cfd modeling of particulates erosive effect on a...

Hindawi Publishing CorporationISRN Chemical EngineeringVolume 2013 Article ID 105912 10 pageshttpdxdoiorg1011552013105912

Research ArticleCFD Modeling of Particulates Erosive Effect on a CommercialScale Pipeline Bend

Vahid Abdolkarimi and Rasool Mohammadikhah

Process Development Department Research Institute of Petroleum Industry Tehran 1485733111 Iran

Correspondence should be addressed to Rasool Mohammadikhah mohammadikhahrripiir

Received 25 June 2013 Accepted 27 August 2013

Academic Editors A Brucato and A B Yu

Copyright copy 2013 V Abdolkarimi and R MohammadikhahThis is an open access article distributed under theCreative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The computational fluid dynamics modeling of solid particles hydrodynamic based on the Lagrangian framework for diluted solid-gas flow through 90∘ gas pipeline bend is carried out to discover the effect of particles size distribution on particles flow patternand their erosive effect on the bend Particles size distribution has been obtained experimentally by measuring the sizes of solidparticles that are flowing through the gas pipelines of Aghajari gas booster station Also the erosion rate at the outer wall of the bendis predicted The pipeline bend under study has a pipe diameter of 56 inches and ratios of the bend radius of the curvature to thepipeline diameter of 15 For the validation of computationalmodel firstly the computationalmodeling is performed for a publishedexperimental solid-gas flow dataThe computational results include radial gas velocity and radial particle velocity profiles on planeswhich are at different angles through the bend The comparison between the predicted numerical results and similar experimentaldata proves that the predictions of the computational model are acceptable Finally the particlesrsquo size distributions on each planethrough the bend and the erosion rate on the outer wall of the bend have been obtained The maximum rate of erosion is found tobe 32 nms occurring between 40 and 65∘ of the bend

1 Introduction

In the oil and gas industry black powder (BP) is the briefname that is used to describe the blackmaterials found insidemost of the gas pipelines worldwide Black powder can befound in several forms such as wet with a tar-like appearanceor dry in the form of a very fine powder [1ndash5] It is composedof different forms of iron sulfide (FeS) iron oxides (Fe

3O4

FeOOH) and iron carbonate (FeCO3) mechanically mixed

or chemically combined with any number of contaminantssuch as salts sand liquid hydrocarbons andmetal debris [2]Once BP exists and is moving with the flow it can representa serious threat to the integrity of the gas pipelines byeroding compressor components and pipeline control valvesplugging metering instrumentation and filters and reducingthe accuracy of the in-line inspection Also BP could havemajor adverse effects on customers by contaminating thecustomersrsquo sales gas supply leading to interruptions of thecustomersrsquo operations andor poor quality of products inwhich the sales gas is used as feedstock [3]

The required fluid velocity has been determined [6 7]to entrain and carry away BP in liquid and gas pipelinesrespectively These two studies concluded that the velocityrequired to move BP particles in gas pipelines is independentof particle size and ranges from 104 ft per second (fps)to 136 fps for 810158401015840 and 3010158401015840 pipelines respectively In liquidpipelines the water velocity required depends on the equiv-alent particle size up to a size of about 50 millimeters afterwhich it depends only on the pipe diameter

The effect of the drag coefficient and inlet conditions(inlet velocity profile) of solid particles on the particle trackscalculations in vertical and horizontal ducts are studied [8]using the commercial computational fluid dynamics (CFDs)package CFX 44 They found that the drag coefficientneeds to be reduced by as much as 35 of the standardvalue to achieve good agreement with the correspondingexperimental data in case of a vertical channel flow On theother hand for a horizontal channel flow it needs to bereduced only by 20 to achieve similar agreement Regardingthe velocity inlet conditions it was reported [8] that the

2 ISRN Chemical Engineering

vertical turbulent flow seems to be insensitive to the inletconditions while for a horizontal flow it is found to bestrongly dependent on inlet conditions

CFD simulations have been performed [9] on a dilutedparticulate turbulent flow in a 90∘ duct bend with a radius ofcurvature equal to a 15 duct (225mm) hydraulic diameter Asin previousworks [8] simulationswere performedusingCFX44 using the differential Reynolds stressmodel (DRSM)withfully developed inlet conditions to solve the turbulent flowin the bend and also used the same test facility to producethe experimental data used in validating the simulationsIn another work [10] the author used different solid sizedistributions rather than a single uniform particle size andalso made use of a modified shear-slip lift force formulawhich is consistent with experimental data From thesestudies [8 9] it was concluded that the DRSM did notcapture the correct pressure gradient effects within the bendAlso it was found that even the finer particles (66 micron)experienced a gas-solid segregation due to the centrifugaleffect This segregation was characterized by a local dropin particle concentration near the inner wall and was wellreflected in predictions where the averaged velocity profilesdiscontinued in the locality The experimental part of thestudy [10] is reported in more details [11]

CFD-based erosion modeling can be applied to predicterosion in many complex geometries To assess the viabilityand accuracy a comparison between computed and mea-sured particle velocities and erosion in both water and airflows in a direct impact test section was performed [12] Itwas found that for a sandwater flow in a direct impact testnot like sandair the particle impact velocity is much lowerthan the velocity of the slurry jet and varies by a wide rangeAlso they found that among the erosion models tested theErosion-Corrosion Research Center erosionmodel andOkarsquoset al erosion model [13 14] are more accurate within thescope of their work To evaluate the performance of elbowsand plugged tees geometries under erosive service condi-tions and using the experimental data [15] to validate thesimulation results a procedure was developed [16] to predicterosion in standard elbows long-radius elbows and pluggedtees This procedure is implemented into the CFD code CFX42 The relative erosion severity between plugged tees andelbows under diluted gasliquid-solid flow conditions hasbeen studied computationally and experimentally In thisstudy [17] it was shown that the relative erosion severity isgreatly affected by the type of carrier fluid (liquid or gas)properties as simulations showed that water-sand flows inplugged tees cause more erosion than in elbows while air-sand flows erosion in plugged tees is found to be two ordersof magnitude less than the erosion in standard elbows Inanother study [18] it was shown that the longer the radius ofcurvature of the elbow the less the erosion it experiences dueto solid particle impact Not only the radius of curvature thataffects the erosion but also the elbow (bend) orientation wasfound to have a large effect on particle motion and thereforeon erosion rates as shown in another study [19]

In the current study the reported problem in Aghajarigas booster station consisting of plugging of the compressorrsquosfilters and the erosion of facilities in gas pipelines due

Table 1 Particles size and mass distribution

Sieve disk no Particles size (120583m) Particles mass (gr) (Wt)6 119889 gt 3350 1473 78 3350 gt 119889 gt 2360 1745 8212 2360 gt 119889 gt 1700 156 7416 1700 gt 119889 gt 1180 194 9220 1180 gt 119889 gt 850 41 19430 850 gt 119889 gt 600 2094 9940 600 gt 119889 gt 425 1588 7550 425 gt 119889 gt 300 1318 6170 300 gt 119889 gt 212 1272 60100 212 gt 119889 gt 150 2842 135200 150 gt 119889 gt 125 1242 58

to particles existence will be investigated from particleshydrodynamic point of view

Solid particulates that are flowing inside gas pipelines(BP) of Aghajari gas booster station have been analyzed Forevaluating the effect of particles size on particles motionand their erosive influence CFD modeling based on theLagrangian framework is performed for a 90∘ gas pipelinebend Particles size distribution is considered in themodelingby Rosin-Rammler distribution function

2 Geometry and Flow Conditions

The considered geometry of gas pipeline is a 90∘ angledbend with ratios of the bend radius of the curvature to thepipeline diameter of 15 which is used for detailed modelingof particles motion which is associated with particles sizedistribution This CFD modeling is performed based on theLagrangian framework

Particles size distribution has been obtained experi-mentally by measuring the size and the relevant mass ofsolid particles that are flowing through the gas pipelines ofAghajari gas booster station by the use of woven wire testsieve (WWTS) Particles size and mass distribution are givenin Table 1

Particles are collected at the sampling point of 56-inche-diameter pipe which is the primary inlet pipeline to Aghajarigas station After 500 hours 300 kg of particles was obtainedindicating that the mass flow rate of particles is 06 kghrThe measured density of particles is 2303 kgm3 The streamof main inlet pipe is distributed between seven compressorsfrom which one of them works at the normal conditionTherefore the gas flow rate at normal condition which is usedfor themodeling purpose is 600 SMMCFHThepressure andtemperature of supplied gas inmain inlet pipe are 80 Barg and40∘C respectively The physical conditions of flowing gas inthe 56-inche-diameter pipe is given in Table 2

3 Mathematical Model

The commercial CFD software FLUENT 63 is used to solvethe Reynolds-averaged Navier-Stokes (RANS) equations forcontinuous gas phase For considering the effect of particles

ISRN Chemical Engineering 3

Table 2 Gas conditions

Temperature (∘C) 40Pressure (barg) 80Density (kgsdotmminus3) 6641Viscosity (pasdots) 13796119864 minus 5

Mass flow rate (kgsdotsminus1) 3780

size distribution on particles motion and particles trajectorythe Lagrangian framework for modeling diluted solid-gasflow is used Flowing particles in the main gas pipeline ofAghajari station have been gathered and analyzed by wovenwire test sieve to determine the size and mass distribution ofparticles (Table 1)The Rosin-Rammler distribution functionis used to specify the fraction of particles with specific sizesThe mass fraction of particles of diameter greater than 119889 isgiven by

119884119889= 119890minus(119889119889)

119899

(1)

where 119889 is the size constant and 119899 is the size distributionparameter

Particles are considered as solid spheres which areinjected in to the computational domain via surface injectionmodel In this model there are eight cells at the inletboundary so that ten particles are injected from each one atevery injection time at velocity of 20 (msdotsminus1) and injectionangle of zero relative to the surface normal According tothe accomplished measurement the total mass flow rate ofparticles is 000017 (kgsdotsminus1) It is considered that when aparticle collides a wall surface it retains all of its normal ortangentialmomentum after the rebound (an elastic collision)

The trajectory of a discrete phase particle is predictedby integrating the force balance on the particle This forcebalance equates the particle inertia with the forces actingon the particle and can be written (for the 119909 direction inCartesian coordinates) as follows

119889119906119901

119889119905= 119865119863+119892119909(120588119901minus 120588)

120588119901

(2)

The drag force imposed on the particles is given by (15)

119865119863=18120583

1205881199011198892119901

119862119863Re24

(119906 minus 119906119901) (3)

where

119862119863= 1198861+1198862

Re+1198863

Re2

Re =120588119889119901

10038161003816100381610038161003816119906 minus 119906119901

10038161003816100381610038161003816

120583

(4)

The particles path is computed by integrating (5) as follows

119889119909

119889119905= 119906119901 (5)

The dispersion of particles due to gas phase turbulence iscalculated by the Discrete RandomWalk Model

Turbulent dispersion of particles is predicted by integrat-ing the trajectory equations for individual particles using theinstantaneous fluid velocity along the particle path during theintegration as follows

119906 = 119906 + 1199061015840

(119905) (6)

Prediction of particle dispersion makes use of the concept ofthe integral time scale 119879 which describes the time spent inturbulent motion along the particle path

119879 = int

infin

0

1199061015840

119901

(119905) 1199061015840

119901

(119905 + 119904)

1199061015840119901

2

119889119904 (7)

For small particles that move with the fluid the integral timebecomes the fluid Lagrangian integral time 119879

119871 This time

scale can be approximated as

119879119871= 015

119896

120576 (8)

Each eddy is characterized by a Gaussian distributed randomvelocity fluctuation 1199061015840 V1015840 and 1199081015840a time scale 120591

119890

1199061015840

V1015840 1199081015840 = 120589radic11990610158402 (9)

where 120589 is a normally distributed random number and theremainder of the right-hand side is the local RMS value ofthe velocity fluctuations

Since the kinetic energy of turbulence is known ateach point in the flow these values of the RMS fluctuatingcomponents can be defined (assuming isotropic flow) as

radic11990610158402

= radic2119896

3 (10)

The characteristic lifetime of the eddy is defined as

120591119890= minus119879119871log (119903) (11)

where 119903 is a uniform random number between 0 and 1 and119879119871is given by (8)The particle eddy crossing time is defined as

119905cross = minus120591 ln[1 minus (119871119890

12059110038161003816100381610038161003816119906 minus 119906119901

10038161003816100381610038161003816

)] (12)

where 120591 119871119890 and |119906 minus 119906

119901| are particle relaxation times

eddy length scale and the magnitude of relative velocityrespectively

120591 =41198891199011205882

31205881119862119863

10038161003816100381610038161198801199031003816100381610038161003816

(13)

The particle is assumed to interact with the fluid phaseeddy over the smaller of the eddy lifetime and the eddycrossing time When this time is reached a new value of the


Experimental data for ductile material5th-degree

108060402

00 10 20 30 40 50 60 70 80 90

y = minus3e minus 009 lowast x5 + 68e minus 007 lowast x4 minus 47e minus 005 lowast x3

+ 000049 lowast x2 + 0047 lowast x

120572 (deg)

F(120572

)

(a)

050301

minus01

minus03

minus050 10 20 30 40 50 60 70 80 90

5th degree norm of residuals = 0075428

120572 (deg)

Residuals

(b)

Figure 1 The 5th-order polynomial of impact angle function for ductile materials

instantaneous velocity is obtained by applying a new value of120589 in (9)

Due to the high gas velocity (33ms) and high strain rateof fluid near the pipe wall the realizable 119896-119890model is used formodeling gas phase turbulence Consider

120597

120597119905(120588119892119896119892) + nabla sdot (120588

119892119896119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla119896119892] + 119866

119896119892minus 120588119892120576119892

(14)

120597

120597119905(120588119892120576119892) + nabla sdot (120588

119892120576119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla120576119892] + 120576119892(minus1205881198921198622

120576119892

119896119892+ radic120592119892120576119892

)

(15)

where 120590120576 120590119896are turbulent Prandtl numbers and 120583

119905119892is

turbulent viscosity119896119892and 120576

119892are turbulent kinetic energy and dissipation

rate respectively Consider

120583119905= 120588119862120583

1198962

120576

119862120583=

1

1198600+ 119860119878(119896119880lowast120576)

119880lowast

= radic119878119894119895119878119894119895

1198600= 404 119860

119878= radic6 cos120601

120601 =1

3cosminus1 (radic6119882) 119882 =

119878119894119895119878119895119896119878119896119894

1198783

119878 = radic119878119894119895119878119894119895 119878

119894119895=1

2(120597119906119895

120597119909119894

+120597119906119894

120597119909119895

)

(16)

Momentum balance equation for gas phase is

120597

120597119905(120588119892

997888rarr119880119892) + nabla (120588

119892

997888rarr119880119892

997888rarr119880119892) = minusnabla119875 + nabla120591

119892+ 119865119863+ 120588119892119892 (17)

The erosion rate at wall boundaries can be evaluated by a newcombination of the Tulsa angle dependent model with Huserand Kvernvold model [20 21]

ER = 1559119861minus059119865119904V119899119865 (120572) (18)

where ER 119861 119865119904 V and 119865(120572) are the erosion rate Brinell hard-

ness particle shape coefficient particle relative velocity and a5th-order polynomial function of impact angle respectivelyThe impact angle function is obtained by a fitting operationon the experimental data as one can see in Figure 1

The erosion rate is computed assuming reflecting wallboundary condition For steel material 119899 = 26 and 119865

119904= 02

(for fully rounded solid particles)

4 Boundary Conditions

According to Table 2 the inlet mass flow rate of gas is setto 3780 (kgsdotsminus1) Solid particles are injected into the domainthrough eight cells at the inlet boundary at total massflow rate of 000017 (kgsdotsminus1) with particle size distributionthat is obtained from (1) Particles are injected normallyto the inlet boundary at velocity of 20 (msdotsminus1) and theircollision with wall boundary is assumed to be elastic At theoutlet boundary gas static pressure is set to 80 (barg) andparticles escape from outlet boundary particle tracking isaccomplished in unsteady mode

The boundary layer mesh generation is considered at thewall to limit 119910+ value

5 Validation of the Mathematical Model

Due to impossibility of measurements on working pipe thepublished experimental data for a diluted gas-solid flowthrough a curved 90∘ duct bend [11] was used to validatethemathematicalmodel based on the Lagrangian frameworkThe curved bend is a squared section (15 cm times 15 cm)and has a radius of curvature 119877 of 15 times the ducthydraulic diameter 119863 (225 cm) Gas phase measurementswere obtained using a Laser Doppler Anemometer (LDA)at a bulk gas velocity 119881

119861 of 10ms in the absence of solid

phaseThe solid phase which is glass spheres with an averagediameter of 66 120583mwas released into the flow from a fluidizedbed The solidsgas mass loading ratio reached is well below


90∘

75∘

60∘

45∘

30∘

0∘Entrance

Flow

R

O

D

Vertical symmetry plane

15∘

Exit

Figure 2 Cross sectional planes through bend [22]

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

250000340000

470000565000

rD

Gas velocity on plane 15∘

VVB

Figure 3 The effect of cell numbers on gas relative radial velocitydistribution

1 so as to setup a diluted gas-solid flow regime The radialvelocity profiles of gas and particles are compared withsimilar measurement data that is obtained from differentcross sectional planes through the squared bend (Figure 2)

In Figure 3 the predicted radial distribution of gas veloc-ity is compared with experimental data

Radial distance 119903 is computed by (19)

119903 = 119877 +119863

2minus 119903lowast

(19)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

rD

Gas velocity 15∘

EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

EXPSim

rD

Gas velocity 45∘

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 08

rD

Gas velocity 75 ∘

EXPSim

VVB

(c)

Figure 4 Radial distribution of relative gas velocity over crosssectional planes (comparison between simulated results and exper-imental data from [11])

where 119877 is the curve radius of duct 119863 is the hydraulicdiameter of duct and 119903lowast is the distance of any point on aspecial cross sectional plane from the origin

The total number of cells that is generated for the compu-tational domain is 565000The results of mesh independencycheck are depicted in Figure 3 In this figure the effect of cellnumbers on gas velocity distribution in radial direction overthe 15∘ cross sectional plane is considered

As it is shown in Figure 4 by increasing the cross sec-tional planes angle the more conformity between predictedprofiles and measured profiles is achievedThis can be due todecreasing the radial component of gas velocity

In Figure 5 the predicted radial distribution of particlesvelocity is compared with experimental measurements Ascan be seen predicted results show that particles velocityprofile does not continue to inner wall This is due to theradial component of gas velocity that leads to moving theparticles toward the outer wall of the bend At each anglein the pipe we use a plane that has been divided radiallyto 20 sections At each section the velocity of particles isgathered over time and the average of values is calculatedfor the particle velocity at the specified radial positionThis procedure of particle velocity calculation may lead todiscrepancy between the measured and calculated values Itis obvious that by increasing the number of sections on eachplane the discrepancy between the measured and calculatedparticle velocities can be decreased


0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD

Particles velocity 15∘

EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(c)

Figure 5 Radial distribution of relative particles velocity overcross sectional planes (comparison between simulated results andexperimental data from [11])

Figure 6 shows the radial velocity vectors of gas inside thebend

An erosion model according to (18) was inserted intoCFD solver by a user-defined-function The model wascapable of predicting the erosion rate so that the maximumerosion rate was obtained as 254119864minus12ms which is in goodagreement with that of 263119864 minus 12ms [22] The erosion rateat the middle of bend along the symmetry plane where themaximum erosion takes place was previously reported [22]

6 Results and Discussion

In this study the particulates flowwith particles size distribu-tion inside a 90∘ angled bendwith ratio of curve radius to pipediameter of 15 and 56 inches of pipe diameter is consideredbased on the Lagrangian framework The particles sizedistribution is obtained from experimental data (Table 1) andtaken into account by Rosin-Rammler distribution functionThe mass fraction of particles of diameter greater than 119889 isgiven by 119884

119889 Table 3 explains the relationship between 119889 and

119884119889according to Table 1The mass flow rate of particles is 06 kghr which is

shared by particles with different diameters according totheir mass fractions In Figure 7 the contours of gas velocityare depicted It shows that near the inner wall of the bendmaximum gas velocity occurs so that the radial componentof gas velocity leads to dropping particles (especially largeparticles) toward the outer wall The trajectory of particles in

Table 3 The values for 119889 and 119884119889

Diameter (120583m) 119884119889

150 0942212 0807300 0747425 0686600 0611850 05121180 03181700 02262360 01523350 007

terms of their diameters are shown in Figure 8Thedispersionpattern of solid particles depends on their size and is shownin Figure 9 As can be seen the larger particles move towardthe outer wall of the bend due to radial component of gasvelocity In Figure 10 the size distribution of particles ondifferent cross sectional planes is drawn versus the relativeradial distance according to (19) This figure shows that atthe outer wall (119903119863 = 0) the mean diameter of particles islarger than its value at the inner wall (119903119863 = 1) which is inconsistence with that mentioned previously about Figure 8We can see from Figure 10 that at cross sectional plane of 15∘there are some small particles near the outer wall (119903119863 =

0) of the bend This plane is located at the region wherethe radial component of gas velocity starts to increase butstill does not reach its final growth In Figure 11 the meanparticle velocity distribution on each plane is depicted Thevariation of particles velocity on each plane is close to astraight line By increasing the angle of the plane the slopeof velocity variation increases This is because of increasingthe gas velocity at the vertical section of the bend

Contours of erosion rate and numerical drawing oferosion rate in terms of impact angel are respectively shownin Figures 12 and 13 describing that the abnormal rate oferosion is related to the angles between 50 and 60∘ Themaximum erosion rate is obtained as 326 nms or 01myearand occurs at the angle of 52∘ which is because of impactingsolid particles with size of up to 2 micron This huge rate oferosion would be dangerous for pipeline fittings and shouldbe controlled by for instance the removal of particles withsize of up to 1mm

7 Conclusion

In this studywe have developed a two-phase LagrangianCFDmodel to simulate three-dimensional particulates motion ingas pipelineThe effect of particles diameter on its fluidizationpattern was considered by Rosin-Rammler distribution func-tion Analysis of particulates motion in the bend indicatesthat due to the increasing trend of radial component of gasvelocity through the bend the larger particles are movedtoward the outer wall of the bend and they increase theerosion rate at this region It is found that the erosion ratein this case is very high due to high particle velocity and high


104e + 01

939e + 00

837e + 00

736e + 00

634e + 00

533e + 00

431e + 00

330e + 00

228e + 00

127e + 00

255e minus 01

minus760e minus 01

minus177e minus 00

minus279e minus 00

minus380e minus 00

minus482e minus 00

minus583e minus 00

minus685e minus 00

minus786e minus 00

minus888e minus 00

minus989e minus 00

Velocity vector colored by radial velocity (ms) (time = 60700e + 01)

Fluent 63 (3d pbns ske unsteady)

Jun 15 2013

Figure 6 Radial velocity vectors of gas (ms)

Contours of velocity magnitude (ms) (time = 60700e + 01)

Fluent 63 (3d pbns ske unsteady)Jun 15 2013

456e + 01

434e + 01

411e + 01

388e + 01

365e + 01

342e + 01

319e + 01

297e + 01

274e + 01

251e + 01

228e + 01

205e + 01

183e + 01

160e + 01

137e + 01

114e + 01

913e + 00

685e + 00

456e + 00

228e + 00

000e + 00Y

XZ

Figure 7 Contours of gas velocity magnitude (ms)


335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04

Particle traces colored by particle diameter (m)


Jun 15 2013

Y

XZ

Figure 8 Particles trajectory colored by particle diameter (m)


Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04

Particale traces colored by partical diameter (m) (time = 61100e + 01)

Figure 9 Particles dispersion pattern colored by particle diameter (m)


0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD

Figure 10 Mean particle diameter distribution on cross sectionalplanes

particle diameterThemaximum rate of erosion is discoveredaround angles between 40 and 65∘ This study proves thatwe can use CFD modeling as a powerful tool for assessingparticulates motion and their erosion effects inside differentindustrial instruments

Nomenclature

120588119896 Phase density (kgsdotmminus3)

120572119896 Phase volume fraction

119880119896 Velocity vector for each phase (msdotsminus1)

120591119896 Stress tensor for each phase (Nsdotmminus2)

120573 Inter phase drag coefficient (Kgsdotmminus3sdotsminus1)119889119901 Particle diameter (m)

119896119892 Turbulent kinetic energy of gas phase

(m2sdotsminus2)120576119892 Turbulent dissipation rate of gas phase

(m2sdotsminus2)120590119896 120590120576 Turbulent Prandtl number

119866119896119892 Generation of turbulence kinetic energy

due to the mean velocity gradients(Kgmminus1sdotsminus3)

] Kinematic viscosity (m2sdotsminus1)119862119863 Single particles drag coefficient

ER Erosion rate (msdotsminus1)119861 Brinell hardness119865119904 Particle shape coefficient

120572 Impact angle (Deg)V Particle relative velocity (msdotsminus1)

Conflict of Interests

The authors of the paper do not have a direct or indirectfinancial relation with the commercial identity mentioned intheir paper that might lead to a conflict of interests for any ofthe authors

0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD

Figure 11 Relative mean particle velocity distribution on crosssectional planes

322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘

Figure 12 Contours of erosion rate (ms)

35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)

Figure 13 Erosion rate (ms) in terms of impact angle


References

[1] A M Sherik ldquoBlack Powdermdash1 study examines sourcesmakeup in dry gas systemsrdquo Oil and Gas Journal vol 106 no30 pp 54ndash59 2008

[2] A M Sherik ldquoBlack PowdermdashConclusion managementrequires multiple approachesrdquo Oil and Gas Journal vol 106no 31 pp 66ndash68 2008

[3] N A Tsochatzidis ldquoStudy addresses black powderrsquos effects onmetering equipmentrdquo Oil and Gas Journal vol 106 no 12 pp56ndash61 2008

[4] N A Tsochatzidis and K E Maroulis ldquoMethods help removeblack powder from gas pipelinesrdquo Oil and Gas Journal vol 105no 10 pp 52ndash58 2007

[5] R M Baldwin ldquoHere are procedures for handling persistentblack-powder contaminationrdquo Oil and Gas Journal vol 96 no43 1998

[6] J Smart ldquoDetermining the velocity required to keep solidsmoving in liquid pipelinesrdquo inProceedings of the Pipeline Piggingand Integrity Management Conference Houston Tex USAFebruary 2007

[7] J Smart and R Winters ldquoBlack powder migration in gaspipelines and associated problemsrdquo in Proceedings of the 20thInternational Pipeline Pigging and Integrity Management Con-ference Houston Tex USA February 2008

[8] B Kuan and M P Schwarz ldquoNumerical prediction of dilutedparticulate flows in horizontal and vertical ductsrdquo inProceedingsof the 3rd International Conference on CFD in the Minerals andProcess Industries (CSIRO rsquo03)MelbourneAustraliaDecember2003

[9] B Kuan W Yang and C Solnordal ldquoCFD simulation andexperimental validation of diluted particulate turbulent flowsin a 90∘ duct bendrdquo in Proceedings of the 3rd InternationalConference on CFD in the Minerals and Process Industries(CSIRO rsquo03) Melbourne Australia December 2003

[10] B Kuan ldquoCFD simulation of dilute gas-solid two-phase flowswith different solid size distributions in a curved 90∘ duct bendrdquoANZIAM Journal vol 46 no 5 pp C744ndashC763 2004

[11] W Yang and B Kuan ldquoExperimental investigation of diluteturbulent particulate flow inside a curved 90∘ bendrdquo ChemicalEngineering Science vol 61 no 11 pp 3593ndash3601 2006

[12] Y Zhang E P Reuterfors B S McLaury S A Shirazi and EF Rybicki ldquoComparison of computed and measured particlevelocities and erosion in water and air flowsrdquo Wear vol 263no 1ndash6 pp 330ndash338 2007

[13] Y I Oka K Okamura and T Yoshida ldquoPractical estimation oferosion damage caused by solid particle impact part 1 effectsof impact parameters on a predictive equationrdquoWear vol 259no 1ndash6 pp 95ndash101 2005

[14] Y I Oka and T Yoshida ldquoPractical estimation of erosiondamage caused by solid particle impact part 2 mechanicalproperties of materials directly associated with erosion dam-agerdquoWear vol 259 no 1ndash6 pp 102ndash109 2005

[15] M M Enayet M M Gibson A M K P Taylor and M Yian-neskis ldquoLaser-Doppler measurements of laminar and turbulentflow in a pipe bendrdquo International Journal of Heat and FluidFlow vol 3 no 4 pp 213ndash219 1982

[16] J K Edwards B S McLaury and S A Shirazi ldquoModeling solidparticle erosion in elbows and plugged teesrdquo Journal of EnergyResources Technology vol 123 no 2ndash4 pp 277ndash284 2001

[17] X Chen B S McLaury and S A Shirazi ldquoNumerical andexperimental investigation of the relative erosion severity

between plugged tees and elbows in dilute gassolid two-phaseflowrdquoWear vol 261 no 7-8 pp 715ndash729 2006

[18] C Hengshuan and X Zhong ldquoNumerical analysis and experi-mental investigation of erosion in variable rectangular-sectionbends by solid particlesrdquo Chinese Journal of Mechanical Engi-neering vol 3 no 1 pp 111ndash118 1990

[19] A Keating and S Nesic ldquoPrediction of two-phase Erosion-corrosion in bendsrdquo in Proceedings of the 2nd InternationalConference on CFD in the Minerals and Process Industries(CSIRO rsquo99) Melbourne Australia December 1999

[20] X Chen B S McLaury and S A Shirazi ldquoA comprehen-sive erosion prediction method for gasliquidsand multiphaseflowrdquo in Proceedings of the ASME 1998 Fluids EngineeringDivision Summer Meeting (ASME FEDSM rsquo98) pp 1290ndash1297Washington DC USA June 2005

[21] A Huser and O Kvernvold ldquoPrediction of sand erosion inprocess and pipe componentsrdquo in Proceedings of the 1st NorthAmerican Conference on Multiphase Technology pp 217ndash227Banff Canada 1998

[22] E Elsaadawy and A M Sherik ldquoBlack powder erosion in salesgas pipeline bendsrdquo Saudi Aramco Journal of Technology 2010

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014


Shock and Vibration


Mechanical Engineering

Advances in


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of


Distributed Sensor Networks


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Advances inOptoElectronics


Volume 2014

RoboticsJournal of


Chemical EngineeringInternational Journal of


Control Scienceand Engineering

Journal of


Antennas andPropagation




Navigation and Observation



vertical turbulent flow seems to be insensitive to the inletconditions while for a horizontal flow it is found to bestrongly dependent on inlet conditions

CFD simulations have been performed [9] on a dilutedparticulate turbulent flow in a 90∘ duct bend with a radius ofcurvature equal to a 15 duct (225mm) hydraulic diameter Asin previousworks [8] simulationswere performedusingCFX44 using the differential Reynolds stressmodel (DRSM)withfully developed inlet conditions to solve the turbulent flowin the bend and also used the same test facility to producethe experimental data used in validating the simulationsIn another work [10] the author used different solid sizedistributions rather than a single uniform particle size andalso made use of a modified shear-slip lift force formulawhich is consistent with experimental data From thesestudies [8 9] it was concluded that the DRSM did notcapture the correct pressure gradient effects within the bendAlso it was found that even the finer particles (66 micron)experienced a gas-solid segregation due to the centrifugaleffect This segregation was characterized by a local dropin particle concentration near the inner wall and was wellreflected in predictions where the averaged velocity profilesdiscontinued in the locality The experimental part of thestudy [10] is reported in more details [11]

CFD-based erosion modeling can be applied to predicterosion in many complex geometries To assess the viabilityand accuracy a comparison between computed and mea-sured particle velocities and erosion in both water and airflows in a direct impact test section was performed [12] Itwas found that for a sandwater flow in a direct impact testnot like sandair the particle impact velocity is much lowerthan the velocity of the slurry jet and varies by a wide rangeAlso they found that among the erosion models tested theErosion-Corrosion Research Center erosionmodel andOkarsquoset al erosion model [13 14] are more accurate within thescope of their work To evaluate the performance of elbowsand plugged tees geometries under erosive service condi-tions and using the experimental data [15] to validate thesimulation results a procedure was developed [16] to predicterosion in standard elbows long-radius elbows and pluggedtees This procedure is implemented into the CFD code CFX42 The relative erosion severity between plugged tees andelbows under diluted gasliquid-solid flow conditions hasbeen studied computationally and experimentally In thisstudy [17] it was shown that the relative erosion severity isgreatly affected by the type of carrier fluid (liquid or gas)properties as simulations showed that water-sand flows inplugged tees cause more erosion than in elbows while air-sand flows erosion in plugged tees is found to be two ordersof magnitude less than the erosion in standard elbows Inanother study [18] it was shown that the longer the radius ofcurvature of the elbow the less the erosion it experiences dueto solid particle impact Not only the radius of curvature thataffects the erosion but also the elbow (bend) orientation wasfound to have a large effect on particle motion and thereforeon erosion rates as shown in another study [19]

In the current study the reported problem in Aghajarigas booster station consisting of plugging of the compressorrsquosfilters and the erosion of facilities in gas pipelines due

Table 1 Particles size and mass distribution

Sieve disk no Particles size (120583m) Particles mass (gr) (Wt)6 119889 gt 3350 1473 78 3350 gt 119889 gt 2360 1745 8212 2360 gt 119889 gt 1700 156 7416 1700 gt 119889 gt 1180 194 9220 1180 gt 119889 gt 850 41 19430 850 gt 119889 gt 600 2094 9940 600 gt 119889 gt 425 1588 7550 425 gt 119889 gt 300 1318 6170 300 gt 119889 gt 212 1272 60100 212 gt 119889 gt 150 2842 135200 150 gt 119889 gt 125 1242 58

to particles existence will be investigated from particleshydrodynamic point of view

Solid particulates that are flowing inside gas pipelines(BP) of Aghajari gas booster station have been analyzed Forevaluating the effect of particles size on particles motionand their erosive influence CFD modeling based on theLagrangian framework is performed for a 90∘ gas pipelinebend Particles size distribution is considered in themodelingby Rosin-Rammler distribution function

2 Geometry and Flow Conditions

The considered geometry of gas pipeline is a 90∘ angledbend with ratios of the bend radius of the curvature to thepipeline diameter of 15 which is used for detailed modelingof particles motion which is associated with particles sizedistribution This CFD modeling is performed based on theLagrangian framework

Particles size distribution has been obtained experi-mentally by measuring the size and the relevant mass ofsolid particles that are flowing through the gas pipelines ofAghajari gas booster station by the use of woven wire testsieve (WWTS) Particles size and mass distribution are givenin Table 1

Particles are collected at the sampling point of 56-inche-diameter pipe which is the primary inlet pipeline to Aghajarigas station After 500 hours 300 kg of particles was obtainedindicating that the mass flow rate of particles is 06 kghrThe measured density of particles is 2303 kgm3 The streamof main inlet pipe is distributed between seven compressorsfrom which one of them works at the normal conditionTherefore the gas flow rate at normal condition which is usedfor themodeling purpose is 600 SMMCFHThepressure andtemperature of supplied gas inmain inlet pipe are 80 Barg and40∘C respectively The physical conditions of flowing gas inthe 56-inche-diameter pipe is given in Table 2

3 Mathematical Model

The commercial CFD software FLUENT 63 is used to solvethe Reynolds-averaged Navier-Stokes (RANS) equations forcontinuous gas phase For considering the effect of particles






119884119889= 119890minus(119889119889)

119899

(1)




119889119906119901

119889119905= 119865119863+119892119909(120588119901minus 120588)

120588119901

(2)


119865119863=18120583

1205881199011198892119901

119862119863Re24

(119906 minus 119906119901) (3)

where

119862119863= 1198861+1198862

Re+1198863

Re2

Re =120588119889119901

10038161003816100381610038161003816119906 minus 119906119901

10038161003816100381610038161003816

120583

(4)


119889119909

119889119905= 119906119901 (5)



119906 = 119906 + 1199061015840

(119905) (6)


119879 = int

infin

0

1199061015840

119901

(119905) 1199061015840

119901

(119905 + 119904)

1199061015840119901

2

119889119904 (7)


119871 This time


119879119871= 015

119896

120576 (8)


119890

1199061015840

V1015840 1199081015840 = 120589radic11990610158402 (9)



radic11990610158402

= radic2119896

3 (10)


120591119890= minus119879119871log (119903) (11)



12059110038161003816100381610038161003816119906 minus 119906119901

10038161003816100381610038161003816

)] (12)

where 120591 119871119890 and |119906 minus 119906



120591 =41198891199011205882

31205881119862119863

10038161003816100381610038161198801199031003816100381610038161003816

(13)




108060402

00 10 20 30 40 50 60 70 80 90



120572 (deg)

F(120572

)

(a)

050301

minus01

minus03

minus050 10 20 30 40 50 60 70 80 90


120572 (deg)

Residuals

(b)




120597

120597119905(120588119892119896119892) + nabla sdot (120588

119892119896119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla119896119892] + 119866

119896119892minus 120588119892120576119892

(14)

120597

120597119905(120588119892120576119892) + nabla sdot (120588

119892120576119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla120576119892] + 120576119892(minus1205881198921198622

120576119892

119896119892+ radic120592119892120576119892

)

(15)


119905119892is




120583119905= 120588119862120583

1198962

120576

119862120583=

1

1198600+ 119860119878(119896119880lowast120576)

119880lowast

= radic119878119894119895119878119894119895

1198600= 404 119860

119878= radic6 cos120601

120601 =1

3cosminus1 (radic6119882) 119882 =

119878119894119895119878119895119896119878119896119894

1198783

119878 = radic119878119894119895119878119894119895 119878

119894119895=1

2(120597119906119895

120597119909119894

+120597119906119894

120597119909119895

)

(16)


120597

120597119905(120588119892

997888rarr119880119892) + nabla (120588

119892

997888rarr119880119892


119892+ 119865119863+ 120588119892119892 (17)


ER = 1559119861minus059119865119904V119899119865 (120572) (18)




119904= 02










90∘

75∘

60∘

45∘

30∘

0∘Entrance

Flow

R

O

D


15∘

Exit


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

250000340000

470000565000

rD


VVB





119903 = 119877 +119863

2minus 119903lowast

(19)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

rD

Gas velocity 15∘

EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

EXPSim

rD

Gas velocity 45∘

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 08

rD

Gas velocity 75 ∘

EXPSim

VVB

(c)







0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(c)










Diameter (120583m) 119884119889

150 0942212 0807300 0747425 0686600 0611850 05121180 03181700 02262360 01523350 007




7 Conclusion



104e + 01

939e + 00

837e + 00

736e + 00

634e + 00

533e + 00

431e + 00

330e + 00

228e + 00

127e + 00

255e minus 01

minus760e minus 01

minus177e minus 00

minus279e minus 00

minus380e minus 00

minus482e minus 00

minus583e minus 00

minus685e minus 00

minus786e minus 00

minus888e minus 00

minus989e minus 00



Jun 15 2013




456e + 01

434e + 01

411e + 01

388e + 01

365e + 01

342e + 01

319e + 01

297e + 01

274e + 01

251e + 01

228e + 01

205e + 01

183e + 01

160e + 01

137e + 01

114e + 01

913e + 00

685e + 00

456e + 00

228e + 00

000e + 00Y

XZ



335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04



Jun 15 2013

Y

XZ



Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04




0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of













119884119889= 119890minus(119889119889)

119899

(1)




119889119906119901

119889119905= 119865119863+119892119909(120588119901minus 120588)

120588119901

(2)


119865119863=18120583

1205881199011198892119901

119862119863Re24

(119906 minus 119906119901) (3)

where

119862119863= 1198861+1198862

Re+1198863

Re2

Re =120588119889119901

10038161003816100381610038161003816119906 minus 119906119901

10038161003816100381610038161003816

120583

(4)


119889119909

119889119905= 119906119901 (5)



119906 = 119906 + 1199061015840

(119905) (6)


119879 = int

infin

0

1199061015840

119901

(119905) 1199061015840

119901

(119905 + 119904)

1199061015840119901

2

119889119904 (7)


119871 This time


119879119871= 015

119896

120576 (8)


119890

1199061015840

V1015840 1199081015840 = 120589radic11990610158402 (9)



radic11990610158402

= radic2119896

3 (10)


120591119890= minus119879119871log (119903) (11)



12059110038161003816100381610038161003816119906 minus 119906119901

10038161003816100381610038161003816

)] (12)

where 120591 119871119890 and |119906 minus 119906



120591 =41198891199011205882

31205881119862119863

10038161003816100381610038161198801199031003816100381610038161003816

(13)




108060402

00 10 20 30 40 50 60 70 80 90



120572 (deg)

F(120572

)

(a)

050301

minus01

minus03

minus050 10 20 30 40 50 60 70 80 90


120572 (deg)

Residuals

(b)




120597

120597119905(120588119892119896119892) + nabla sdot (120588

119892119896119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla119896119892] + 119866

119896119892minus 120588119892120576119892

(14)

120597

120597119905(120588119892120576119892) + nabla sdot (120588

119892120576119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla120576119892] + 120576119892(minus1205881198921198622

120576119892

119896119892+ radic120592119892120576119892

)

(15)


119905119892is




120583119905= 120588119862120583

1198962

120576

119862120583=

1

1198600+ 119860119878(119896119880lowast120576)

119880lowast

= radic119878119894119895119878119894119895

1198600= 404 119860

119878= radic6 cos120601

120601 =1

3cosminus1 (radic6119882) 119882 =

119878119894119895119878119895119896119878119896119894

1198783

119878 = radic119878119894119895119878119894119895 119878

119894119895=1

2(120597119906119895

120597119909119894

+120597119906119894

120597119909119895

)

(16)


120597

120597119905(120588119892

997888rarr119880119892) + nabla (120588

119892

997888rarr119880119892


119892+ 119865119863+ 120588119892119892 (17)


ER = 1559119861minus059119865119904V119899119865 (120572) (18)




119904= 02










90∘

75∘

60∘

45∘

30∘

0∘Entrance

Flow

R

O

D


15∘

Exit


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

250000340000

470000565000

rD


VVB





119903 = 119877 +119863

2minus 119903lowast

(19)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

rD

Gas velocity 15∘

EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

EXPSim

rD

Gas velocity 45∘

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 08

rD

Gas velocity 75 ∘

EXPSim

VVB

(c)







0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(c)










Diameter (120583m) 119884119889

150 0942212 0807300 0747425 0686600 0611850 05121180 03181700 02262360 01523350 007




7 Conclusion



104e + 01

939e + 00

837e + 00

736e + 00

634e + 00

533e + 00

431e + 00

330e + 00

228e + 00

127e + 00

255e minus 01

minus760e minus 01

minus177e minus 00

minus279e minus 00

minus380e minus 00

minus482e minus 00

minus583e minus 00

minus685e minus 00

minus786e minus 00

minus888e minus 00

minus989e minus 00



Jun 15 2013




456e + 01

434e + 01

411e + 01

388e + 01

365e + 01

342e + 01

319e + 01

297e + 01

274e + 01

251e + 01

228e + 01

205e + 01

183e + 01

160e + 01

137e + 01

114e + 01

913e + 00

685e + 00

456e + 00

228e + 00

000e + 00Y

XZ



335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04



Jun 15 2013

Y

XZ



Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04




0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of










108060402

00 10 20 30 40 50 60 70 80 90



120572 (deg)

F(120572

)

(a)

050301

minus01

minus03

minus050 10 20 30 40 50 60 70 80 90


120572 (deg)

Residuals

(b)




120597

120597119905(120588119892119896119892) + nabla sdot (120588

119892119896119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla119896119892] + 119866

119896119892minus 120588119892120576119892

(14)

120597

120597119905(120588119892120576119892) + nabla sdot (120588

119892120576119892

997888rarr119880119892)

= nabla[(120583 +120583119905119892

120590119896

)nabla120576119892] + 120576119892(minus1205881198921198622

120576119892

119896119892+ radic120592119892120576119892

)

(15)


119905119892is




120583119905= 120588119862120583

1198962

120576

119862120583=

1

1198600+ 119860119878(119896119880lowast120576)

119880lowast

= radic119878119894119895119878119894119895

1198600= 404 119860

119878= radic6 cos120601

120601 =1

3cosminus1 (radic6119882) 119882 =

119878119894119895119878119895119896119878119896119894

1198783

119878 = radic119878119894119895119878119894119895 119878

119894119895=1

2(120597119906119895

120597119909119894

+120597119906119894

120597119909119895

)

(16)


120597

120597119905(120588119892

997888rarr119880119892) + nabla (120588

119892

997888rarr119880119892


119892+ 119865119863+ 120588119892119892 (17)


ER = 1559119861minus059119865119904V119899119865 (120572) (18)




119904= 02










90∘

75∘

60∘

45∘

30∘

0∘Entrance

Flow

R

O

D


15∘

Exit


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

250000340000

470000565000

rD


VVB





119903 = 119877 +119863

2minus 119903lowast

(19)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

rD

Gas velocity 15∘

EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

EXPSim

rD

Gas velocity 45∘

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 08

rD

Gas velocity 75 ∘

EXPSim

VVB

(c)







0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(c)










Diameter (120583m) 119884119889

150 0942212 0807300 0747425 0686600 0611850 05121180 03181700 02262360 01523350 007




7 Conclusion



104e + 01

939e + 00

837e + 00

736e + 00

634e + 00

533e + 00

431e + 00

330e + 00

228e + 00

127e + 00

255e minus 01

minus760e minus 01

minus177e minus 00

minus279e minus 00

minus380e minus 00

minus482e minus 00

minus583e minus 00

minus685e minus 00

minus786e minus 00

minus888e minus 00

minus989e minus 00



Jun 15 2013




456e + 01

434e + 01

411e + 01

388e + 01

365e + 01

342e + 01

319e + 01

297e + 01

274e + 01

251e + 01

228e + 01

205e + 01

183e + 01

160e + 01

137e + 01

114e + 01

913e + 00

685e + 00

456e + 00

228e + 00

000e + 00Y

XZ



335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04



Jun 15 2013

Y

XZ



Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04




0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









90∘

75∘

60∘

45∘

30∘

0∘Entrance

Flow

R

O

D


15∘

Exit


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

250000340000

470000565000

rD


VVB





119903 = 119877 +119863

2minus 119903lowast

(19)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

rD

Gas velocity 15∘

EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15

EXPSim

rD

Gas velocity 45∘

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 08

rD

Gas velocity 75 ∘

EXPSim

VVB

(c)







0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(c)










Diameter (120583m) 119884119889

150 0942212 0807300 0747425 0686600 0611850 05121180 03181700 02262360 01523350 007




7 Conclusion



104e + 01

939e + 00

837e + 00

736e + 00

634e + 00

533e + 00

431e + 00

330e + 00

228e + 00

127e + 00

255e minus 01

minus760e minus 01

minus177e minus 00

minus279e minus 00

minus380e minus 00

minus482e minus 00

minus583e minus 00

minus685e minus 00

minus786e minus 00

minus888e minus 00

minus989e minus 00



Jun 15 2013




456e + 01

434e + 01

411e + 01

388e + 01

365e + 01

342e + 01

319e + 01

297e + 01

274e + 01

251e + 01

228e + 01

205e + 01

183e + 01

160e + 01

137e + 01

114e + 01

913e + 00

685e + 00

456e + 00

228e + 00

000e + 00Y

XZ



335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04



Jun 15 2013

Y

XZ



Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04




0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(a)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(b)

0

01

02

03

04

05

06

07

08

09

1

0 1 2

rD


EXPSim

VVB

(c)










Diameter (120583m) 119884119889

150 0942212 0807300 0747425 0686600 0611850 05121180 03181700 02262360 01523350 007




7 Conclusion



104e + 01

939e + 00

837e + 00

736e + 00

634e + 00

533e + 00

431e + 00

330e + 00

228e + 00

127e + 00

255e minus 01

minus760e minus 01

minus177e minus 00

minus279e minus 00

minus380e minus 00

minus482e minus 00

minus583e minus 00

minus685e minus 00

minus786e minus 00

minus888e minus 00

minus989e minus 00



Jun 15 2013




456e + 01

434e + 01

411e + 01

388e + 01

365e + 01

342e + 01

319e + 01

297e + 01

274e + 01

251e + 01

228e + 01

205e + 01

183e + 01

160e + 01

137e + 01

114e + 01

913e + 00

685e + 00

456e + 00

228e + 00

000e + 00Y

XZ



335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04



Jun 15 2013

Y

XZ



Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04




0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









104e + 01

939e + 00

837e + 00

736e + 00

634e + 00

533e + 00

431e + 00

330e + 00

228e + 00

127e + 00

255e minus 01

minus760e minus 01

minus177e minus 00

minus279e minus 00

minus380e minus 00

minus482e minus 00

minus583e minus 00

minus685e minus 00

minus786e minus 00

minus888e minus 00

minus989e minus 00



Jun 15 2013




456e + 01

434e + 01

411e + 01

388e + 01

365e + 01

342e + 01

319e + 01

297e + 01

274e + 01

251e + 01

228e + 01

205e + 01

183e + 01

160e + 01

137e + 01

114e + 01

913e + 00

685e + 00

456e + 00

228e + 00

000e + 00Y

XZ



335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04



Jun 15 2013

Y

XZ



Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04




0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04



Jun 15 2013

Y

XZ



Jun 15 2013

Y

XZ

335e minus 03

319e minus 03

303e minus 03

287e minus 03

271e minus 03

255e minus 03

239e minus 03

223e minus 03

207e minus 03

191e minus 03

175e minus 03

159e minus 03

143e minus 03

127e minus 03

111e minus 03

950e minus 04

790e minus 04

630e minus 04

470e minus 04

310e minus 04

150e minus 04




0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









0

00005

0001

00015

0002

00025

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le d

iam

eter

(m)

15-deg30-deg45-deg

60-deg75-deg

rD



Nomenclature
















0

02

04

06

08

1

12

14

0 01 02 03 04 05 06 07 08

Mea

n pa

rtic

le v

eloc

ityb

ulk

gas v

eloc

ity

15-deg30-deg45-deg

60-deg75-deg

rD


322e minus 09

107e minus 09

820e minus 10

436e minus 10

874e minus 11

356e minus 11

901e minus 12

218e minus 12

986e minus 13

161e minus 13

40∘

65∘


35

3

25

2

15

1

05

00 10 20 30 40 50 60 70 80 90

Eros

ion

rate

(ms

)

times10minus9

120572 (deg)



References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









References

























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of








cfd modeling of particulates erosive effect on a...

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