numerical model can offer moredetailed knowledge of the transient flow field where comprehensiveexperimental measurements are challenging.

Following the work presented in this paper, additional studies canbe performed to improve the knowledge of the coupling betweenblade vibration and rotating stall. Parameter studies can be carriedout to study the effect of vibration frequency, nodal diameter, rotortip clearance and operating point, with the aim to establish a rela-tionship between characteristics of vibration and stall. Moreover,fully coupled calculations can be performed by allowing free vibra-tion of R1 blades, based on which conditions for spatial as well asfrequency lock-in can be investigated.

ACKNOWLEDGMENTThe authors thank Rolls-Royce plc for both sponsoring this work

and allowing its publication. They gratefully acknowledge the con-tribution of their colleagues at Rolls-Royce plc.

References[1] I. J. Day, E. M. Greitzer, and N. A. Cumpsty, “Prediction of

Compressor Performance in Rotating Stall,” J. Eng. Power,vol. 100, no. 1, p. 1, 1978.

[2] H. W. Emmons, C. E. Pearson, and H. P. Grant, “Compressorsurge and stall propagation,” Trans. ASME, vol. 77, no. 4, pp.455–469, 1955.

[3] I. J. Day and C. Freeman, “The Unstable Behavior of Low andHigh-Speed Compressors,” J. Turbomach., vol. 116, no. 2, p.194, 1994.

[4] J. Dodds, “Rotating stall in variable geometry compressors,”Ph.D. dissertation, Imperial College London, 2016.

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