Prediction of an axial turbomachine performancedegradation due to sand ingestionA Ghenaiet1�, S C Tan2, and R L Elder3

1Thermal Power Laboratory, Polytechnic School, Algiers, Algeria2National Institute for Aviation Research/Aircraft Icing, Wichita State University, USA3PCA Engineering, Bedford, UK

The manuscript was received on 27 July 2004 and was accepted after revision for publication on 13 January 2005.

DOI: 10.1243/095765005X7592

Abstract: Erosion of compressor blades due to operation in particulate environments is aserious problem for the manufacturers and users of industrial and aeronautical gas turbines,because of drastic degradations in performance, mostly through blunting of blade leadingedges, reduction of chord and increase of tip clearance and surface roughness. This paper pre-sents a numerical study to assess the effects of erosion by sand ingestion on blade geometrydeterioration and the subsequent performance degradation. These computations were carriedout for an axial turbomachine in steps; first, calculations of particle trajectories and erosionresulting from cumulative impacts by sand particles (MIL-E 5007E, 0–1000 mm) were carriedout, then, the required data were used in the estimation of performance degradation basedon a mean-line method that included Lieblein and Koch–Smith loss correlations, in additionto an erosion fault model derived from blade geometry deterioration. This global procedurewas successfully validated upon an axial fan stage, and can be generalized easily to otheraxial compressor designs.

Keywords: axial turbomachine, particle trajectories, particle impacts, erosion, geometrydeterioration, mean-line method, pressure losses, performance degradation

1 INTRODUCTION

The reality of the danger posed by sand ingestion tothe front compressor stages of gas turbines has beendramatically illustrated during Desert Shield/DesertStorm operations in extremely erosive desertenvironments polluted with particulates varying insize from sub-microns to several millimetres, andwith quartz as the most abundant erosive constitu-ent. The ingestion of sand particles and their abrasiveimpacts are known to cause considerable erosionnear the leading edge and tip of axial compressorblades [1]. Balan and Tabakoff [2] studied exper-imentally the effects of sand ingestion on an axialcompressor and found severe erosion of the leadingedge and pressure side of rotor blades, with

increased roughness. Also, Dunn et al. [3] carriedout tests on a full-scale engine and found similarcharacteristics during blades removal; increase oftip clearance and erosion of blade leading edges,which resulted in a substantial performance dropin both HP and LP compressors. Traditional pro-cedures (based on experiments) for assessing turbo-machinery erosion and performance degradationremain very expensive and revealed limited infor-mation; consequently, research efforts are more con-centrated on numerical simulations, because of thelower cost and time, especially at early design stages.

This paper presents a complete numericalprocedure for simulating particle trajectories, ero-sion, blade geometry deterioration and subsequentaerodynamic performance degradation. Particletrajectories were solved separately from theflow field, by using a Lagrangian trackingmethod, and considering random particle size dis-tribution (0–1000 mm) for sand particle type,MIL-E5007E.

All authors were formerly at the School of Mechanical Engineer-

ing, Cranfield University, UK.�Corresponding author: Thermal Power Laboratory, Polytechnic

School, BP339, Didouche Mourad, Algiers, Algeria.

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The estimated drop in aerodynamic performance(adiabatic efficiency, pressure rise coefficient andstall margin) was based on a mean-line method.The blade profile loss and the endwall losses wereestimated from existing empirical correlations,which have been extensively used for a wide varietyof axial compressors [4, 5]. Additional losses due toblade erosion were modelled through an erosionfault model derived from the deteriorated blade geo-metry, which is presented herein. This complete pre-dictive methodology was validated upon a testedaxial fan [6], consisting of ten twisted C4 rotorblades rotating at a constant speed, and seven C4inlet guide vanes made from cast aluminium(Fig. 1). The details of the geometrical data anddesign parameters for this turbomachine are avail-able in Table 1.

2 PARTICLE TRACKING AND EROSIONCOMPUTATION

2.1 Particle tracking

The simulation of particle motion in turbulentflows requires the determination of the

instantaneous flow velocity, which consists of themean and fluctuating flow components. The fluctu-ating fluid velocity corresponds to a particulareddy, and can be calculated from the local turbu-lence properties of the flow and a randomnumber [7]. The full solutions of the flow field atseveral operating mass flow rates (0.6–1.0 kg/s)were obtained by using the commercial code TASC-flow. Then, the necessary flow parameters werepassed to an in-house developed trajectory code(PARTRJ) in order to predict trajectories, locationsof impacts and erosion.

The equations of motion for solid particles withinturbomachinery blades are derived in cylindricalcoordinates, considering centrifugal, coriolis, gravity,drag and Saffman force [8]. The drag force(expression below) is usually written in the form ofa drag coefficient [9] based on a spherical particle,and corrected using a shape factor, since particlesare irregularly shaped.

FD ¼p

8d2

prCD

f(W � Vp)kWj � jVpk (1)

As a result, a set of second-order nonlinear differen-tial equations is written in polar coordinates for therotating frame as

@2rp

@t2¼ G(Wr � Vpr)þ rp Vþ

Vpu

rp

� �2

�g 1�r

rp

!sin up þ

FSr

mp

rp

@2uP

@t2¼ G(Wu � Vpu)� 2Vpr Vþ

Vpu

rp

� �

�g 1�r

rp

!cos up þ

FSu

mp

@2zp

@t2¼ G(Wz � Vpz)þ

FSz

mp

8>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>:

(2)

Fig. 1 The axial turbomachine

Table 1 Axial fan stage design parameters

Geometrical parameters Design point

Shroud diameter 170.02 mm Flow coefficient 0.5Rotor root diameter 110 mm Pressure rise coefficient 0.4Rotor tip diameter 169.37 mm Rotational speed 11 300 rpmRotor tip chord 45.57 mmRotor root chord 43.08 mmRotor tip stagger angle 55.258Rotor root stagger angle 488Rotor root inlet blade angle 67.728Rotor tip inlet blade angle 72.698IGV chord 57.14 mmIGV stagger angle 27.368Roughness Ra 2.95 mmIGV-rotor spacing 15 mm

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The aerodynamic factor G depends on fluid and par-ticle velocities.

G¼3

4dp

r

rp

CD

f

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffijWr�Vprj

2 þ jWu � Vpuj2 þ jWz � Vpzj

2q

(3)

A developed trajectory code (PARTRJ) based on aLagrangian method [6] was used for particle tracking.The nonlinear differential equations (2) governingparticle motion were solved by the seventh-orderRunge–Kutta Fehlberg method [10], considering athree-dimensional structured grid (shown in meri-dional plane, Fig. 2). Particle trajectories wereobtained in the physical coordinates, but the trackingof particles in the different cells constituting inletguide vane (IGV) and rotor domains was based ontheir local coordinates calculated by the finiteelement method [7].

The initial release points and velocities of particlesconformed to the measured concentration distri-bution and particle velocity obtained by means oflaser transit anemometer [6]. A high concentration(775 mg/m3) of sand particle MIL-E5007E was usedin these computations, similarly to the experimentalwork.

The computation of the trajectory proceededthrough the periodic planes and the stator–rotor inter-face planes. At a point of impact on a solid surface, thevelocity and angle of impingement were used for ero-sion calculation, and the trajectory computation wasthen continued using the rebound factors (restitutionratios) obtained experimentally by Tabakoff et al. [11].

2.2 Erosion prediction

The intensity and pattern of erosion are dependenton the physical properties of particle, size,

concentration, velocity and angle of impingement,the geometry and material of blades. The erosionrate (defined as mass of material removed per massof impacting particle) depends on kinetic energyexchange between an impacting particle and atarget surface, which was estimated by an existingsemi-empirical correlation [12].

1 ¼ K1f (bp1)(V 2p1u � V 2

p2u)þ f (Vp1n) (4)

The overall erosion rate per blade is related to thetotal ingested mass of particles through one bladepassage by the following expression.

10 ¼Dme

Q=(NB)(5)

The nodal values of erosion on the blade, huband shroud surfaces were calculated by means ofbilinear interpolation. Because sand particles areassumed to be spherical, the depths of penetrationare easily calculated. As a result, the eroded bladeprofile is regenerated (Fig. 3), and percentages ofchord and tip clearance deteriorations are com-puted as follows.

. The mean reduction of blade chord:

Dcm(%) ¼ 100 1�1

cminh

ðh

0

Dc dh

" #(6)

. The mean increase of tip clearance:

Dt(%) ¼ 1001

tinAt

Xk

i¼1

tiDAi � 1

" #(7)

Fig. 3 Deteriorated rotor blade

Fig. 2 The computational grid showing IGV and rotor

blades, with periodic boundaries

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3 AERODYNAMIC PERFORMANCEDEGRADATION

The aerodynamic performance degradation wasdetermined in terms of the blade geometry, axialflow velocity, flow angles, and upstream pressure,temperature and Reynolds number. The blade profileloss [4] and endwall losses [5] were estimated fromexisting empirical correlations, which had beenapplied to a wide variety of axial compressors. Thereference stage efficiency excluding tip clearanceand secondary losses is calculated as

href ¼ 1�4IGV(V1=U)2 þ4R(W1=U)2

2(DHt=U2)

� �(8)

IGV losses. The total pressure loss contains theprofile and secondary flow losses, which are esti-mated by analogy to a turbine nozzle guide vane(NGV) [13].

4IGV ¼ 4s þ4p (9)

Rotor profile loss. The minimum profile loss par-ameter is based on the defect of flow momentum atthe blade trailing edge, which is correlated againstthe equivalent diffusion factor [14].

4p ¼ 2u�

c

� �s

cosb2

cosb1

cosb2

� �2 2

3� 1=H2

� �

� 1�u�

c

� �sH2

cosb2

� ��3

(10)

The effect of roughness is usually specified in terms ofan equivalent sand grain roughness, which is related tothe surface centre-line-averaged roughness [15]. Abovethe dimensionless roughness Reynolds number of 90,the boundary layer characteristics depend only onthe ratio of surface roughness to chord length.

The losses due to the wall boundary layer and sec-ondary flow are usually lumped together into theso-called endwall losses, [16]. Koch and Smith [5]related the efficiency loss due to the presence of end-wall effects to the two properties of the endwallboundary layer, the displacement and tangentialforce thickness, which are related to the effectivestage static pressure rise coefficient ratio definedaccording to Koch [17].

h ¼ href

1� (2�d�=s cos j)(s cos j=h)

1� (2�n=2�d�)(2�d

�=s cos j)(s cos j=h)

(11)

3.1 Additional losses due to erosion

Aerodynamic losses due to erosion by sand particlesare mainly attributed to blade chord reduction and

increase of tip clearance [18]. As the percentage ofblade chord reduction was calculated fromexpression (6), the eroded blade chord is computedby an expression derived from the basic C4 aerofoiland blade geometry deterioration model (Fig. 4) as

ce ¼ c

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR

c

� �2

�Dcm

c�

1

2

� �2s

�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR

c

� �2

�1

4

s24

35

28<:

þ 1�Dcm

c

� �2)1=2

(12)

The variation of blade stagger and camber angle werecomputed by expressions derived according to Fig. 4.

Dj ¼ tan�1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRc

� �2� Dcm

c �12

� �2q

�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRc

� �2� 1

4

q1� (Dcm=c)

(13)

ue ¼ 2 tan�1 4R

ce

� �2

�1

" #�1=2

(14)

The inlet blade angle is computed from the tangentto the camber line.

beG1 ¼ tan�1 4R

ce

� �2

�1

" #�1=2

(15)

The absolute variation of inlet blade angle is thesummation of the relative variations of blade angleand stagger angle.

DbG ¼ (bG1 � beG1)þ Dj (16)

Fig. 4 Modelling of blade geometry deterioration

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For noncircular blade profiles, these equations are atbest an approximation.

The significant rotor blade erosion (predicted andmeasured) was concentrated around the blade lead-ing edge, spanning two-thirds of blade height andextending over a large area of the pressure sidetowards the tip. This deterioration in rotor blade pro-file is accompanied by a drop in aerodynamic liftcoefficient, which is estimated by an expressionderived from classical thin airfoil theory [6].

DCL ¼ 2p Dbþ1

p

ðp0

cos u(cos u� 1)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4(R=c)2 � cos2 u

p du

"

�1

p

ðp0

cos u(cos u� 1)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4(R=ce)2 � cos2 u

p du

#(17)

The effect of changes in chord and leading edge dueto erosion appears as a supplement to the drag coef-ficient.

DCD ¼ CDe � CD (18)

The new value of drag coefficient is calculated fromthe variation of flow angle and the drop in lift coeffi-cient given as follows.

CDe ¼1

tanbme

�CD tanbm þ DCL

� 2

�s

c

cosbm tanb1 � tanb2

� �

�s

c

ecosbme( tanb1e � tanb2e)

��(19)

The drop in adiabatic efficiency is related to thesupplement in drag coefficient, computed byexpressions (18) and (19).

Dhe ¼ DCD

cosb21e

cosb3me

c

s

e

(W 21 =U2

m)

2(DHt=U2m)e

(20)

An additional term for the increase in endwall lossesdue to relative changes in tip clearance is also esti-mated by the Koch and Smith correlation.

3.2 Off-design performance

The off-design performance was calculated by themean-line method at different operating mass flowrates. The variation of blade profile loss is estimatedfrom a relationship between the minimum profileloss and flow conditions. The minimum profile loss(at minimum flow incidence) is obtained fromequation (10), whereas the minimum incidenceangle can be obtained iteratively by calculating the

maximum lift–drag ratio, and taking the referenceincidence angle as an initial guess.

iref ¼ (Ki)sh(Ki)th(i0)10 þNu (21)

At high stagger angle, a blend between cascade andisolated aerofoil design methods is used for the devi-ation parameter via a modified graphical relation dueto Wallis [19].

m ¼ 10�8j4 � 10�6j3 þ 0:0001j2�0:001j

þ 0:2307 (22)

The rotor flow deviation angle is dependent on inci-dence and inlet flow angle. For a fixed stagger anglethe variation in flow angle is equal to the variationin incidence. Hence, the derivative of the deviationwith incidence is taken as the summation of thetwo components.

dd

di

����j

¼@d

@i

����b1

þ@d

@b1

����i

!(23)

The first derivative was introduced by Lieblein [20],whereas the second derivative is developed in the fol-lowing expression.

@d

@b1

����i

¼@d

@b1

����i¼iref

�@d

@i

����b1

!@i

@b1

� �i¼iref

(24)

By knowing the slope of the deviation angle at a con-stant stagger angle, the variation of deviation flowangle is related to incidence angle by an approximatelinear relation.

d ¼ dref þdd

di

� �j

(i � iref) (25)

As the minimum blade profile loss is known at theminimum incidence angle, the off-design blade pro-file loss between choking and stalling incidence areestimated by using a graphical relation due toMiller and Wasdell [21]

4

4m

¼ fi � imin

is � imin

� �(26)

The endwall losses are strongly dependent on tipclearance, aspect ratio and stage loading. Theselosses were computed at different operating con-ditions and used for calculating stage adiabaticefficiency.

The IGV profile used for this type of turbomachineis geometrically similar to a turbine NGV, thus, the

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outlet flow angle is simply related to the exit throatarea and the blade pitch by a relation given in refer-ence [14].

The stage-loading factor is derived from the Eulerpump equation and velocity triangles for this typeof contra-whirl axial fan stage (Fig. 5). The centralregion of the rotor blade section will therefore doless work than is estimated from the velocity tri-angles based on the mean axial velocity, thus a cor-rection for the axial velocity was introduced interms of blockage factor estimated according toreference [22]. A work done factor was introducedin expression (27) in order to compensate for thedeteriorating axial velocity profile near the hub andshroud downstream of the IGV blade, as confirmedby computational fluid dynamics (CFD) compu-tations [6]. A value equal to 0.975 for this factorwas selected [22] to give extra work to cater for amargin of error [23].

DHt

U2¼

0:975( tanb1 � Kb tanb2)

tanb1 � tana1(27)

The stage total pressure increase and the stage load-ing factor are related by the total-to-total adiabaticefficiency as

DPt

�rU2¼ h

DHt

U2(28)

The pressure rise coefficient is equivalent to the totalpressure head normalized by the square of the tiprotational speed.

c ¼DPt

rU2t

(29)

The stall limit for this type of axial fan depends on highblade staggering and endwall effects and is related tothe tip clearance and aspect ratio. The stalling pressurerise coefficient for a blade passage, which was corre-lated against the two-dimensional diffuser perform-ance [17], was adopted here as a criterion forpredicting stall onset. Thus, the estimation of drop install margin was related to the reduction of chordand increase of blade tip. The surge margin was calcu-lated according to a definition [24], which considersthe change in the outlet flow function (mfr

pcpTt/APt)

between the working line (design point) and thesurge line for the given rotational speed. After simplifi-cations the surge margin was related to pressure riseand inlet mass flow rate by

SM(%) ¼ 100 1�PW

Ps

mfrs

mfrw

� �(30)

4 DISCUSSION

Because of the pre-rotation induced by the IGV(Fig. 5), high rotational speed and the flow velocityand direction upstream rotor blade leading edge(Fig. 6), several particle impacts were found aroundthe leading edge, extending to two-thirds of theblade height, with the strongest erosion levels onthe upper corner of the blade pressure side andtowards the tip. Particles entrained by flow leakagefrom pressure to suction side through tip clearance,induced erosion on the blade tip and shroud, asshown by particles’ trajectories in Fig. 7(a) and theimpacts locations depicted in Fig. 7(b). Predictederosion patterns (Figs 8, 9, and 10) are seen to

Fig. 6 Flow velocity vectors at mid span near the

design pointFig. 5 Off-design velocity triangles

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Proc. IMechE Vol. 219 Part A: J. Power and Energy A09204 # IMechE 2005

depend on the axial fan operating conditions, forexample, the throttling of mass flow rate. At a highmass flow rate, the predicted erosion pattern isshown to occupy a larger area of the rotor bladepressure side starting from the leading edge. At avery low mass flow rate, for example, near stall, alarge eroded area is also evident near the trailing

edge, in addition to an eroded area near the leadingedge. However, erosion of the rotor blade suctionside is insignificant in all operating conditions.

The predicted mass and rate of erosion per bladenear design mass flow rate were 1146 mg and0.6783 mg/g, respectively, compared to experimentalvalues of 999 mg and 0.653 mg/g [6]. The predictedblade mass erosion at different operating mass flowrates (0.6–1.0 kg/s) tends to increase with air massflow (Fig. 11), and becomes steeper above the valueof 0.9 kg/s, because of the higher flow velocity andnumber of particles involved. In all operating con-ditions the measured and predicted geometrychanges for the IGV blade were negligible.

The computation of blade geometry deteriorationfor the rotor blade was based on the procedure out-lined in section 2.2. In order to obtain a relationbetween the air mass flow and the blade geometrydeterioration, particle trajectories and erosion simu-lations were performed at a constant concentration(775 mg/m3) for different operating conditions overa period of 9 hours. As a consequence, the materialremoval and geometry deterioration were related to

Fig. 7 (a) Predicted sand particles’ trajectories; (b) predicted impacts on the rotor blade pressure

side, with fan operating near the design point

Fig. 8 Erosion of rotor blade pressure side by sand

(MIL-E5007E); axial fan operating near design

point 0.8 kg/s, over a period of 9 h

Fig. 9 Erosion of rotor blade pressure side by sand

(MIL-E5007E); axial fan operating at mass flow

1.0 kg/s, over a period of 9 h

Fig. 10 Erosion of rotor blade pressure side by sand

(MIL-E5007E); axial fan operating near stall

limit 0.6 kg/s, over a period of 9 h

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mass of sand ingested and duration. The resultsdeplicted in Figs 12 and 13 show evidence of vari-ations in blade profile with air mass flow, by areduction of blade chord and noticeable increaseof tip clearance. When operating near the designpoint, the predicted deterioration of tip chordand tip clearance were 5.27 and 49.30 per cent,respectively, compared to the measured values of10.42 and 65.75 per cent [6]. The underpredictionof the chord reduction might be attributed to the

progressive changes of flow pattern around theeroded blade tip corner, which was not consideredin the CFD modelling prior to particle trajectoriesand erosion computations within periods of sandingestion. It is also noted that there is a slight discre-pancy in tip and hub chord from design, due to themanufacturer’s accepted tolerance for such low-cost fans; thus, measurements were different fromthe intended design as used for the simulations.

Table 2 gives the steps of performance degradationaccording to experiments [6], where sand particleswere injected at a high concentration (775 mg/m3)for a pre-defined duration near the design point.This was repeated at several discrete points withthe same rotor, simulating a total period of 9 hoursof sand ingestion. The reason for this is to evaluatethe step change in aerodynamic performance ofthis axial turbomachine. Table 3 and Fig. 14 showthat the predicted performance degradation basedon eroded rotor blades obtained from erosion exper-iments are generally good compared to test results ofperformance degradation. The predicted degra-dations in adiabatic efficiency and pressure rise atthe design mass flow were 5.40 and 8.23 per cent,respectively, compared to the measured values of6.70 and 3.44 per cent, respectively (Table 3). Thepredicted stalling mass flow was 0.695 kg/s, com-pared to a measured value of 0.71 kg/s, which is

Fig. 11 Rotor blade erosion (mg) over a period of 9 h of

sand (MIL-E5007E) ingestion

Fig. 12 Blade tip clearance increase over a period of

9 h of sand (MIL-E5007E) ingestion

Fig. 13 Blade chord decrease over a period of 9 h of

sand (MIL-E5007E) ingestion

Table 2 Measured performance degradation based on the original blade profile

Time(hours)

Efficiency atdesign flow

Degradationefficiency (%)

Pressure risecoefficient atdesign flow

Degradation ofpressure risecoefficient (%)

Mass flowat stall (kg/s)

Stall margin(%)

Degradation ofstall margin (%)

0 0.8025 — 0.3952 — 0.616 20.94 —2.2 0.7815 2.616 0.3930 0.556 0.634 20.37 2.7184.6 0.7687 4.211 0.3878 1.872 0.648 18.83 10.0856.9 0.7492 6.641 0.3813 3.517 0.680 15.57 25.6519 0.7487 6.704 0.3816 3.441 0.710 10.07 51.892

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Proc. IMechE Vol. 219 Part A: J. Power and Energy A09204 # IMechE 2005

equivalent to a stall margin degradation of 51.8 percent compared to the measured value of 54.2 percent. The difference between the predicted andmeasured performance degradation at low mass

flow could be attributed to underestimated endwalllosses, which are related to the effective pressurerise coefficient, flow condition and the geometry oferoded blades (rounded leading edge). Table 4shows the predicted performance degradationbased on predicted eroded blade profile (obtainedby particle trajectories simulation and erosionmodel). The results as seen from Table 4 depict asimilar trend with the measurements shown inTable 2, but differ at the later periods of sand inges-tion, where measured degradation was higher thanpredicted. This might be attributed to the differencebetween the predicted and measured geometry ofdeterioration, where the nonlinear process of erosioncould not be accounted for in the prediction model.In addition, the complex eroded shape of the leadingedge, spanning two-thirds of the blade height,had a significant influence on the stall limit due toincreased flow leakage around the blade corner andshift of the leading edge stagnation point.

The erosion damage is found to have a significanteffect on lift coefficient, because of static pressureredistribution over the eroded profile, owing to anincrease of tip clearance and rounding of the bladeleading edge. CFD computations carried out for theeroded blade (as measured) gave an estimation ofthe deterioration in aerodynamic lift coefficient of5.6 and 1.2 per cent for the tip and mid-span bladeprofile, respectively. Figures 15(a) and (b) showstatic pressure distribution at mid-span and tip ofthe blade, respectively. The loss of the profile liftcoefficient is clearly evident from the reduced areabetween the curves of static pressure distributionsover the pressure and suction side of the rotorblade. Figures 16(a) and (b) illustrate the pitchwiseaveraged flow incidence and relative velocity with

Table 3 Predicted performance degradation based on measurements taken from actual blade profile

Time(hours)

Efficiency atdesign flow

Degradationefficiency (%)

Pressure risecoefficient atdesign flow

Degradation ofpressure risecoefficient (%)

Mass flowat stall (kg/s)

Stall margin(%)

Degradation ofstall margin (%)

0 0.797 — 0.394 — 0.608 14.86 —2.2 0.780 2.133 0.387 1.776 0.608 18.53 —4.6 0.765 4.015 0.379 3.807 0.658 11.1 25.2716.9 0.751 5.771 0.369 6.345 0.685 8.54 42.4879 0.740 7.151 0.360 8.502 0.699 6.8 54.219

Fig. 14 Predicted performance degradation of the

axial fan

Table 4 Predicted performance degradation based on changes in the blade profile computed by the erosion fault model

Time(hours)

Efficiency atdesign flow

Degradationefficiency (%)

Pressure risecoefficient atdesign flow

Degradation ofpressure risecoefficient (%)

Mass flowat stall (kg/s)

Stall margin(%)

Degradation ofstall margin (%)

0 0.8020 — 0.3890 — 0.5966 16.92 —2.2 0.7859 2.005 0.3784 2.738 0.6021 16.70 1.304.6 0.7676 4.294 0.3662 5.855 0.6599 11.95 29.376.9 0.7475 6.798 0.3533 9.17 0.7038 7.66 54.719 0.7264 9.429 0.3402 12.55 0.7384 5.64 66.62

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blade height upstream of the rotor blade leadingedge before and after erosion, as computed byCFD. A greater difference is illustrated for flow inci-dence along the blade height, which means that ero-sion not only affects flow over the eroded corner, butalso the flow pattern, globally. Figure 18 as comparedto Fig. 17 shows further evidence of the increaseof losses in the blade tip and over eroded uppercorner of the rotor blade.

This complete computational procedure wasrepeated for different operating conditions (throt-tling), over a range of mass flow rate from 0.6 to1.0 kg/s, in order to generate the intermediatecurves of performance degradation, such as

adiabatic efficiency, pressure rise coefficient andstall margin, as shown by Fig. 19 (for different oper-ating mass flow rates). The overall performancedegradation curves as plotted in Fig. 20 werededuced from Fig. 19 by taking values of pressurerise coefficient and adiabatic efficiency correspond-ing to sand injection at different throttling. Thecurves as plotted in Fig. 20 describe the generaltrend in performance degradation at different oper-ating conditions in extremely polluted environmentsby sand particles. Figure 21 represents the relativeperformance drop (in percentage), and shows aminimum occurring near the design mass flow rate;this is because of low flow incidence at that

Fig. 15 (a) Pressure around rotor blade at mid span, axial fan operating near design point; (b)

pressure around rotor blade near tip, axial fan operating near design point

Fig. 16 (a) Averaged flow incidence upstream leading edge of rotor blade, axial fan operating

near design point; (b) averaged relative flow velocity upstream leading edge of rotor

blade, axial fan operating near design point

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Proc. IMechE Vol. 219 Part A: J. Power and Energy A09204 # IMechE 2005

particular working condition, whereas at low andhigh mass flow rates, the increased relative dropmight be attributed to higher incidence angles.

The main contributors to performance degra-dation for this type of turbomachine are: chordreduction and blunting of the blade leading edge,which affect flow incidence, aerodynamic lift coeffi-cient, and stall inception. Near the design point theestimated percentage of pressure rise and adiabaticefficiency degradation due to chord reduction are71.85 and 73.27 per cent, respectively (Fig. 22). Atthe maximum air mass flow, these degradations are83.9 and 89.5 per cent, respectively. At the minimummass flow rate these percentages are 59.63 and 56.28per cent, respectively, as seen from Fig. 22. Anotherparametric analysis using the mean-line methodrevealed that a reduction of 1.5 per cent in rotorblade chord produced a loss of 14 per cent in stallmargin, which is also equivalent to an increase of150 per cent in tip clearance. As a conclusion, thereis a predominant effect of blade profile erosion, com-pared to the effect of tip clearance increase.

Rotor blade erosion and geometry deteriorationare strongly dependent on particle concentrationand duration of sand ingestion. In order to derive arelation between sand particle concentrations andduration of exposure, the particle trajectory, erosionand performance degradation computations werecarried out for several concentration levels and

Fig. 17 Relative total pressure in tip clearance of the

original rotor blade, axial fan operating near

design point

Fig. 18 Relative total pressure in the tip clearance of

the eroded rotor blade, axial fan operating

near design point

Fig. 19 Predicted intermediate performance

degradation after 9 h of sand (MIL-E5007E)

ingestion

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A09204 # IMechE 2005 Proc. IMechE Vol. 219 Part A: J. Power and Energy

periods of sand ingestion. In this way, a relationshipbetween adiabatic efficiency drop with time of run-ning was obtained and presented graphically asshown in Fig. 23. The life time of this turbomachinewas related to a certain limit of adiabatic efficiencydrop, which was generally specified at 10 per centby gas turbine users. From the curves of adiabaticefficiency degradation (Fig. 23), the life time was esti-mated graphically for different concentration. As aresult, an interpolated curve for the life time was

obtained for these rotor blades made from cast alu-minium, which tends to follow an exponentialdecay with sand concentration, as shown by Fig. 24.

In order to study the effect of material hardnesson rotor blade geometry deterioration and the sub-sequent degradation in aerodynamic performanceand the expected life time, these numerical com-putations were repeated for harder materialssuch as stainless steel 510. As a result, an approxi-mate expression for the life time was modified toinclude the Brinell hardness of materials, whichcan be used for other blade configurations andmaterials based on similar turbomachinery designs.

lifetime ¼HB

HBal� 1

� �B1 exp (� C=b1)

þ B2 exp (� C=b2)�

� A0HB

HBal� 1

� �A1 exp (� C=a1)½

þ A2 exp (� C=a2)� (31)

Fig. 20 Predicted overall performance degradation

after 9 h of sand (MIL-E5007E) ingestion

Fig. 21 Relative performance degradation over a

period of 9 h of sand ingestion

Fig. 22 Relative performance degradation over a

period of 9 h due to chord reduction only

Fig. 23 Predicted adiabatic efficiency degradation

with time of running for different sand

particle concentrations

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Proc. IMechE Vol. 219 Part A: J. Power and Energy A09204 # IMechE 2005

where A0 ¼ 0.536, A1 ¼ 929.73, A2 ¼ 48.32,B1 ¼ 3.23 � 105, B2 ¼ 0.17 � 105, a1 ¼ 91, a2 ¼ 860,b1 ¼ 17.6, b2 ¼ 305.2, and HBal ¼ 110.

Erosion patterns in multistage axial compressorsare strongly influenced by the nonuniform particledistribution in both tangential and radial directionsbetween each pair of sequential blade rows, due tocentrifugation and impacts on the previous rotorblade pressure side, through which sand particlesacquire circumferential velocities and are sub-sequently centrifuged to the outer annulus. Thesetendencies continue throughout the latter stages,with few particles in the inner half span, leading toincreased particle concentration toward the outerannulus. As a consequence, blade impacts for thesestages are expected to be found mostly near theouter radii and extending from the leading edgefurther along the blade chord. Erosion of the latterstages is particularly severe as the erodent particlescrowd near the outer annulus in a region with thesmallest blade height and a reduced flow path; con-sequently, erosion intensity per unit surface area isexpected to be higher. On the other hand, becauseof the reduced particle size and inertia due to particlefragmentation following repeated impacts, inaddition to the increased drag force due to higherflow density in these latter rotor blade rows, a largefraction of particles is diverted towards the bladetrailing edge after impacting the tip of the bladeand shroud. The frequency of impacts at the trailingedge upper corner region as well as the local rates ofwear are increased, which leads to thinning andmaterial break-up by cutting from the upper cornerof the blade trailing edge.

5 CONCLUSIONS

High erosion levels were predicted near the leadingedges and at the tip corner of the rotor blades due

to direct exposure to a flux of sand particles at highconcentration and peripheral velocity. This erodedarea covered the upper corner of the pressure side,extending to the tip of the rotor blade, due to cen-trifugal force. The erosion patterns were found todepend on the operating conditions (throttling),because of variations in flow velocity and incidence.Erosion was insignificant over the rotor blade suctionside in all operating conditions.

The derived mean-line method involving erosionfault model and loss correlations gave reasonablygood results in comparison with experimental dataand showed that the Lieblein and Koch–Smith corre-lations were sufficient for the current method. The pre-dicted results for performance degradation indicatederosion of the blade leading edge and tip clearancewere the main contributors to the degradation of thepressure rise coefficient, adiabatic efficiency and stallmargin. However, the blade chord reduction had a pre-dominant effect compared to tip clearance. Thederived overall degradation characteristics and thegeneralized life time expression for this turbomachinecan be used as a tool by engineers for estimatingperformance degradation and the life time expectancyof similar turbomachinery designs, due to in-serviceerosion resulting from operation in environmentsexcessively polluted by sand particles.

REFERENCES

1 Tabakoff, W. Review turbomachinery performancedeterioration exposed to solid particulate environment.ASME J. Fluids Engng, 1984, 106, 125–134.

2 Balan, C. and Tabakoff, W. Axial flow compressorperformance deterioration, AIAA paper 84-1208, June1984.

3 Dunn, M. G., Padova, C., Moller, J. E., and Adams,R. M. Performance deterioration of a turbofan and aturbojet engine upon exposure to a dust environment.ASME J. Engng Gas Turbine Power, 1987, 109, 336–343.

4 Lieblein, S. Experimental flow in two dimensionalcascades, NASA SP-36, Chapter VI, 1965.

5 Koch, C. C. and Smith, Jr. L. H. Loss sources andmagnitudes in axial flow compressors. J. Engng Power,1976, 411–424.

6 Ghenaiet, A. Turbomachinery performance degra-dation due to erosion effect, PhD thesis, Cranfield Uni-versity, 2001.

7 Ghenaiet, A., Elder, R. L., and Tan, S. C. Particle trajec-tories through an axial fan and performance degra-dation due to sand ingestion, 2001–GT–0497, ASMEpaper TURBO EXPO Land Sea & Air, New Orleans,USA, 4–6 June 2001.

8 Sommerfeld, M. Theoretical and experimental model-ling of particulate flow—overview and fundamentals,Lecture series 2000-06, 3–7 April 2000 (Ed. J.-M.Buchlin), 2000 (Von Karman Institute, Belgium).

Fig. 24 Predicted life time (aluminium blade) function

with sand particle concentration

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A09204 # IMechE 2005 Proc. IMechE Vol. 219 Part A: J. Power and Energy

9 Morsi, S. A. and Alexander, A. J. An investigation ofparticle trajectories in two phase flow system. J. FluidMech., 1992, 55(2), 193–208.

10 Fehlberg, E. Classical fifth, sixth, seventh and eighthorder RK formulas with step size control, NASA TR-287, October 1968.

11 Tabakoff, W. Hamed, A., and Murugan, D. M. Effect oftarget materials on the particle restitution character-istics for turbomachinery application. J. Propulsionand Power, 1996, 12(2), 260–266.

12 Grant, G. and Tabakoff, W. Erosion prediction inturbomachinery resulting from environmental solidparticles. J. Aircraft, 1975, 12(5), 471–478.

13 Horlock, J. H. Axial Flow Turbines, 1973 (R.E. KriegerPub. Co, Huntington, N.Y.).

14 Gordon, D. W. and Korakianitis, T. The Design of HighEfficiency Turbomachinery and Gas Turbines, 1998(Prentice Hall, New Jersey).

15 Schaffler, A. Experimental and analytical investigationof the effects of Reynolds number and blade surfaceroughness on multistage axial flow compressors,ASME paper 79-GT-2 16 April 1979.

16 Lakshminarayana, B. Fluid Mechanics and HeatTransfer of Turbomachines, 1996 (John Wiley & Sons,New York).

17 Koch, C. C. Stalling pressure rise capability of axial flowcompressor stages. ASME J. Power, 1981, 103, 645–656.

18 Ghenaiet, A., Tan, S. C., and Elder, R. L. Numerical simu-lation of the axial fan performance degradation due tosand ingestion, GT-2002-30644, ASME Turbo Expo 2002,Amsterdam, The Netherlands, 3–6 June 2002.

19 Wallis, R. A. The development of blade sections foraxial flow fans, Mech. Chem. Engng, Trans IE, 1992,MC8 (2), 111–116.

20 Lieblein, S. Incidence and deviation angle correlationsfor compressor cascades. J. Basic Engng, 1960, 82,575–586.

21 Miller, D. C. and Wasdell, D. L. Off–design predictionof compressor blade losses, C279/87, IMechEProceeding.

22 Howell, A. R. and Calvert, W. J. Axial flow compressorperformance prediction by stage stacking—determi-nation of stage aerodynamics, NGTE Report No.R81002 UDC 621.45.037-154, June 1981.

23 Wall, R. A. Axial flow compressor performance predic-tion, (Roll’s-Royce, Derby, 1971)—Modern PredictionMethods for Turbomachine Performance AGARD-LS-83, 14–18 June 1976.

24 Cumpsty, N. Compressor Aerodynamics, 1989(Longman Scientific & Technical, UK).

APPENDIX

Notation

A areac chordC concentration, mg/m3

CD drag coefficientCL lift coefficient

cp specific heat at constant pressuredp diameter of particleFD drag forceFS saffman forceh blade heightg gravitational constantH enthalpyH2 boundary layer shape factori incidence angle(i0)10 incidence angle for zero camber(Ki)sh shape correction for incidence angle(Ki)th thickness correction for incidence angleK1 material constantKb blockage factormp mass of a particleDme eroded massm deviation parametermfr mass flow rateN slope of the incidence angle variation with

camberNB number of bladesP pressureR radius of camber liner radial coordinateQ mass of ingested sand, gs pitch of blade cascadeSM stall margint timeU peripheral velocityV absolute flow velocityW relative flow velocityVp particle velocityz axial coordinate

Greek letters

a absolute flow angleb relative flow anglebG blade anglebp particle impact angled deviation flow angled� displacement thickness1, 10 erosion rate, overall erosion parameter,

mg/gf particle shape factorh adiabatic efficiencyv loss coefficientV speed of rotation, rad/sn endwall boundary layer tangential force

thicknessr densityP pressure ratios solidityt tip clearancec pressure rise coefficientj stagger angle

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Subscripts

al aluminiume erodedin initialle leading edgem meanmin minimumn normalp profiler radialR rotor

ref referencet total, tipte trailing edges secondary, stallz axialu tangentialCFD computational fluid dynamicsIGV inlet guide vane1, 2 inlet and outlet/exist of a blade row, at

impact and rebound from a surfacew working point (design point)

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