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Approximate Design Criterion for Spike Stalling Tendency inAxial Flow Compressors

Prabhav Sharma, Amit Kumar, Narayan Ananthkrishnan, Bhaskar Roy

Indian Institute of Technology Bombay, Mumbai 400076, INDIA

I. INTRODUCTION

The study of instability (rotating stall and surge) inception in

high-speed multistage axial flow compressors used in modern

aircraft gas turbine engines has been a matter of continuing in-

terest over the past few decades [1], [2]. Once the mechanisms

leading to stall inception are understood and models that capture

the instability onset process are developed, it becomes possible

to apply active control strategies to suppress stall onset and ex-

tend the stable range of compressor operation [3].

For a long while, it was generally accepted that stall onset in

axial compressors occurs nearabout the peak of the compressor

characteristic [4]. There was experimental evidence to suggest

that the stall onset mechanism was essentially two-dimensional

in nature and that the only precursors to rotating stall were long

lengthscale circumferential waves called modal waves [5], [6].

A two-dimensionalmodel for the growth and decay of the modal

waves in axial compressors had been developed by Moore and

Greitzer [7], [8], which had been successful in predicting on-

set of modal stall at the peak of the compressor characteris-

tic. Nevertheless, it was frequently observed that compressors

tended to stall to the right of the characteristic peak, on the

negatively-sloped part of the compressor characteristic, at sig-

nificantly larger values of the flow coefficient than otherwise ex-

pected [9]. This could be accounted for in practice by defining a

Surge Line at a certain distance to the right of the characteristicpeak and operating the compressor at a safe distance away from

the surge line as shown in Fig. 1.

In an attempt to understand why compressors stalled to the

right of the characteristic peak, McDougall [9] suggested that

tip clearance was likely to be an important factor in determin-

ing compressor stall inception. His experiments with small tip

clearances showed stall onset close to the peak of the charac-

teristic, but for the larger tip clearance cases stall onset was

observed well short of the peak, at an increased value of flow

coefficient, where the characteristic slope was clearly negative.

Shortly after, in a significant piece of work, Day [10] showed

that rotating stall onset in axial compressors could occur due to a

short lengthscale disturbance, called a spike, spanning only 14blade passages. Day [10], and Camp and Day [11], established

that spike-induced stall, or simply spike stall, was related to a

three-dimensional breakdown of the flow field associated with

high rotor incidences at the blade tip, and that spike stall onset

occurred to the right of the peak, on the negatively-sloped part

of the compressor characteristic when a certain Critical Rotor

Address for correspondence: Dr. N. Ananthkrishnan, Department ofAerospace Engineering, Indian Institute of Technology Bombay, Mumbai400076, India; E-mail: [email protected]. This work was funded by Pratt& Whitney, E ast Hartford, CT, USA; thanks are due to Dr. Somanath Nagendra,Dr. Gavin Hendricks, and Dr. Jayant Sabnis, Pratt and Whitney.

Fig. 1. Sketch showing definition of surge line and compressor operating pointson the compressor characteristic [6].

Incidence was reached (see Fig. 2). Of particular concern was

Fig. 2. Stall inception points on the compressor characteristic for the modal and

spike stall onset mechanisms [11].

the fact that a compressor typically stalls within 3 4 revolu-

tions after spike formation, which makes it nearly impossible tosense a stall precursor signal for use in an active control scheme.

As against this, the clearly identifiable modal waves that emerge

prior to stalling by the modal mechanism provide a reliable stall

inception indication in axial compressors where, with suitable

stall warning, the operating point can be reliably moved closer

to the surge line as shown in Fig. 1, or even to the left of the

surge line by use of active stabilization [12].

Attention has since been focussed on understanding the flow

mechanisms leading to spike formation and evolution in ax-

ial compressors with a view to obtaining a criterion for spike-

induced stall inception [13]. A flow model to explain spike


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propagation in a row of highly loaded blades was proposed by

Emmons et al. [14] way back in 1955 which correctly predicted

the propagation speed of the spike to be always lower than the

rotational speed of the blades. The formation of spikes and their

evolution into stall cells was clearly captured in experiments by

Camp and Day [11] which showed that the spike inception phe-

nomenon was three-dimensional in nature originating near the

tip section of the blade. Subsequently, there has been interest in

simulating the three-dimensional flow structures in the tip regionat onset of spike stall and in identifying critical events that cor-

relate well with the spike formation and evolution process [15],

[16]. From the designers perspective, however, it is important

to predict the likelihood of spike stall inception for a particu-

lar compressor, though the actual stall inception process would

necessarily depend on the compressor operating conditions. The

aim of the present work is to come up with an approximate de-

sign criterion that captures the spike stalling tendency of an axial

compressor. This is done by defining a new design parameter,

called the Sparameter, which is used to identify the critical ro-tor incidence shown in Fig. 2 that marks the point of spike stall

onset. If the critical rotor incidence is predicted to the right of

the compressor characteristic peak, then the compressor may beexpected to spike stall.

II . SPARAMETER

It has been recognized that the radial distribution of axial ve-

locity along the blade span is an important parameter that deter-

mines the mode of stall inception in axial compressors [17]. A

lower axial velocity at the casing could be associated with higher

incidence and turning, causing higher loading on the blades in

the tip region, which in turn could cause the critical rotor inci-

dence to occur at a larger flow coefficient than that at the peak,

making the compressor prone to spike stall. Spakovszky et al.

[17] confirmed that an altered axial velocity distribution that de-

creased the incidence at the tip, by blowing for instance, could

revert a spike-stalling compressor to show modal stall.

The Sparameter is the nondimensional slope of the axial ve-locity Ca with respect to the blade radius r, and is defined as

S=Ct1a C

h1a

(rt1 rh1)=

ct1a ch1a

t1 h1(1)

where ca = Ca/Um, = r/rm, = Um/rm is the compressorRPM, U is the blade speed, and m refers to the blade mid-station. The points t1 and h1 refer to representative tip and hubstations respectively, and are defined as shown in Fig. 3 which

shows a typical variation of ca with , and the annulus mass-

averaged linear fit to the curve. The points where the linear fitintersects the original curve are the representative hub and tip

stations, h1 and t1, and the Sparameter is in fact just the slopeof the linear fit. For typical compressor designs [18], [19], es-

pecially at the later rotor stages, the Sparameter is found to benegative, as shown in Fig. 3. As described by Horlock [20], the

Sparameter becomes less negative under off-design conditionsat lower flow coefficients and may even become positive. Thus,

a typical variation of the S parameter appears as the curve Sc

sketched in Fig. 4, where refers to the design flow coeffi-cient. The aim of the present exercise is to locate the point on

the Sc curve where the tip station t1 stalls this can be used as

ca

Point h 1

Point t 1

.

Fig. 3. Definition of the S parameter.

S

S

S

t

c

Fig. 4. Typical variation of the S parameter with flow coefficient.

an identifier for the critical rotor incidence and hence possible

spike stall onset. To this end, a locus of tip-stalled solutions (St

in Fig. 4) at each value of the flow coefficient is obtained as de-scribed below. The intersection of the Sc and St curves marksthe compressor operating point on the Sc curve where the tipstation t1 stalls, i.e., the spike stall inception point.

III. TIP-STALLED LOCUS

For a given value of flow coefficient , the point on the Sc

curve in Fig. 4 is the slope of the annulus mass-averaged linear

fit to the ca versus profile, as shown in Fig. 3. Now, keepingthe flow coefficient fixed, consider changing the slope of the

linear fit to such an extent that the tip station t1 just stalls in asense to be made precise below. For large flow coefficients, this

would require ca to be decreased at the tip and correspondinglyincreased at the hub, so that the new slope is more negative,i.e., St is more negative than Sc. For the point on the Sc curvewhere the tip station t1 actually stalls, no change in slope of thelinear fit is required, and the Sc and St curves share the samevalue of slope. For still lower values of flow coefficient, the St

curve will show a larger slope, and hence the two curves may

be expected to intersect as depicted in Fig. 4. Note that all the

points on the St curve except the one where it intersects the Sc

curve are non-physical in the sense that they do not satisfy the

conservation equations for fluid flow through the annulus.

The key to obtaining a simple linear form for the graph ofSt


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with is to assume the following variation ofca with for theannulus mass-averaged linear fit in Fig. 3:

ca = k0 +k1

(2)

For high hub-to-tip ratio compressors, this function is very close

to being linear in the region of interest, i.e., 1. In fact, at themid-span ( = 1), ca = k0 + k1 and the slope S is simplydca/d = k1. Additionally, the flow coefficient can be evalu-ated to be

=

th

2

0ca(rm)2dt

h

2

0(rm)2d

= k0 + k1 (3)

This is exactly equal to ca at mid-span. From the followingexpression for the incidence angle at the t1 station:

it1 = tan1(t1

ct1a tan1)

1

t1 (4)

on successively using Eqs. (2) and (3), one can derive the fol-

lowing linear relation between the slope of the tip-stalled locusSt and the flow coefficient :

St = k1 =(t1)2/(t1 1)

tan(1t1 + i) + tan1

t1

t1 1 (5)

where i is the critical rotor incidence at the t1 station which isgiven by the following condition at the t1 station:

d(P02 P01)

di

t1

= 0 (6)

The total pressure rise can be written as an isentropic compo-

nent minus losses,

P02 P01 = (Pds=002

P01) Losses (7)

where,

Pds=002

P01 = P01

U2(tan 1 tan2)

CpT01(tan 1 + tan1)+ 1

1

1

1 =

1+ i; 2 =

1+ i

The blade profile losses and are available from cascade data asfunctions of incidence, and the other loss contributions need to

be modeled, so that Eq. (6) can be solved for the critical rotor

incidence i

at the tip station t1.

IV. VALIDATION

The procedure described above is validated against compres-

sor data given in Robinson [21]. The Sc curve is obtained fromnumerical simulation results given for two values of flow coeffi-

cient: = 0.4063 (close to modal stall onset) and = 0.4890,and is therefore approximated to be linear. The St curve followsfrom the expression derived in Eq. (5) on using the procedure

described above given data at the design point, = 0.5667. Thetwo curves are plotted in Fig. 5 where they are seen to intersect

at a flow coefficient just short of 0.3. The figure also plots the

Fig. 5. Validation of stall inception prediction against compressor data in Robin-

son [21].

pressure rise coefficient obtained by convertingSc to c, and St

to t, where c is the actual compressor characteristic, and t

is a non-physical tip-stalled characteristic. The diamonds in the

figure are experimental data points which are very closely traced

by the computed c curve. The peak of the c curve is seen tooccur near the stall data point at = 0.4063, while the criticalrotor tip incidence, given by the intersection of the Sc and St

curves, occurs to the left of the characteristic peak, confirming

that stall onset is indeed modal in this case.

V. SPIKE STALL PREDICTION FOR NASA STAGE 35 ROTOR

The NASA Stage 35 is a transonic rotor that is known to ex-hibit spike stall inception when subjected to inlet radial distor-

tion [17]. Onset of stall is reported to occur at a corrected mass

flow of about 15.5 kg/s where the characteristic slope is still neg-ative, i.e., to the right of the peak, as shown in Fig. 6. Design

data for the Stage 35 rotor is available from Refs. [17], [22]. Thepeak of the compressor characteristic is estimated to correspondto a flow coefficient of = 0.32.

The procedure described earlier is now applied to investigate

the spike stalling tendency of the Stage 35 rotor. The criticalrotor incidence is first calculated to be i = 14.2 deg. Thisinformation along with the available design data is then used to

calculate the St curve according to Eq. (5) as follows:

St = 2.875 6.808 (8)

The radial variation of axial velocity at two different flow coef-

ficients is provided in Spakovszky [17]. By finding the annulus


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14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 190.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

Corrected Mass Flow [kg/s]

Totalto

StaticPressureRatio

Fig. 6. NASA Stage 35 rotor showing stall onset on the negatively-sloped partof the characteristic [17].

mass-averaged linear fit for these two cases, one obtains two

points on the Sc curve, which may be used to draw a linear vari-ation ofSc with . The Sc and St curves so obtained are plotted

in Fig. 7 where they are seen to intersect at = 0.38, well to theright of the characteristic peak. Thus, the procedure described

Fig. 7. Computed Sc and St curves for NASA Stage 35 rotor.

in this work is successful in predicting the tendency of the Stage

35 rotor to spike stall.

VI . CONCLUSIONS

The present work has devised an approximate criterion that

can be used at an early stage of the compressor design process

to predict the likelihood of spike stall inception. The tendency

for spike stall onset is linked to an unfavorable design axial ve-

locity distribution along blade radius leading to onset of critical

rotor incidence at the blade tip section at flow coefficients largerthan that at the characteristic peak. A new parameter, called

the S parameter, is defined that captures the radial variation ofaxial velocity to a linear approximation and is used to identify

the critical rotor incidence point on the compressor operating

characteristic. The method proposed here has been successfully

applied to predict the spike stalling tendency in the NASA Stage

35 rotor.It must be mentioned that the occurrence of spike stall in prac-

tice will depend on the actual axial velocity variation with radius

which may be different from the design variation due to various

factors such as radial distortion. Other factors, such as tip clear-

ance, are known to aggravate the tendency of a compressor to

show spike stall, though this can be included in the present anal-

ysis by incorporating additional tip clearance losses in Eq. (7).

REFERENCES

[1] Hendricks, G.J., Sabnis, J.S., and Feulner, M.R., Analysis of Instabil-ity Inception in High-Speed Multistage Axial-Flow Compressors, ASME

Journal of Turbomachinery, Vol. 119, No. 4, 1997, pp. 714-722.[2] Hoying, D.A., Stall Inception in a Multistage High-Speed Axial Com-

pressor, AIAA Journal of Propulsion and Power, Vol. 11, No. 5, 1995,pp. 915-922.

[3] Paduano, J.D., Greitzer, E.M., and Epstein, A.H., Compression Sys-tem Stability and Active Control, Annual Reviews of Fluid Mechanics,Vol. 33, 2001, pp. 491-517.

[4] Stenning, A.H., Rotating Stall and Surge, ASME Journal of Fluids En-gineering, Vol. 102, No. 1, 1980, pp. 14-21.

[5] McDougall, N.M., Cumpsty, N.A., and Hynes, T.P., Stall Inception inAxial Compressors, ASME Journal of Turbomachinery, Vol. 112, No. 1,1990, pp. 116-125.

[6] Garnier, V.H., Epstein, A.H., and Greitzer, E.M., Rotating Waves as aStall Inception Indication in Axial Compressors, ASME Journal of Tur-bomachinery, Vol. 113, No. 2, 1991, pp. 290-302.

[7] Moore, F.K., and Greitzer, E.M., A Theory of Post-Stall Transients inAxial Compression Systems: Part I Development of Equations, ASME

Journal of Engineering for Gas Turbines and Power, Vol. 108, No. 1,1986, pp. 68-76.

[8] Greitzer, E.M., and Moore, F.K., A Theory of Post-Stall Transients inAxial Compression Systems: Part II Application, ASME Journal of En-gineering for Gas Turbines and Power, Vol. 108, No. 2, 1986, pp. 231-239.

[9] McDougall, N.M., A Comparison Between the Design Point and Near-Stall Performance of an Axial Compressor, ASME Journal of Turboma-chinery, Vol. 112, No. 1, 1990, pp. 109-115.

[10] Day, I.J., Stall Inception in Axial Flow Compressors, ASME Journal ofTurbomachinery, Vol. 115, No. 1, 1993, pp. 1-9.

[11] Camp, T.R., and Day, I.J., A Study of Spike and Modal Stall Phenomenain a Low-Speed Axial Compressor, ASME Journal of Turbomachinery,Vol. 120, No. 3, 1998, pp. 393-401.

[12] Haynes, J.M., Hendricks, G.J., and Epstein, A.H., Active Stabilizationof Rotating Stall in a Three-Stage Axial Compressor, ASME Journal ofTurbomachinery, Vol. 116, No. 2, 1994, pp. 226-239.

[13] Vo, H.D., Tan, C.S., and Greitzer, E.M., Criteria for Spike Initiated Ro-tating Stall, GT2005-68374, ASME Turbo Expo 2005, Reno-Tahoe, NV,June 6-9, 2005.

[14] Emmons, H.W., Pearson, C.E., and Grant, H.P., Compressor Surge and

Stall Propagation, Transactions of the ASME, Vol. 77, No. 4, 1955,pp. 455-467.

[15] Gong, Y., Tan, C.S., Gordon, K.A., and Greitzer, E .M., A ComputationalModel for Short-Wavelength Stall Inception and Development in Multi-stage Compressors, ASME Journal of Turbomachinery, Vol. 121, No. 4,1999, pp. 726-734.

[16] Hoying, D.A., Tan, C.S., Vo, H.D., and Greitzer, E.M., Role of BladePassage Flow Structures in Axial Compressor Rotating Stall Inception,

ASME Journal of Turbomachinery, Vol. 121, No. 4, 1999, pp. 735-742.[17] Spakovszky, Z.S., Weigl, H.J., Paduano, J.D., van Schalkwyk, C.M.,

Suder, K.L., and Bright, M.M., Rotating Stall Control in a High-SpeedStage with Inlet Distortion, Part I: Radial Distortion, ASME Journal ofTurbomachinery, Vol. 121, No. ?, 1999, pp. 510-516.

[18] Smith, L.H., Jr., Axial Compressor Aerodesign Evolution at GeneralElectric, ASME Journal of Turbomachinery, Vol. 124, No. 3, 2002,pp. 321-330.

[19] Lewis, R.I., Turbomchinery Performance Analysis, Arnold, London, 1996,

pp. 136-139.[20] Horlock, J.H., Axial Flow Compressors: Fluid Mechanics and Thermody-namics, Butterworth, London, 1958, p. 97, 104-105.

[21] Robinson, C.J., Endwall Flows and Blading Design for Axial Flow Com-pressors, in Axial Flow Compressors, AGARD LS 1992-02, von KarmanInstitute for Fluid Dynamics, Rhode Saint Genese, Belgium, Jan 27-30,1992.

[22] Cahill, J.E., Identification and Evaluation of Loss and Deviation Modelsfor Use in Transonic Compressor Stage Performance Prediction, MastersThesis, Virginia Tech., Sep. 1997.

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