research article modeling of particle trajectory and...

Research ArticleModeling of Particle Trajectory and Erosion ofLarge Rotor Blades

Adel Ghenaiet

Faculty of Mechanical and Process Engineering University of Sciences and Technology (USTHB) BP 32 El-AliaBab-Ezzouar 16111 Algiers Algeria

Correspondence should be addressed to Adel Ghenaiet ag1964yahoocom

Received 5 July 2015 Revised 5 November 2015 Accepted 16 November 2015

Academic Editor Shaoping Wang

Copyright copy 2016 Adel GhenaietThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

When operating in hostile environments engines components are facing a serious problem of erosion leading to a drastic dropin aerodynamic performance and life-cycle This paper outlines the modeling and simulation of particle trajectory and erosioninduced by sand particles The governing equations of particle dynamics through the moving of large rotor blades are introducedand solved separately from the flow field by using our in-house particle tracking code based on the finite element method As thelocations of impacts are predicted the erosion is assessed by semiempirical correlations in terms of impact conditions and particleand target surface characteristics The results of these computations carried out for different concentrations of suspended dust(sand) cloud generated at takeoff conditions reveal the main areas of impacts with high rates of erosion seen over a large strip fromthe blade suction side around the leading edge and the pressure side of blade The assessment of the blade geometry deteriorationreveals that the upper corner of blade suffers from an intense erosion wear

1 Introduction

Aeroengines manipulating airflows laden by dust or volcanicash suffer from extreme erosion wear especially the frontcomponents Inevitably a great deal of dust generated by aground vortex that has the capability of picking up particlesfrom the ground enters the engine In addition the fine par-ticles of dust cloud generated by rotor turning remain sus-pended for a considerable time and when the blades movethey are continually bombarded by the entrained particles [1]In these circumstances erosion is often seen on the leadingedge as well as the aft of rotor blade body thus leading topremature stall and producing a sudden change in torque anda rise in required power [2]The role of erosion has been wellrecognized in turbomachinery applications where the dam-age is evident in pitting on the blade leading edge andtrailing edge and ensues in increased surface roughness [3]Predominantly in this context erosion by solid particles andother particulates have shown detrimental effects on theaerodynamics of blades and life-cycle One of themain effectsof deterioration and fault is the modification of compressor

and turbine performance maps [4] and subsequently thedegradation of engine performance

Sage and Tilly [5] were among the early researchers whoattempted to quantify the erosion in turbomachinery andsince the past decades this phenomenon has been the subjectof many analytical and experimental investigations Husseinand Tabakoff [6 7] were the first to examine the role of par-ticle material density and size on impacts locations andrebounds in 3D particle trajectory calculations through axialflow turbomachines Later Hamed and Fowler [8] demon-strated that within twisted vanes 3D particle trajectoriesare greatly influenced by the countering of hub and tip fordifferent particle sizes Hamed and Tabakoff [9] developeda methodology to predict blade surface erosion using thestatistical impact data computed from the particle trajectorysimulations and the correlations derived from erosion testresults which have been widely used in both axial and radialturbomachinery for automotive and gas turbine applications

Early studies on high-pressure compressors [10 11] andfans [12] atmospheric erosive regimes indicated that rotor-blade erosion occurred over the outer 50 of blade span

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2016 Article ID 7928347 15 pageshttpdxdoiorg10115520167928347

2 International Journal of Aerospace Engineering

X

Y

Z

(a)X

Y

Z

0793m

0910m

0145m

(b)

Figure 1 (a) Straight twisted four blades propeller (b) Spinner and blades

Balan and Tabakoff [11] studied experimentally the effectsof sand ingestion on an axial flow compressor and foundsevere erosion of blade leading edge which increased the flowincidence that shifted the pressure rise coefficient and effi-ciency Ghenaiet et al [12 13] found an increased tip to casingclearance and a reduction of blade chord in a high-speedaxial fan following sand ingestion and also noticed a 10drop in efficiency and pressure rise coefficient due to bladeleading edge blunting and erosive wear over the upper cornerof blade Hamed et al [14] have reviewed in the detail theerosion and deposition in turbomachinery and the associatedperformance degradation of both aeronautical and groundbased gas turbines More recently Ghenaiet [15] presentednumerical results of erosion through the front compressionstage of a turbofan revealing the impact frequency rates oferosion and critical areas of extreme erosion Also Schradeet al [16] investigated numerically and experimentally theerosive change of a compressor blade shape based on differentamounts of standardized Arizona test dust

According to the literature the study of erosion is stillchallenging due to numerous factors of complex interactioninfluencing the erosion process These include flow condi-tions geometry and material of blades impact conditionstype of erodent synergy of different erodents and exposuretime Moreover most of the researches concentrated oncompressors and turbines but propellers practically receivedless interest Therefore further studies of particle dynamicsand erosion facing open rotor blades (propellers) moresusceptible tomanipulate airflows laden by solid particles arerequired to foresee the critical areas prone to erosionwear andsubsequent blade shape deterioration As noticed hithertothere is no satisfactory protection for the leading edge evenwith stainless-steel coating [2]

This present study is a contribution to tackle the problemof erosion of large open rotor blades (propeller) at takeoff

operation For this purpose our in-house particle trackingcode [12 13 15] was adapted to this configuration of turbo-machinery The flow data were obtained separately and thenfollowed the computations of particle trajectories and thedetermination of locations and conditions of impacts whichserved in evaluating the erosion rates and in the assessment ofblade profile deterioration The obtained results consideringsand (quartz) particle (0ndash1000mm) depict erosion wear thatincreases with particle concentration and reveal the maineroded areas along the fore of blade suction side and leadingedge as well as the spinner

2 Case Study

This study concerns a model of straight twisted propeller(Figure 1(a)) with large four blades of a diameter equal to4117m made from aluminum alloy and operated by a singleshaft gas turbine running at a constant speed of 13820 rpm viaa gear box of a reduction ratio of 11352The overall length ofspinnermade from composite material (Figure 1(b)) is 091mand its maximum diameter is 0793m The 3D geometrywas reconstituted by stacking different profiles from root totip according to the measured blade twist At the takeoffoperation the blade setting angle is equal to 25 deg measuredbetween the blade chord and the tangential direction (at thereference radius 11987775) and the advance speed is equal to746ms (145 knots)

3 Computational Domain

The computational domain (Figure 2) contains a rotatingdomainmodeling one blade passage and a stationary domainconsisting of extended inlet and outlet domains and a topdomain over the propeller tip At the pitchwise sides ofthese domains the periodic boundary condition is used

International Journal of Aerospace Engineering 3

Periodic plane Inlet Outlet

Rotor blade

Zoom detail

Spinner

Periodic plane Periodic plane

Periodic plane

Topplane

Direction of flow

Figure 2 Full computational domain showing the rotor blade and the spinner and the boundary conditions

(a) (b) (c)

Figure 3 Grids of H type plotted from hub to tip meridional plane (a) and over hub and 11987775 planes (b c)

Many of the difficulties encountered when applying CFD toan open rotor (a propeller) arise due to removal of casingexisting in a conventional turbomachinery The distances atupstream and downstream of the rotating domain are takento sufficiently prevent any influence of the finite domainsize on the aerodynamic performance of rotor The mesh inthe radial direction was sufficiently extended to capture thepropeller stream-tube and tominimize the effects of the finitedomain size The locations of the rotating domain interfacesplanes and the distances upstream and downstream of thespinner are critical and have a strong influence upon flowsolution Accordingly the sizes of upstream downstreamand top domainswere examined to get a compromisewith theparticle trajectories computations that used the same gridsThe distances upstream and downstream of the blade weretaken as equal to 05119888 (119888 axial mean chord) and the extendeddistances for inlet outlet and top were equal to 15119863 25119863and 3119863 (119863 rotor diameter) respectively

The rotating domain was meshed by CFX-TurboGridwhereas the stationary domain used CFX-TASCgrid Multi-block H type meshes were generated (Figure 3) with denseclustering around the blade in order to guarantee a betterboundary layer resolution in addition to the refinements nearhub and tip The transition from the rotating to stationarydomain occurred with a smooth change of computation cellsto make sure that the conservative quantities are satisfiedAs far as the quality of the meshes was concerned someparameters have to be checked such as grid orthogonalitycharacterized by a skew angle (between vertices) between 15and 120 deg minimum positive volumes and cell aspect rationot exceeding 100 The effect of computational domain meshsize was investigated for both the rotating domain and thestationary separately To study the effect of propeller meshon the propulsive efficiency seven grids were used and thepropulsive efficiency was assessed The number of cells fromone grid to another was scaled by a factor of 105 in all


three directions As a conclusion about 450000 nodes wereselected for the rotor domain The influence of the meshsize of the stationary domain was explored by testing threedifferent grids Because of the computing time that mightincrease drastically for the third large grid size it was decidedto keep the first grid size of 350000 nodes for the stationarydomain

The adopted turbulence closure model for RANS equa-tions is the 119896-120596 model (Shear Stress Transport) with anautomatic near-wall treatment [17] This latter automaticallyswitches from wall functions to a low-Reynolds near-wallformulation as the mesh is refined but this cannot beguaranteed inmost applications at all walls and some regionsfor instance blade junction to hub This turbulence modelwas chosen for several reasons First the effects of free streamturbulence and surface roughness are easily included in themodel [18] Second the transition can be calculated usingthe low-Reynolds number version of the model [19] ThirdMenter has shown that this model does well for flows withadverse pressure gradients [20 21] Finally it should behavewell numerically since it avoids using the distance to thewall and the complicated damping functions requiring a highcomputer power Near walls nodes were positioned in sucha way that the value of 119910

+= 120588119910119901119906119905120583119891 119906119905= 119881119891radic1198912 (119881

119891is

flow velocity) and the friction factor is based on a flat plate119891 = 0025Reminus01428

119909 For an average value 119910

+= 40 the last

relation is simplified to 119910119901

= 35777119888Reminus092119888

based on anaverage blade chord and used to position the near-wall firstlines In order to cover regions of high Reynolds numberthe maximum flow velocity at the blade tip was used in theprevious relation

4 Flow Field Solution

Particle trajectory simulations through the components of aturbomachine are based on the numerical integration of par-ticle equations of motion which require the 3D flow solutionof the RANS (Reynolds averaged Navier-Stokes) equationsfor turbulent flows by means of CFD (computational fluiddynamics) tools In this study the flow solution used the codeCFX-TASCflow [17] which is a finite volume based solverA sliding interface is used to connect two regions together(different frames of reference) in order to account for thechange in the frame of reference and support steady-statepredictions in the local frame The interface sides must bea surface of revolution and sweep out the same surface ofrevolution and account internally for the pitch change byscaling up or down the local flows as they cross the inter-face The boundary conditions used are periodic boundariesapplied at one pitch of the blade whereas symmetry is appliedat the intersection planes joining on the axis of rotation Arotating wall at the speed of 107 rds is selected for the bladeand the spinner A constant total pressure of 1045414 Pa andtemperature 28815 K are applied at the inlet of the upstreamdomain whereas at the outlet a static pressure of 101300 Pais set at a single face near the top A free stream velocityof 746ms is set over the top domain At the inlet theturbulence intensity was set at 5 and a value of turbulentviscosity 120583

119905was evaluated using Wilcoxrsquos model [18 19]

The flow field within the blades is obtained in a relativeframe and assumed to be steady By adopting the approachof a frozen rotor the stationary and rotating frames havefixed positions during the calculations In the finite volumeapproach [17] all the diffusion terms are evaluated by sum-mation of the derivatives of the shape functionThe advectionterms are computed by using a linear profile scheme (LPS)and a mass weighted skew upstream differencing schemewhich incorporate the physical advection correction Initiallythe robust upwind scheme was used and then changed to alinear profile scheme for producing better results The localtime step was based on the tip blade chord and flow velocityTo ensure a good convergence two criteria were consideredan RMS residual less than 10minus5 and an imbalance in theconservation equations less than 10minus2 which are usually suffi-cient for an adequate convergence in most of the engineeringapplicationsThe RMS residual is the square root of the meanof all square residuals throughout the computational domainThe target imbalance for the conservation equations is usedto ensure that the global balances are met which is specifiedas the maximum fractional imbalance equal to the ratio ofthe subdomain imbalance and the maximum one over allsubdomains

As a result Figure 4 plots the vectors of flow velocity nearthe blade hub at 11987775 and blade tip showing an increase invelocity with blade span The relative flow velocity increasesfrom the blade leading edge till a critical point over thesuction side and afterwards tends to reduce toward the trail-ing edge As noticed the shape of spinner and its extendedcontour cause a flow blockage that increases the axial velocityand reduces the flow incidence onto the leading edge At thetakeoff operating regime the relative Mach number is shownto increase along the blade span (Figure 5) to reach highervalues beyond 11987775 but its value at blade tip does not exceed0712 Also the relative Mach number contours depict a wakearea expanding behind the blade As the static pressure overthe lower surface of blade is larger than at the upper oneand the surrounding the flow tends to curl as being forcedfrom a high-pressure region just underneath the tip of bladeto a low-pressure region As a result there is a spanwisecomponent of the flow from the tip toward the root causingthe flow streamlines at the upper surface to bend towardthe root Similarly on the lower surface there is a spanwisecomponent of flow from root to tip forcing the streamlines tobend towards the tip These two streams combine at trailingedge and the velocity difference causes the air to roll up intoa vortex just inboard This mechanism is observed in theformation of vortices (Figure 6) detaching from the blade tipto follow helicoidal flow paths in the same direction of bladerotation which later dissipateswith the downstreamdistance

5 Particle Dynamics

The basis for particle trajectory simulations in turbomachin-ery continues to be Eulerian and Lagrangian with one-waycoupling between the particles and flow The Lagrangianapproach considers the tracking of individual particles fromdifferent starting positions thus giving an ability to handlein more detail some physical aspects such as the interaction


2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Relat

ive fl

ow v

eloc

ity (m

s)

(a) (b) (c)

Figure 4 Relative flow velocity vectors (a) near hub (b) at 11987775 and (c) at blade tip

7124E minus 01

6768E minus 01

6411E minus 01

6055E minus 01

5699E minus 01

5343E minus 01

4987E minus 01

4630E minus 01

4274E minus 01

3918E minus 01

3562E minus 01

3205E minus 01

2849E minus 01

2493E minus 01

2137E minus 01

1781E minus 01

1424E minus 01

1068E minus 01

7124E minus 02

3562E minus 02

00000E + 00

Rela

tive M

ach

num

ber

(a) (b) (c)

Figure 5 Relative Mach number (a) near hub (b) at 11987775 and (c) at tip

2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Flow

velo

city

(ms

)

Y

XZ

Figure 6 Counter-rotating vortex downstream of the rotor blade


withwallsThis approach is somewhatmore economical sincethe effect of particle phase on the flow solution is neglected forvery low volume fractions

The particle trajectory equations are derived from thesuperposition of different involved forces but in most partic-ulate air flows the drag force is dominantThe general expres-sion for the drag coefficient 119862

119863is given (as below) according

to Haider and Levenspiel [22] for Reynolds number from001 to 26 times 10

5 For small Reynolds numbers (Re lt 05)the viscous effect is dominating and this is referred to as theStokes regime 119862

119863= 24Re The constants 119860 119861 119862 and 119863

depend on the particle shape

119863

=120587

81198892

119901120588119891119862119863

(997888rarr119881119891

minus997888rarr119881119901)10038161003816100381610038161003816

10038161003816100381610038161003816119891

10038161003816100381610038161003816minus

10038161003816100381610038161003816119901

10038161003816100381610038161003816

10038161003816100381610038161003816

119862119863

=24

Re119901

(1 + 119860Re119861119901) +

119862

(1 + 119863Re119901)

Re119901

=

120588119891

120583119891

119889119901

10038161003816100381610038161003816119891

minus 119901

10038161003816100381610038161003816

(1)

If a particle is sufficiently large and there is a large velocitygradient there will be a lift force called Saffman force dueto fluid shearing forces which depends on the particle basedReynolds number and the shear flow Reynolds number [23]as follows

119878=

120587120588119891

81198893

119901119862119871119878

(119891

minus 119901) times nabla

119891

119862119871119878

=41126

radicRe119878

119891 (Re119901Re119878)

Re119878=

120588119891

120583119891

1198892

119901

10038161003816100381610038161003816Ω119891

10038161003816100381610038161003816

(2)

The particle inertia forces namely the centrifugal and Cori-olis forces are derived from the second derivative of thevector position By considering the drag and Saffman forceas the main external forces the following set of second-ordernonlinear differential equations is derived

1205972119903119901

1205971199052= 119866 (119881

119891119903minus 119881119901119903

) + 119903119901(120596 +

119881119901120599

119903119901

)

2

+119865119878119903

119898119901

1205972120579119901

1205971199052= 119866

(119881119891120599

minus 119881119901120599

)

119903119901

minus 2

119881119901119903

119903119901

(120596 +

119881119901120599

119903119901

) +119865119878120599

119903119901119898119901

1205972119911119901

1205971199052= 119866 (119881

119891119911minus 119881119901119911

) +119865119878119911

119898119901

119866 =3

4119889119901

120588119891

120588119901

sdot 119862119863radic

10038161003816100381610038161003816119881119891119903

minus 119881119901119903

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891120599

minus 119881119901120599

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891119911

minus 119881119901119911

10038161003816100381610038161003816

2

(3)

Turbulence EffectThe fluctuating components correspondingto a particular eddy are obtained from the local turbulenceproperties Turbulence effect is assumed to prevail as long asthe particle-eddy interaction time (minimum between eddylifetime and transit time Brown and Hutchinson [24]) isless than the eddy lifetime The eddy lifetime and dissipationlength scale are estimated according to Shirolkar et al [25]

119905119890= 119860

119896

120576

119897119890=

11986111989632

120576

119860

119861= radic15

(4)

The transit time scale is estimated from a linearized form ofequation of motion given by Gosman and Ionnides [26]

119905119903= minus120591119901Ln[

[

1 minus119897119890

120591119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

997888rarr119881119891

100381610038161003816100381610038161003816minus

100381610038161003816100381610038161003816

997888rarr119881119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

]

]

120591119901

=

241205881199011198892

119901

18120583119891119862119863Re119901

(5)

BoundaryConditionsThe boundary conditions implementedin the particle trajectory code include the interface betweenstationary frame and rotating frame where the vector ofparticle velocity is decomposed into a tangential and a relativevelocityThe tangential component is modified by adding thecircumferential velocity while the other components remainthe same At the periodical lateral sides the velocity vectorcomponents are conserved while the tangential coordinateis modified by the angular shift At the axis of revolution(condition of symmetry) for the velocity vector a purereflection is used The impact physics is required to tracethe particle trajectory after an impact with a surface wherethe restitution coefficients (a measure of the kinetic energyexchange upon impact) are used to define variations in themagnitude and direction of a particle velocity The impactangle 120573

1is defined as the angle formed between the vector

velocity of a particle at an impact point and its tangentialcomponent In the course of particle trajectory computationthe restitution coefficients are estimated statistically basedon the experimental values of mean and standard deviation(Tabakoff et al [27]) given as polynomial regressions

1198811198752

1198811198751

=

4

sum

119894=0

119886119894120573119894

119894

1205731198752

1205731198751

=

4

sum

119894=0

119887119894120573119894

119894

(6)

Particle Distribution The particle mass rate was obtained bymultiplying the inlet air volume flow rate at the inlet bythe mean value of particle concentration The number andsizes of sand particles depend on the cumulative distribution


curve 0ndash1000 120583m (of mean diameter and variance equal to2374 120583mand 1645 120583m resp) and the specified concentrationprofile In the present simulations particle concentration wasvaried in between 10 and 500mgm3 As sand particles werereleased randomly with size distribution from 0 to 1000120583man iterative procedure involving particle number and sizein addition to the radial and circumferential seeding posi-tions was repeated until a convergence in the total mass ofparticles

Solving Procedure The flow data at the grids nodes were usedto interpolate for the local flow properties in the courseof particle trajectory integration based on the Runge-Kutta-Fehlberg seventh-order technique The integration time stepdepends on the computational cells sizes and the local flowvelocities However this time step is reduced within theintegration procedure to keep the leading truncation errorwithin the tolerance If a particle interacts with an eddy theinteraction time is considered as the effective time stepNear aboundary condition a more accurate time step is reevaluatedto get an impact within a half-diameter distance After animpact the restitution coefficients are used and the derivedparticle fragmentation factor (based on experiments by Tanand Elder [28]) is considered

The particle tracking algorithm is based on the finite ele-mentmethodwhich requires transforming a particle positioninto its local coordinates by solving nonlinear equations (7)If these values do not exceed unity that means the particle isstill in the same cell otherwise the algorithm starts to checkall surrounding cells and the cell increment for a specifieddirectrix is used to update the exact cell

119909119901

=

8

sum

119894=1

119873119894119909119894

119910119901

=

8

sum

119894=1

119873119894119910119894

119911119901

=

8

sum

119894=1

119873119894119911119894

(7)

6 Erosion Assessment

This later depends on the physical properties of target surfaceand erodent particle concentration and size and the velocityand angle of impact Finnie [29] attempted to develop thebasic theoretical analysis of sand erosion based on Hertzrsquoscontact theory but his model did not exactly predict theweight loss for high impact angles Bitter suggested themech-anism of sand erosion which consists of deformation wearand cuttingwear [30] Bitterrsquosmodel that accounts for erosionat all impact angles gives the sufficient prediction for both ofductile and brittle materials but it is too complex Neilsonand Gilchrist [31] modified Bitterrsquos model by assuming thatthe total erosion is an arithmetic combination of brittleand ductile contributions and thus erosion loss can be pre-dicted at intermediate impact angles However the resulting

equations are still complex as requiring experimentally deter-mined parameters The most successful erosion predictionmodel used in turbomachinery was developed by Grantand Tabakoff [32 33] based on erosion measurements of2024 aluminum alloy at particle speeds of 61ndash183ms andsand (quartz) as abrasive particles (20ndash200 micron) Thislatter is implementing two mechanisms one predominantat low impact angle and another at high impact angle asfollows

119864 = 1198701119891 (1205731) 1198812

1198751cos2120573

1(1 minus 119877

2

120579)

+ 1198703(1198811198751sin1205731)4

(8)

119891 (1205731) = 1 + 119862119870(119870

2sin 90

120573119900

1205731)

119862119870 =

1 1205731le 120573119900

0 1205731gt 120573119900

(9)

Erosion rate is expressed as the amount (milligram) of mate-rial removed per unit of mass (gram) of impacting particles119877120579is the tangential restitution factor derived from (6) the

unit of velocity should be in fts Thematerial constants1198701=

367 times 10minus6 1198702

= 0585 and 1198703

= 6 times 10minus12 and the angle

of maximum erosion 120573119900= 20 deg are available for aluminum

based alloyIt was shown by many authors that the erosion dam-

age increases with particle size up to some plateau valueFurther the influence of particle size on erosion is morepronounced at higher particle velocities [32] The effect ofparticle size was included to correct the predicted erosionrate based on semiempirical correlation (8) It should benoted that for the spinner made from a composite mate-rial the specific restitution coefficient and erosion correla-tion were adopted from the experiments due to Drensky etal [34]

The local values of mass erosion (milligram) are calcu-lated from the local erosion rates and then cumulated overa given mesh element surface 119860

119890in order to compute the

equivalent erosion rate expressed inmggcm2This latterwasinterpolated for the same node sharing the elements facesto get the nodal value distribution which served to plot thecontours of equivalent erosion rates

119864eq =1

119860119890sum119873119901

1119898119901119894

119873119901

sum

1

119898119901119894

119864119894 (10)

The depth of penetration per a unit of time for an elementface is calculated from the cumulative mass erosion of thegiven face For the elements sharing the same node thenodal values of penetration are estimated based on bilinearinterpolation As a result the new coordinates are evaluatedby knowing the normal vector and the depth of penetrationat the given nodeThe assessment of blade geometry deterio-ration in terms of percentages of averaged reduction in blade


(a) (b) (c) (d)

Figure 7 Sample of sand particle (10 120583m) trajectories (a) streamwise from hub to shroud (b) near the tip (c) downstream of rotor bladeand (d) downstream of rotor blade reflecting particles crossing over the blade tip

chord and blade thickness is based on the whole blade lengthas follows

(i) Average reduction in blade chord

Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)

(ii) Average reduction in blade thickness

Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)

7 Results and Discussion

The air and particles experience different degrees of turn-ing through the rotor blade depending on their sizes Thedeviations from air flow paths increase with particle inertiato provoke repeated impacts with the various surfaces ofrotor blade Figure 7 shows samples of simulated particletrajectories corresponding to small size particles for instance10 microns which tend to follow the flow paths closely(Figure 7(a)) along the blade passage from hub to shroudMany of them are shown to collide with the spinner withrepeated impacts At outer radii these particles are deviateddownward owing to the rotational flow structure emanatingfrom the tip and also because ofmoving from a rotating frameto a stationary one The other view around the blade neartip (Figure 7(b)) depicts small particles circulating aroundthe blade and many of them impact around the leadingedge and bounce closely to hit another time the suction sideDue to the formation of flow vortices (Figure 6) downstreamof the blade these tiny particles tend to follow a helicoidaltrajectory (Figure 7(c)) and are strongly influenced by theflow turbulence Detailed Figure 7(d) describes the trajec-tories of particles arriving toward the tip of blade showingparticles being entrained by the vortex and many others arecentrifuged outward from the blade tip

When inertia of particles becomes more important suchas the case of 250microns they deviate considerably from theflow streamlines as shown in Figure 8 Many of these largesize particles impact spinner wall (Figure 8(a)) and hence aredeflected upward to follow ballistic trajectories Also owingto high centrifugal forces imparted these particles are seen todeviate towards outer radii At exit from rotor and becauseof changing from a rotating frame to a stationary one thelarge particles are heavily deviated tangentially As seen inFigure 8(b) after hitting the fore part of suction side theseparticles are deflected and follow bowed trajectories DetailedFigure 8(c) depicts trajectories of large sand particles whenarriving around the outer blade radius they are shown to beentrained over the blade tip and receive high centrifugationprojecting them upward from the rotor Even for theseheavy particles some of them are being entrained by thevortex causing them to deviate downward (Figure 8(c)) aftercrossing the rotor

Figure 9 shows that all particle trajectories related to sizedistribution (0ndash1000120583m) released upstreamof the rotor com-bine all the features related to small and large size particlesLarge particles are shown to deviate upwards due to highimparted centrifugal forces as compared to the drag forceThese particles are accelerated in the axial direction and thenimpact the spinner to be largely deflected Sand particles aftercrossing the rotor blade are deviated considerably towards thetangential direction and are entrained by the vortex structurebehind the rotor blade

Figure 10 shows impacts induced by a reduced sample(for the sake of plots clarity) of sand particles of a randomsize distribution (0ndash1000 120583m) As revealed the region ofmaximum impact frequency and erosion rate appears on thehub portion and the spinner in addition to a large band at thefront suction side and the back of pressure side Figure 10(a)shows that a large number of particles tend to impact aroundthe leading edge of propeller blade and many others hit thesuction side over a large strip from the leading edge andbounce to reach the pressure side towards the mid of trailing


(a)

XY

Z

(b)

X

Y

Z

(c)

Figure 8 Sample of sand particle (250 120583m) trajectories (a) streamwise from hub to shroud (b) near the tip and (c) downstream of rotorblade reflecting particles crossing over the blade tip

808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)

Figure 9 Sample of sand (0ndash1000 120583m)particles trajectories crossingthe rotor blade

edge Also some particles are shown to impact around thetrailing edge from suction side Impacts on spinner areconcentrated on the fore part with a large crowd of particlesseen along suction side at blade junction and around leadingedge from both sides Large impact velocities (Figures 10(b)and 11(b)) reaching a velocity of 2235ms are predictedabove the upper part and around the leading edge from bothsides owing to high flow velocities and rotation effect Asconsequence the high local rates of erosion are observed overthe front part of suction side and around the leading edgefrom both sides (Figures 10(c) and 11(c)) The critical area ofpronounced erosion is seen over the tip corner Also thereare regions of impacts towards the trailing edge from bothsides

The impacts frequency the velocities and angles ofimpacts and their distribution over the impacted surfaces

strongly affect the erosion patterns estimated by semiem-pirical equation (8) The values of mass erosion (mg) atdiscrete points of an element face are calculated based onthe local erosion rates in mgg and cumulated to computethe equivalent erosion levels in mggcm2 Figures 12 and13 depict the equivalent erosion rates corresponding to alow concentration (10mgm3) and a high concentration(500mgm3) of sand particles All figures show noticeableerosion wear of the blade leading edge from the root to tiprelated to particles arriving at high velocity and also becauseof spanwise twist of the rotor blade that changed effectivelythe angle of particle incidence The areas of erosion wearare seen to expand towards the tip in a triangular patternwith a spot area over the tip corner On the blade pressureside erosion is seen from the leading edge in addition toa region of low erosion rates towards the trailing edge Onthe spinner there is a large spread of erosion but with lowrates Practically similar patterns of erosion are obtained foreach concentration but the local mass erosion rates differAs expected for this large rotor blade the actual equivalentrates of erosion are lower in comparison with for instancethe front stages of an axial compressor according to thenumerical results obtained by Ghenaiet [15] and this becauseof moderate flow velocity related to low rotational speed andthe relatively large blade size

The estimated mass erosion and blade geometry dete-rioration after one hour of sand ingestion are presented inTable 1 It is clear that the material removal and geometrychanges are related to the size and mass (concentration)of particles impacting the blade surfaces and duration ofexposure The eroded mass from the rotor blade and spin-ner (Figure 14) and the subsequent geometry deteriorationsestimated as percentages reductions of chord thicknessand blade length are plotted in Figure 15 depicting anincrease with concentration The erosion wear is manifestedby a drastic reduction in blade chord towards the tip and


Table 1 Erosion parameters and geometry deterioration of one blade after one hour

Erosion parametersDifferent concentrations (mgm3)

sand (0ndash1000 120583m)10 25 50 100 250 400 500

Sand particle rate (mgs) 253 632 1266 2528 6325 10124 12659Ingested mass of sand (g) 911812 2275119 4558279 910022 2276899 3644832 4557392Erosion of blade (mg) 32167 79376 156849 317950 782065 1265903 1573407Erosion of spinner (mg) 1595 3954 8252 16365 41326 66218 82361Reduction of chord at R75 () 2197119864 minus 03 634119864 minus 03 787119864 minus 03 162119864 minus 02 600119864 minus 02 01029 01183Reduction of chord at tip () 4449119864 minus 03 802119864 minus 03 128119864 minus 02 231119864 minus 02 762119864 minus 02 01111 01503Average reduction of R75 bladethickness () 1344119864 minus 02 4774119864 minus 02 8638119864 minus 02 1636119864 minus 01 3915119864 minus 01 6485119864 minus 01 8130119864 minus 01

Average reduction of tip bladethickness () 3621119864 minus 02 7169119864 minus 02 1335119864 minus 01 3766119864 minus 01 1365 1954 2321

Decrease of blade length () 196119864 minus 05 237119864 minus 05 304119864 minus 05 557119864 minus 05 140119864 minus 04 2071119864 minus 04 238119864 minus 04

Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)

Figure 10 Sample of local impacts on suction side (a) particles sizes (120583m) (b) impact velocities (ms) and (c) erosion rates (mgg)

Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)

Figure 11 Sample of local impacts on pressure side (a) particles sizes (120583m) (b) impact velocities (ms) and (c) erosion rates (mgg)


Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)

Figure 12 Equivalent erosion rates (mggcm2) at low concentration (10mgm3) (a) Suction side and (b) pressure side

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)

Figure 13 Equivalent erosion rates (mggcm2) at high concentration (500mgm3) (a) Suction side and (b) pressure side

a distortion (blunt) of leading edge which are generally themain sources in the aerodynamic performance degradationAccordingly the mass erosion of one blade increases withparticle concentration (between 10 and 500mgm3) from32167mg to 1573407mg as illustrated in Figure 14(a) Alsothe mass erosion of one quarter of spinner increases withparticle concentration (between 10 and 500mgm3) from1595mg to 82361mg but erosion is less important comparedto rotor which is well illustrated in Figure 14(b) The overallerosion rate is almost constant and has an average value of347 times 10

minus2mgg According to Table 1 and Figure 15(a) thereduction in blade length is from 196times 10minus5 to 238times 10minus4after one hour of sand ingestion for concentration between10 and 500mgm3 As seen in Figure 15(b) the blade chord atradius11987775 is reduced from 2197times10

minus3 to 01183 whereas

that at tip is from 4449 times 10minus3 to 01503 Moreover the

thickness at radius 11987775 is reduced from 1344 times 10minus2 to

08130 whereas that at tip is from 3621 times 10minus2 to 3321

as seen in Figure 15(c)As exhibited in Figure 16 the erosion phenomenon is

shown to distort the leading edge and reduce the chord andthickness of blade progressively beyond 40 span till the tipThe process of erosion wear is clearer over the fore part ofthe suction side for all blade sections and the thickness issubsequently reduced and even more towards the tip sectionErosion damage is especially evident on the outboard sectionsof the rotor blades where the tip approaches the sonic speed[1] In addition the distortion at leading edge affects the flowcirculation and moves the stagnation point which shouldalter the static pressure distribution and the aerodynamic


0 50 200100 300 400 500250 450350150

Concentration (mgm3)

0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)

Figure 14 Mass erosion (mg) after one hour of sand ingestion (a) blade and (b) spinner

quality of the upper part of blade and subsequently the pro-duced torque As the maximum propeller thrust is obtainedfrom 40 to 80 of blade span (R40ndashR80) there should be asubsequent drop in torque and performance coefficient to beevaluated in a next paper

8 Conclusion

The present paper provides a reasonable insight into theparticle dynamics and erosion of large blades propellers whenexposed to different concentrations of sand particles Tinyparticles are shown to circulate around the rotor blade andstick to the flow path and also impact around the leadingedge Downstream of blade these particles are deviated tan-gentially and follow helicoidal trajectories When inertia ofparticles becomes more important they deviate considerablyfrom the flow path as a result of high drag and centrifugationMany of these large particles impact the spinner and deflectto follow ballistic trajectories At exit from rotor they aredeviated tangentially and projected upward and many ofthem are entrained by the vortex and deviated downwardMultiple impacts are predicted around the blade leading edgedue to its direct exposure to incoming particles and oversuction side by particles arriving at high velocity and angleincidence Extreme erosion area is revealed over the outer halfof blade with blunting of the leading edge and thinning ofthe corner part of blade As the maximum propeller thrust isexpected to be from 40 to 80 of blade span a subsequentdrop in aerodynamic performance is related to this partThisinformation will in turn help to design propeller blades forminimum erosion and to envisage a coating for the criticalregions with a hard material

Nomenclature

119860 Area (m2)119860119890 Area of an element (m2)

119888 Chord (m)119862 Concentration (mgm3)119862119863 Drag coefficient

119862119871 Lift coefficient

119863 Diameter of rotor (m)119889 Diameter of particle (m)119890 Thickness (m)119864 Erosion rate (mgg)119864eq Equivalent erosion rate (mggcm2)119865 Force (N)ℎ Length or height of blade (m)119896 Turbulent kinetic energy (m2s2)1198701 1198702 1198703 Material constants

119897119890 Dissipation length scale

119898 Mass (kg)119873119894 Shape function

119873119901 Number of impacts on an element face

119875 Pressure (Pa)119903 Radius radial coordinate (m)11987775 Radius at 75 of blade lengthRe Reynolds number119905 Time (s)119905119890 Eddy lifetime (s)

119880 Peripheral velocity (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)119911 Axial coordinate (m)119909 119910 119911 Cartesian coordinates


0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500

Concentration (mgm3)Reduction of chord at R75Reduction of chord at tip

000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500

Concentration (mgm3)Average reduction of blade thickness at R75Average reduction of blade thickness at tip

00

05

15

10

20

25

Redu

ctio

n (

)

(c)

Figure 15 Blade geometry deteriorations with concentration after one hour of sand ingestion (a) reduction of length (b) reduction of chordand (c) reduction of thickness

Greek Letters

120573 Impact angle (deg)120576 Turbulence rate of dissipation (m2s3)120588 Density (kgm3)120583 Dynamic viscosity (kgmsdots)120596 Speed of rotation (rads)120579 Angular position (rad)120591119901 Relaxation time (s)

Subscript

av Average119863 Drag119891 Fluid119901 Particle119900 Related to maximum erosion119903 Radial120599 Tangential component


(a) (b)

Figure 16 Eroded profiles after one hour of sand ingestion of a concentration (500mgm3) (a) 11987775 profile (b) tip profile (dashed line is theinitial profile and solid line is the eroded profile)

119878 Saffman119911 Axial direction1 2 At impact and rebound from a surface

Abbreviations

CFD Computational fluid dynamicsRANS Reynolds averaged Navier-StokesLPS Linear profile scheme

Conflict of Interests

The author declares no conflict of interests

References

[1] T Warren S C Hong C-J Yu and E L RosenzweigldquoEnhanced erosion protection for rotor bladesrdquo in Proceedingsof the American Helicopter Society 65th Annual Forum pp2678ndash2686 Grapevine Tex USA May 2009

[2] P Brotherhood and D W Brown ldquoFlight measurements ofthe effects of simulated leading-edge erosion on helicopterblade stall torsional loads and performancerdquo Reports andMemoranda 3809 RAE Bedford UK 1976

[3] W Tabakoff AHamed andV Shanov ldquoBlade deterioration in agas turbine enginerdquo International Journal of RotatingMachineryvol 4 no 4 pp 233ndash241 1998

[4] M Morini M Pinelli P R Spina and M Venturini ldquoInfluenceof blade deterioration on compressor and turbine performancerdquoASME Journal of Engineering for Gas Turbines and Power vol132 no 3 Article ID 032401 11 pages 2009

[5] W Sage and G P Tilly ldquoThe significance of particles sizes insand erosion of small gas turbinesrdquo The Royal AeronauticalSociety Journal vol 73 pp 427ndash428 1969

[6] M F Hussein and W Tabakoff ldquoDynamic behavior of solidparticles suspended by polluted flow in a turbine stagerdquo Journalof Aircraft vol 10 no 7 pp 434ndash440 1973

[7] M F Hussein and W Tabakoff ldquoComputation and plotting ofsolid particle flow in rotating cascadesrdquoComputersampFluids vol2 no 1 pp 1ndash15 1974

[8] A Hamed and S Fowler ldquoErosion pattern of twisted blades byparticle laden flowsrdquo Journal of Engineering for Power vol 105no 4 pp 839ndash843 1983

[9] A Hamed and W Tabakoff ldquoExperimental and numericalsimulations of the effects of ingested particles in gas turbineenginesrdquo Tech Rep AGARD-CP-558 Erosion Corrosion andForeign Object Effects in Gas Turbines 1994

[10] G P Sallee H D Kruckenburg and E H Toomey ldquoAnalysisof turbofan engine performance deterioration and proposedfollow-on testsrdquo Tech Rep NASA-CR-134769 1978

[11] C Balan andW Tabakoff ldquoAxial compressor performance dete-riorationrdquo inProceedings of the 20th Joint PropulsionConferencevol No ofAIAA Paper no 84-1208 Cincinnati Ohio USA June1984

[12] A Ghenaiet R L Elder and S C Tan ldquoParticles trajectoriesthrough an axial fan and performance degradation due to sandingestionrdquo in Proceedings of the ASME Turbo Expo Power forLand Sea and Air ASME Paper 2001-GT-0497 12 pages NewOrleans La USA June 2001

[13] A Ghenaiet S C Tan and R L Elder ldquoNumerical simulationof the axial fan performance degradation due to sand ingestionrdquoin Proceedings of the ASME Turbo Expo Power for LandSea and Air ASME Paper no GT2002-30644 pp 1181ndash1190Amsterdam The Netherlands June 2002

[14] A HamedW Tabakoff and RWenglarz ldquoErosion and deposi-tion in turbomachineryrdquoAIAA Journal of Propulsion and Powervol 22 no 2 pp 350ndash360 2006


[15] A Ghenaiet ldquoStudy of sand particle trajectories and erosioninto the first compression stage of a turbofanrdquo Journal of Tur-bomachinery vol 134 no 5 Article ID 051025 17 pages 2012

[16] M Schrade S Staudacher and M Voigt ldquoExperimental andnumerical investigation of erosive change of shape for high-pressure compressorsrdquo in Proceedings of the ASME Turbo ExpoTurbine Technical Conference and Exposition ASME PaperGT2015-42061 9 pages Montreal Canada June 2015

[17] CFX-TASCflow Version 211 AEA Technology EngineeringSoftware Ltd 2001

[18] D C Wilcox Turbulence Modeling for CFD DCW IndustriesLa Canada Calif USA 1994

[19] D C Wilcox ldquoSimulation of transition with a two-equationturbulence modelrdquo AIAA Journal vol 32 no 2 pp 247ndash2551994

[20] F R Menter ldquoPerformance of popular turbulence models forattached and separated adverse pressure gradient flowsrdquo AIAAJournal vol 30 no 8 pp 2066ndash2072 1992

[21] F RMenter ldquoImproved two-equation k-120596 turbulencemodel foraerodynamic flowsrdquo NASA TM-103975 1992

[22] A Haider and O Levenspiel ldquoDrag coefficient and terminalvelocity of spherical and nonspherical particlesrdquo Powder Tech-nology vol 58 no 1 pp 63ndash70 1989

[23] M Sommerfeld Theoretical and Experimental Modeling ofParticulate FlowmdashOverview and Fundamentals VKI LectureSeries Von Karman Institute Brussels Belgium 2000

[24] D J Brown and P Hutchinson ldquoThe interaction of solid orliquid particles and turbulent fluid flow fieldsmdasha numericalsimulationrdquo Journal of Fluids Engineering vol 101 no 2 pp265ndash269 1979

[25] J S Shirolkar C F M Coimbra and M Q McQuay ldquoFun-damental aspects of modeling turbulent particle dispersion indilute flowsrdquo Progress in Energy and Combustion Science vol22 no 4 pp 363ndash399 1996

[26] A D Gosman and E Ionnides ldquoAspects of computer simu-lation of liquid fuelled combustorsrdquo in Proceedings of the 19thAerospace Science Meeting AIAA 81-0323 St Louis Mo USAJanuary 1981

[27] W Tabakoff A Hamed and D M Murugan ldquoEffect of targetmaterials on the particle restitution characteristics for turbo-machinery applicationrdquo Journal of Propulsion and Power vol12 no 2 pp 260ndash266 1996

[28] S C Tan and R L Elder ldquoAssessment of particle rebounds andfragmentation characteristicsrdquo Progress Report Cranfield Uni-versity 1992

[29] I Finnie ldquoErosion of surfaces by solid particlesrdquo Wear vol 3no 2 pp 87ndash103 1960

[30] J G A Bitter ldquoA study of erosion phenomena Part IIrdquo Wearvol 6 no 3 pp 169ndash190 1963

[31] J H Neilson and A Gilchrist ldquoErosion by a stream of solidparticlesrdquoWear vol 11 no 2 pp 111ndash122 1968

[32] G Grant andW Tabakoff ldquoErosion prediction in turbomachin-ery due to environmental solid particlesrdquo in Proceedings of the12th AIAA Aerospace Sciences Meeting AIAA Paper no 74-16Washington DC USA January-February 1974

[33] G Grant andW Tabakoff ldquoErosion prediction in turbomachin-ery resulting from environmental solid particlesrdquoAIAA Journalof Aircraft vol 12 no 5 pp 471ndash478 1975

[34] G Drensky A HamedW Tabakoff and J Abot ldquoExperimentalinvestigation of polymer matrix reinforced composite erosioncharacteristicsrdquoWear vol 270 no 3-4 pp 146ndash151 2011

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Civil EngineeringAdvances in

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



X

Y

Z

(a)X

Y

Z

0793m

0910m

0145m

(b)

Figure 1 (a) Straight twisted four blades propeller (b) Spinner and blades

Balan and Tabakoff [11] studied experimentally the effectsof sand ingestion on an axial flow compressor and foundsevere erosion of blade leading edge which increased the flowincidence that shifted the pressure rise coefficient and effi-ciency Ghenaiet et al [12 13] found an increased tip to casingclearance and a reduction of blade chord in a high-speedaxial fan following sand ingestion and also noticed a 10drop in efficiency and pressure rise coefficient due to bladeleading edge blunting and erosive wear over the upper cornerof blade Hamed et al [14] have reviewed in the detail theerosion and deposition in turbomachinery and the associatedperformance degradation of both aeronautical and groundbased gas turbines More recently Ghenaiet [15] presentednumerical results of erosion through the front compressionstage of a turbofan revealing the impact frequency rates oferosion and critical areas of extreme erosion Also Schradeet al [16] investigated numerically and experimentally theerosive change of a compressor blade shape based on differentamounts of standardized Arizona test dust

According to the literature the study of erosion is stillchallenging due to numerous factors of complex interactioninfluencing the erosion process These include flow condi-tions geometry and material of blades impact conditionstype of erodent synergy of different erodents and exposuretime Moreover most of the researches concentrated oncompressors and turbines but propellers practically receivedless interest Therefore further studies of particle dynamicsand erosion facing open rotor blades (propellers) moresusceptible tomanipulate airflows laden by solid particles arerequired to foresee the critical areas prone to erosionwear andsubsequent blade shape deterioration As noticed hithertothere is no satisfactory protection for the leading edge evenwith stainless-steel coating [2]

This present study is a contribution to tackle the problemof erosion of large open rotor blades (propeller) at takeoff

operation For this purpose our in-house particle trackingcode [12 13 15] was adapted to this configuration of turbo-machinery The flow data were obtained separately and thenfollowed the computations of particle trajectories and thedetermination of locations and conditions of impacts whichserved in evaluating the erosion rates and in the assessment ofblade profile deterioration The obtained results consideringsand (quartz) particle (0ndash1000mm) depict erosion wear thatincreases with particle concentration and reveal the maineroded areas along the fore of blade suction side and leadingedge as well as the spinner

2 Case Study

This study concerns a model of straight twisted propeller(Figure 1(a)) with large four blades of a diameter equal to4117m made from aluminum alloy and operated by a singleshaft gas turbine running at a constant speed of 13820 rpm viaa gear box of a reduction ratio of 11352The overall length ofspinnermade from composite material (Figure 1(b)) is 091mand its maximum diameter is 0793m The 3D geometrywas reconstituted by stacking different profiles from root totip according to the measured blade twist At the takeoffoperation the blade setting angle is equal to 25 deg measuredbetween the blade chord and the tangential direction (at thereference radius 11987775) and the advance speed is equal to746ms (145 knots)

3 Computational Domain

The computational domain (Figure 2) contains a rotatingdomainmodeling one blade passage and a stationary domainconsisting of extended inlet and outlet domains and a topdomain over the propeller tip At the pitchwise sides ofthese domains the periodic boundary condition is used



Rotor blade

Zoom detail

Spinner


Periodic plane

Topplane

Direction of flow


(a) (b) (c)







+= 120588119910119901119906119905120583119891 119906119905= 119881119891radic1198912 (119881

119891is



+= 40 the last


= 35777119888Reminus092119888







5 Particle Dynamics



2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Relat

ive fl

ow v

eloc

ity (m

s)

(a) (b) (c)


7124E minus 01

6768E minus 01

6411E minus 01

6055E minus 01

5699E minus 01

5343E minus 01

4987E minus 01

4630E minus 01

4274E minus 01

3918E minus 01

3562E minus 01

3205E minus 01

2849E minus 01

2493E minus 01

2137E minus 01

1781E minus 01

1424E minus 01

1068E minus 01

7124E minus 02

3562E minus 02

00000E + 00

Rela

tive M

ach

num

ber

(a) (b) (c)


2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Flow

velo

city

(ms

)

Y

XZ










119863

=120587

81198892

119901120588119891119862119863

(997888rarr119881119891

minus997888rarr119881119901)10038161003816100381610038161003816

10038161003816100381610038161003816119891

10038161003816100381610038161003816minus

10038161003816100381610038161003816119901

10038161003816100381610038161003816

10038161003816100381610038161003816

119862119863

=24

Re119901

(1 + 119860Re119861119901) +

119862

(1 + 119863Re119901)

Re119901

=

120588119891

120583119891

119889119901

10038161003816100381610038161003816119891

minus 119901

10038161003816100381610038161003816

(1)


119878=

120587120588119891

81198893

119901119862119871119878

(119891


119891

119862119871119878

=41126

radicRe119878

119891 (Re119901Re119878)

Re119878=

120588119891

120583119891

1198892

119901

10038161003816100381610038161003816Ω119891

10038161003816100381610038161003816

(2)


1205972119903119901

1205971199052= 119866 (119881

119891119903minus 119881119901119903

) + 119903119901(120596 +

119881119901120599

119903119901

)

2

+119865119878119903

119898119901

1205972120579119901

1205971199052= 119866

(119881119891120599

minus 119881119901120599

)

119903119901

minus 2

119881119901119903

119903119901

(120596 +

119881119901120599

119903119901

) +119865119878120599

119903119901119898119901

1205972119911119901

1205971199052= 119866 (119881

119891119911minus 119881119901119911

) +119865119878119911

119898119901

119866 =3

4119889119901

120588119891

120588119901


10038161003816100381610038161003816119881119891119903

minus 119881119901119903

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891120599

minus 119881119901120599

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891119911

minus 119881119901119911

10038161003816100381610038161003816

2

(3)


119905119890= 119860

119896

120576

119897119890=

11986111989632

120576

119860

119861= radic15

(4)


119905119903= minus120591119901Ln[

[

1 minus119897119890

120591119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

997888rarr119881119891

100381610038161003816100381610038161003816minus

100381610038161003816100381610038161003816

997888rarr119881119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

]

]

120591119901

=

241205881199011198892

119901

18120583119891119862119863Re119901

(5)




1198811198752

1198811198751

=

4

sum

119894=0

119886119894120573119894

119894

1205731198752

1205731198751

=

4

sum

119894=0

119887119894120573119894

119894

(6)






119909119901

=

8

sum

119894=1

119873119894119909119894

119910119901

=

8

sum

119894=1

119873119894119910119894

119911119901

=

8

sum

119894=1

119873119894119911119894

(7)




119864 = 1198701119891 (1205731) 1198812

1198751cos2120573

1(1 minus 119877

2

120579)

+ 1198703(1198811198751sin1205731)4

(8)

119891 (1205731) = 1 + 119862119870(119870

2sin 90

120573119900

1205731)

119862119870 =

1 1205731le 120573119900

0 1205731gt 120573119900

(9)



367 times 10minus6 1198702

= 0585 and 1198703








119864eq =1

119860119890sum119873119901

1119898119901119894

119873119901

sum

1

119898119901119894

119864119894 (10)



(a) (b) (c) (d)




Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)


Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)







(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Rotor blade

Zoom detail

Spinner


Periodic plane

Topplane

Direction of flow


(a) (b) (c)







+= 120588119910119901119906119905120583119891 119906119905= 119881119891radic1198912 (119881

119891is



+= 40 the last


= 35777119888Reminus092119888







5 Particle Dynamics



2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Relat

ive fl

ow v

eloc

ity (m

s)

(a) (b) (c)


7124E minus 01

6768E minus 01

6411E minus 01

6055E minus 01

5699E minus 01

5343E minus 01

4987E minus 01

4630E minus 01

4274E minus 01

3918E minus 01

3562E minus 01

3205E minus 01

2849E minus 01

2493E minus 01

2137E minus 01

1781E minus 01

1424E minus 01

1068E minus 01

7124E minus 02

3562E minus 02

00000E + 00

Rela

tive M

ach

num

ber

(a) (b) (c)


2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Flow

velo

city

(ms

)

Y

XZ










119863

=120587

81198892

119901120588119891119862119863

(997888rarr119881119891

minus997888rarr119881119901)10038161003816100381610038161003816

10038161003816100381610038161003816119891

10038161003816100381610038161003816minus

10038161003816100381610038161003816119901

10038161003816100381610038161003816

10038161003816100381610038161003816

119862119863

=24

Re119901

(1 + 119860Re119861119901) +

119862

(1 + 119863Re119901)

Re119901

=

120588119891

120583119891

119889119901

10038161003816100381610038161003816119891

minus 119901

10038161003816100381610038161003816

(1)


119878=

120587120588119891

81198893

119901119862119871119878

(119891


119891

119862119871119878

=41126

radicRe119878

119891 (Re119901Re119878)

Re119878=

120588119891

120583119891

1198892

119901

10038161003816100381610038161003816Ω119891

10038161003816100381610038161003816

(2)


1205972119903119901

1205971199052= 119866 (119881

119891119903minus 119881119901119903

) + 119903119901(120596 +

119881119901120599

119903119901

)

2

+119865119878119903

119898119901

1205972120579119901

1205971199052= 119866

(119881119891120599

minus 119881119901120599

)

119903119901

minus 2

119881119901119903

119903119901

(120596 +

119881119901120599

119903119901

) +119865119878120599

119903119901119898119901

1205972119911119901

1205971199052= 119866 (119881

119891119911minus 119881119901119911

) +119865119878119911

119898119901

119866 =3

4119889119901

120588119891

120588119901


10038161003816100381610038161003816119881119891119903

minus 119881119901119903

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891120599

minus 119881119901120599

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891119911

minus 119881119901119911

10038161003816100381610038161003816

2

(3)


119905119890= 119860

119896

120576

119897119890=

11986111989632

120576

119860

119861= radic15

(4)


119905119903= minus120591119901Ln[

[

1 minus119897119890

120591119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

997888rarr119881119891

100381610038161003816100381610038161003816minus

100381610038161003816100381610038161003816

997888rarr119881119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

]

]

120591119901

=

241205881199011198892

119901

18120583119891119862119863Re119901

(5)




1198811198752

1198811198751

=

4

sum

119894=0

119886119894120573119894

119894

1205731198752

1205731198751

=

4

sum

119894=0

119887119894120573119894

119894

(6)






119909119901

=

8

sum

119894=1

119873119894119909119894

119910119901

=

8

sum

119894=1

119873119894119910119894

119911119901

=

8

sum

119894=1

119873119894119911119894

(7)




119864 = 1198701119891 (1205731) 1198812

1198751cos2120573

1(1 minus 119877

2

120579)

+ 1198703(1198811198751sin1205731)4

(8)

119891 (1205731) = 1 + 119862119870(119870

2sin 90

120573119900

1205731)

119862119870 =

1 1205731le 120573119900

0 1205731gt 120573119900

(9)



367 times 10minus6 1198702

= 0585 and 1198703








119864eq =1

119860119890sum119873119901

1119898119901119894

119873119901

sum

1

119898119901119894

119864119894 (10)



(a) (b) (c) (d)




Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)


Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)







(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












+= 120588119910119901119906119905120583119891 119906119905= 119881119891radic1198912 (119881

119891is



+= 40 the last


= 35777119888Reminus092119888







5 Particle Dynamics



2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Relat

ive fl

ow v

eloc

ity (m

s)

(a) (b) (c)


7124E minus 01

6768E minus 01

6411E minus 01

6055E minus 01

5699E minus 01

5343E minus 01

4987E minus 01

4630E minus 01

4274E minus 01

3918E minus 01

3562E minus 01

3205E minus 01

2849E minus 01

2493E minus 01

2137E minus 01

1781E minus 01

1424E minus 01

1068E minus 01

7124E minus 02

3562E minus 02

00000E + 00

Rela

tive M

ach

num

ber

(a) (b) (c)


2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Flow

velo

city

(ms

)

Y

XZ










119863

=120587

81198892

119901120588119891119862119863

(997888rarr119881119891

minus997888rarr119881119901)10038161003816100381610038161003816

10038161003816100381610038161003816119891

10038161003816100381610038161003816minus

10038161003816100381610038161003816119901

10038161003816100381610038161003816

10038161003816100381610038161003816

119862119863

=24

Re119901

(1 + 119860Re119861119901) +

119862

(1 + 119863Re119901)

Re119901

=

120588119891

120583119891

119889119901

10038161003816100381610038161003816119891

minus 119901

10038161003816100381610038161003816

(1)


119878=

120587120588119891

81198893

119901119862119871119878

(119891


119891

119862119871119878

=41126

radicRe119878

119891 (Re119901Re119878)

Re119878=

120588119891

120583119891

1198892

119901

10038161003816100381610038161003816Ω119891

10038161003816100381610038161003816

(2)


1205972119903119901

1205971199052= 119866 (119881

119891119903minus 119881119901119903

) + 119903119901(120596 +

119881119901120599

119903119901

)

2

+119865119878119903

119898119901

1205972120579119901

1205971199052= 119866

(119881119891120599

minus 119881119901120599

)

119903119901

minus 2

119881119901119903

119903119901

(120596 +

119881119901120599

119903119901

) +119865119878120599

119903119901119898119901

1205972119911119901

1205971199052= 119866 (119881

119891119911minus 119881119901119911

) +119865119878119911

119898119901

119866 =3

4119889119901

120588119891

120588119901


10038161003816100381610038161003816119881119891119903

minus 119881119901119903

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891120599

minus 119881119901120599

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891119911

minus 119881119901119911

10038161003816100381610038161003816

2

(3)


119905119890= 119860

119896

120576

119897119890=

11986111989632

120576

119860

119861= radic15

(4)


119905119903= minus120591119901Ln[

[

1 minus119897119890

120591119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

997888rarr119881119891

100381610038161003816100381610038161003816minus

100381610038161003816100381610038161003816

997888rarr119881119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

]

]

120591119901

=

241205881199011198892

119901

18120583119891119862119863Re119901

(5)




1198811198752

1198811198751

=

4

sum

119894=0

119886119894120573119894

119894

1205731198752

1205731198751

=

4

sum

119894=0

119887119894120573119894

119894

(6)






119909119901

=

8

sum

119894=1

119873119894119909119894

119910119901

=

8

sum

119894=1

119873119894119910119894

119911119901

=

8

sum

119894=1

119873119894119911119894

(7)




119864 = 1198701119891 (1205731) 1198812

1198751cos2120573

1(1 minus 119877

2

120579)

+ 1198703(1198811198751sin1205731)4

(8)

119891 (1205731) = 1 + 119862119870(119870

2sin 90

120573119900

1205731)

119862119870 =

1 1205731le 120573119900

0 1205731gt 120573119900

(9)



367 times 10minus6 1198702

= 0585 and 1198703








119864eq =1

119860119890sum119873119901

1119898119901119894

119873119901

sum

1

119898119901119894

119864119894 (10)



(a) (b) (c) (d)




Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)


Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)







(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Relat

ive fl

ow v

eloc

ity (m

s)

(a) (b) (c)


7124E minus 01

6768E minus 01

6411E minus 01

6055E minus 01

5699E minus 01

5343E minus 01

4987E minus 01

4630E minus 01

4274E minus 01

3918E minus 01

3562E minus 01

3205E minus 01

2849E minus 01

2493E minus 01

2137E minus 01

1781E minus 01

1424E minus 01

1068E minus 01

7124E minus 02

3562E minus 02

00000E + 00

Rela

tive M

ach

num

ber

(a) (b) (c)


2461E + 02

2338E + 02

2215E + 02

2092E + 02

1969E + 02

1846E + 02

1723E + 02

1599E + 02

1476E + 02

1353E + 02

1230E + 02

1107E + 02

9846E + 01

8615E + 01

7384E + 01

6153E + 01

4923E + 01

3692E + 01

2461E + 01

1230E + 01

9999E minus 11

Flow

velo

city

(ms

)

Y

XZ










119863

=120587

81198892

119901120588119891119862119863

(997888rarr119881119891

minus997888rarr119881119901)10038161003816100381610038161003816

10038161003816100381610038161003816119891

10038161003816100381610038161003816minus

10038161003816100381610038161003816119901

10038161003816100381610038161003816

10038161003816100381610038161003816

119862119863

=24

Re119901

(1 + 119860Re119861119901) +

119862

(1 + 119863Re119901)

Re119901

=

120588119891

120583119891

119889119901

10038161003816100381610038161003816119891

minus 119901

10038161003816100381610038161003816

(1)


119878=

120587120588119891

81198893

119901119862119871119878

(119891


119891

119862119871119878

=41126

radicRe119878

119891 (Re119901Re119878)

Re119878=

120588119891

120583119891

1198892

119901

10038161003816100381610038161003816Ω119891

10038161003816100381610038161003816

(2)


1205972119903119901

1205971199052= 119866 (119881

119891119903minus 119881119901119903

) + 119903119901(120596 +

119881119901120599

119903119901

)

2

+119865119878119903

119898119901

1205972120579119901

1205971199052= 119866

(119881119891120599

minus 119881119901120599

)

119903119901

minus 2

119881119901119903

119903119901

(120596 +

119881119901120599

119903119901

) +119865119878120599

119903119901119898119901

1205972119911119901

1205971199052= 119866 (119881

119891119911minus 119881119901119911

) +119865119878119911

119898119901

119866 =3

4119889119901

120588119891

120588119901


10038161003816100381610038161003816119881119891119903

minus 119881119901119903

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891120599

minus 119881119901120599

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891119911

minus 119881119901119911

10038161003816100381610038161003816

2

(3)


119905119890= 119860

119896

120576

119897119890=

11986111989632

120576

119860

119861= radic15

(4)


119905119903= minus120591119901Ln[

[

1 minus119897119890

120591119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

997888rarr119881119891

100381610038161003816100381610038161003816minus

100381610038161003816100381610038161003816

997888rarr119881119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

]

]

120591119901

=

241205881199011198892

119901

18120583119891119862119863Re119901

(5)




1198811198752

1198811198751

=

4

sum

119894=0

119886119894120573119894

119894

1205731198752

1205731198751

=

4

sum

119894=0

119887119894120573119894

119894

(6)






119909119901

=

8

sum

119894=1

119873119894119909119894

119910119901

=

8

sum

119894=1

119873119894119910119894

119911119901

=

8

sum

119894=1

119873119894119911119894

(7)




119864 = 1198701119891 (1205731) 1198812

1198751cos2120573

1(1 minus 119877

2

120579)

+ 1198703(1198811198751sin1205731)4

(8)

119891 (1205731) = 1 + 119862119870(119870

2sin 90

120573119900

1205731)

119862119870 =

1 1205731le 120573119900

0 1205731gt 120573119900

(9)



367 times 10minus6 1198702

= 0585 and 1198703








119864eq =1

119860119890sum119873119901

1119898119901119894

119873119901

sum

1

119898119901119894

119864119894 (10)



(a) (b) (c) (d)




Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)


Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)







(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















119863

=120587

81198892

119901120588119891119862119863

(997888rarr119881119891

minus997888rarr119881119901)10038161003816100381610038161003816

10038161003816100381610038161003816119891

10038161003816100381610038161003816minus

10038161003816100381610038161003816119901

10038161003816100381610038161003816

10038161003816100381610038161003816

119862119863

=24

Re119901

(1 + 119860Re119861119901) +

119862

(1 + 119863Re119901)

Re119901

=

120588119891

120583119891

119889119901

10038161003816100381610038161003816119891

minus 119901

10038161003816100381610038161003816

(1)


119878=

120587120588119891

81198893

119901119862119871119878

(119891


119891

119862119871119878

=41126

radicRe119878

119891 (Re119901Re119878)

Re119878=

120588119891

120583119891

1198892

119901

10038161003816100381610038161003816Ω119891

10038161003816100381610038161003816

(2)


1205972119903119901

1205971199052= 119866 (119881

119891119903minus 119881119901119903

) + 119903119901(120596 +

119881119901120599

119903119901

)

2

+119865119878119903

119898119901

1205972120579119901

1205971199052= 119866

(119881119891120599

minus 119881119901120599

)

119903119901

minus 2

119881119901119903

119903119901

(120596 +

119881119901120599

119903119901

) +119865119878120599

119903119901119898119901

1205972119911119901

1205971199052= 119866 (119881

119891119911minus 119881119901119911

) +119865119878119911

119898119901

119866 =3

4119889119901

120588119891

120588119901


10038161003816100381610038161003816119881119891119903

minus 119881119901119903

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891120599

minus 119881119901120599

10038161003816100381610038161003816

2

+10038161003816100381610038161003816119881119891119911

minus 119881119901119911

10038161003816100381610038161003816

2

(3)


119905119890= 119860

119896

120576

119897119890=

11986111989632

120576

119860

119861= radic15

(4)


119905119903= minus120591119901Ln[

[

1 minus119897119890

120591119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

997888rarr119881119891

100381610038161003816100381610038161003816minus

100381610038161003816100381610038161003816

997888rarr119881119901

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

]

]

120591119901

=

241205881199011198892

119901

18120583119891119862119863Re119901

(5)




1198811198752

1198811198751

=

4

sum

119894=0

119886119894120573119894

119894

1205731198752

1205731198751

=

4

sum

119894=0

119887119894120573119894

119894

(6)






119909119901

=

8

sum

119894=1

119873119894119909119894

119910119901

=

8

sum

119894=1

119873119894119910119894

119911119901

=

8

sum

119894=1

119873119894119911119894

(7)




119864 = 1198701119891 (1205731) 1198812

1198751cos2120573

1(1 minus 119877

2

120579)

+ 1198703(1198811198751sin1205731)4

(8)

119891 (1205731) = 1 + 119862119870(119870

2sin 90

120573119900

1205731)

119862119870 =

1 1205731le 120573119900

0 1205731gt 120573119900

(9)



367 times 10minus6 1198702

= 0585 and 1198703








119864eq =1

119860119890sum119873119901

1119898119901119894

119873119901

sum

1

119898119901119894

119864119894 (10)



(a) (b) (c) (d)




Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)


Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)







(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119909119901

=

8

sum

119894=1

119873119894119909119894

119910119901

=

8

sum

119894=1

119873119894119910119894

119911119901

=

8

sum

119894=1

119873119894119911119894

(7)




119864 = 1198701119891 (1205731) 1198812

1198751cos2120573

1(1 minus 119877

2

120579)

+ 1198703(1198811198751sin1205731)4

(8)

119891 (1205731) = 1 + 119862119870(119870

2sin 90

120573119900

1205731)

119862119870 =

1 1205731le 120573119900

0 1205731gt 120573119900

(9)



367 times 10minus6 1198702

= 0585 and 1198703








119864eq =1

119860119890sum119873119901

1119898119901119894

119873119901

sum

1

119898119901119894

119864119894 (10)



(a) (b) (c) (d)




Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)


Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)







(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c) (d)




Δ119888av () = 100[

[

1 minus1

119888avℎ

119898

sum

119895=1

120575119888119895sdot 120575ℎ119895

]

]

(11)


Δ119890av () = 100[

[

1 minus1

119890avℎ

119898

sum

119895=1

1

119888119895

119899

sum

119894=1

120575119890 sdot 120575119888119894

]

]

(12)







(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

XY

Z

(b)

X

Y

Z

(c)


808

735

663

590

517

445

372

299

227

154

81

8

Size

(mic

ron)









sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












sand (0ndash1000 120583m)10 25 50 100 250 400 500




Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

LEY

X

Z

(b)

Eros

ion

rate

(mg

g)

26

23

20

17

14

11

09

06

03

00

LEY

X

Z

(c)


Size

(mic

ron)

7567

6738

5908

5078

4249

3419

2589

1759

930

100

LEY

X

Z

(a)

LEY

XZ

Impa

ct v

eloci

ty (m

s)

2235

1987

1738

1490

1242

993

745

497

249

00

(b)

LEY

X

Z

Eros

ion

rate

(mg

g)26

23

20

17

14

11

09

06

03

00

(c)



Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(a)

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

1476

1265

1054

844

633

422

211

000

LE

Y

X

Z

(b)


1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(a)

1220

174

349

523

697

871

1045

000

Equi

vale

nt er

osio

n ra

te (m

gg

cm2)

LE

Y

X

Z

(b)











0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 200100 300 400 500250 450350150


0

2000

4000

6000

8000

10000

12000

14000

16000

Mas

s ero

sion

(mg)

(a)

0 50 200100 300 400 500250 450350150


0

100

200

300

400

500

600

700

800

900

Mas

s ero

sion

(mg)

(b)



8 Conclusion


Nomenclature











0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 100 150 200 250 300 350 400 450 500


00E + 00

50E minus 05

10E minus 04

15E minus 04

20E minus 04

25E minus 04

Redu

ctio

n (

)

(a)

0 50 100 150 200 250 300 350 400 450 500


000

002

004

006

008

010

012

014

016

Redu

ctio

n (

)

(b)

0 50 100 150 200 250 300 350 400 450 500


00

05

15

10

20

25

Redu

ctio

n (

)

(c)


Greek Letters


Subscript



(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)



Abbreviations




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article modeling of particle trajectory and...

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