Chen, X., B.S. Mclaury, And S.a. Shirazi, Application and Experimental Validation of a Computational...

Computers & Fluids 33 (2004) 1251–1272www.elsevier.com/locate/compfluid

Application and experimental validation of acomputational fluid dynamics (CFD)-based erosion

prediction model in elbows and plugged tees

Xianghui Chen *, Brenton S. McLaury, Siamack A. Shirazi

Department of Mechanical Engineering, The University of Tulsa, 600 South College Avenue,

Tulsa, OK 74104, USA

Received 13 August 2003; received in revised form 20 December 2003; accepted 25 February 2004

Available online 30 April 2004

Abstract

This paper presents a computational fluid dynamics (CFD)-based erosion prediction model and its

application to oilfield geometries specifically elbows and plugged tees. This comprehensive procedureconsists of three major components: flow simulation, particle tracking, and erosion calculation. The effect

of the particle rebound model on the particle trajectories as well as erosion pattern in the elbow and plugged

tee is also investigated. Experimental erosion tests were performed in both an elbow and a plugged tee to

evaluate the simulation results. The results from the model show good agreement of the erosion trend with

the erosion data for elbow and plugged tee geometries. Experiment confirms that a stochastic rebound

model is required in simulations to give a reasonable estimate of erosion rate and pattern in a plugged tee.

� 2004 Elsevier Ltd. All rights reserved.

1. Introduction

Many engineering industries, such as the oil and gas industry, have the need to transport fluidswith entrained solid particles. The momentum of particles carries them across streamlines and theparticles impinge the wall of the fittings resulting in erosion damage. Erosion of the fittings mayresult in the failure of the piping system, which can be extremely dangerous and expensive. It isessential to have a method to determine the erosion rate for a given set of operating conditions toprevent any failures from occurring. The prediction of erosion not only allows one to estimate

* Corresponding author. Tel.: +1-918-631-2755; fax: +1-918-631-2397.

E-mail address: [email protected] (X. Chen).

0045-7930/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compfluid.2004.02.003

mail to: [email protected]

1252 X. Chen et al. / Computers & Fluids 33 (2004) 1251–1272

service life, but also enables the detection of locations in the geometry where severe erosion islikely to occur. Elbows and plugged tees are common geometries used in piping systems to redirectfluids. Both elbows and plugged tees are susceptible to erosion when sand particles are presentbecause particles deviate from the fluid streamlines and impact the wall when they pass throughthe transition section (such as the bend section of the elbow and the joint section of the pluggedtee) of these geometries.

Sand erosion phenomenon is highly complicated and a wide range of factors contribute to theerosion severity. These parameters include fluid flow rate, sand rate, properties of the fluid,properties of sand particles, wall material of equipment or fitting, and the characteristics ofgeometries such as size and shape. In order to combat the erosion caused by solid particles, avariety of erosion prediction methods have been developed. Most methods are based on a limitedamount of experimental data, so these models are only applicable to specific conditions. Due tothe lack of an accurate and general erosion prediction model, ‘‘rule of thumb’’ design guidelinesare adopted for many situations in industrial practice, which usually lead to designs that are tooconservative or not realistic. The most well-known guideline in oil and gas industry is theAmerican Petroleum Institute Recommended Practice 14E (API RP 14E) [1]. This guidelinesuggests a limiting flow velocity for erosive service. The guideline states that severe erosion shouldnot occur if production velocities are maintained below this limit. The velocity recommended byAPI RP 14E is given by Eq. (1):

Ve ¼Cffiffiffiq

p ð1Þ

where Ve is the erosional velocity limit in ft/s, q is the carrier fluid density in lb/ft3, andC is a constant.The API guideline recommends that the value of C should be 100 for continuous service and 125 forintermittent service. The only variable accounted for directly in Eq. (1) is fluid density. Therefore,API RP 14E is not capable of incorporating all the important factors involved such as fluid viscosity,properties of sand particles, and the sand production rate. Industrial applications have demon-strated these parameters can have a significant impact on the erosion. Salama and Venkatesh [2] andSvedeman and Arnold [3] have introduced significant modifications to API RP 14E. McLaury andShirazi [4] have provided alternative methods, which include the effect of parameters such asproperties of carrier fluid, sand particles, as well as material of pipe, to API RP 14E.

Significant efforts have been taken by researchers and engineers to study the erosion problemand many erosion prediction models have been developed. For example, Nesic and Postlethwaite[5] studies the local erosion in chokes by determining the local fluid velocity and particle im-pingement information. McLaury [6] and Shirazi et al. [7,8] developed mechanistic models forpredicting erosion in elbows. Salama [9] formulated a semi-mechanistic model for erosion inmulti-phase flow. In another study, McLaury [10] proposed a generalized erosion predictionprocedure that involves flow simulation, particle tracking, and erosion prediction. Wang et al. [11]applied this approach to investigate the effects of elbow radius of curvature on erosion rate. Theerosion in oilfield control valves was calculated by Forder et al. [12] using flow simulation andparticle tracking method. More recently, Edwards [13] implemented the generalized erosionprediction procedure in a commercially available Computational Fluid Dynamics (CFD) code. Inanother study, Keating and Nesic [14] applied the CFD approach to investigate the erosion–corrosion problems in U-bends.

X. Chen et al. / Computers & Fluids 33 (2004) 1251–1272 1253

2. CFD-based erosion prediction model and computational models

The erosion prediction procedure [13] was implemented into a commercially available CFDcode, CFX, which was developed by AEA Technology [15]. This CFD-based erosion technique isa comprehensive procedure that is able to predict the erosion for a wide range of three-dimen-sional geometries. By applying this procedure, the maximum erosion for a certain case can becalculated, as well as the erosion profile on the surface of the geometry. This comprehensiveprocedure has three major steps: flow modeling, particle tracking, and erosion prediction. Thissection discusses some important issues of the comprehensive procedure and relative theories andcomputational models for each step.

2.1. Erosion simulation procedure

Flow simulation of the continuous fluid (carrier fluid) is the first step of the CFD-based erosionprediction procedure. CFX uses a finite difference approach to solve the Navier–Stokes equations.The first task of flow simulation is to generate the computational grid of the geometry. Pre-processors available in the software are used to perform this task. CFX uses a multi-blockstructured grid. The second task is to specify the boundary conditions as well as solution optionssuch as differencing scheme and turbulence model. The final step is to run the solver to generatethe flow field simulation. Patankar [16] describes the procedure that is used to solve the equationsof fluid motion.

For flow conditions of interest in oil and gas production, the sand concentration is fairly smallso that the effect of sand particles on the carrier fluid is assumed negligible. Thus, one-waycoupling method is employed to calculate sand particles trajectories in this study. One-waycoupling assumes that the presence of solid particles has little effect on the flow field. CFX has theoption of applying two-way coupling, but it is not used in this study. In two-way coupling, theinteraction between the carrier fluid and the particles is accounted for to calculate the continuousflow field as well as the trajectories of solid particles. In this step, the user can specify theappropriate particle–wall rebound model as well as the forces exerted on the sand particles.Usually, for a given mass of sand, the trajectories of tens of thousands of particles that arerandomly distributed at the inlet are determined to obtain statistically representative sandimpingements on the wall in order to acquire representative erosion profiles for the geometry.

Impingement information, such as particle impact speed, impact angle, and impact locations,are obtained from the particle trajectory calculations. The impingement information is applied toerosion models to finally predict the erosion caused by sand particles within the entire simulatedgeometry. The properties of pipe wall material as well as particle shape can be accounted for toquantify the erosion. In the post-processor section, the user can visualize the profile of erosion aswell as flow variables such as velocity components.

2.2. Description of computational models

2.2.1. Governing equations of fluid motion (Navier–Stokes equations)

The governing equations of flow employed in CFX-4 are discussed in this section. The conti-nuity and momentum equations are given in Eqs. (2) and (3), respectively [15]:


oqot

þr � ðq~UÞ ¼ 0 ð2Þ

oðq~UÞot

þr � ðq~U � ~UÞ ¼ ~Bþr � ð�qu0 � u0 þ rÞ ð3Þ

where q is the fluid density, ~U is the instantaneous velocity vector, ~B is the body force, u0 is thefluctuating velocity due to turbulence (i.e. ~U ¼ uþ u0, where u is the mean velocity component),qu0 � u0 is the Reynolds stress; and the stress tensor, r, is given by

r ¼ � pqI þ l

q½r~U þ ðr~UÞT� ð4Þ

where p and l are the local pressure and viscosity of the fluid, and I is the identity matrix. Severalturbulence models are included in CFX-4, such as Standard, Low Reynolds Number and RNGversions of Turbulent Kinetic Energy-Dissipation ðk � eÞ models; Differential and AlgebraicReynolds Stress models; and a Reynolds Flux model. According to Edwards’ findings [17], theDifferential Reynolds Stress turbulence model [18] is utilized in this research. A third order dif-ferencing scheme, QUICK [15], is used to solve the governing equations.

2.2.2. Particle tracking

According to Newton’s second law, Clift et al. [19] proposed the governing equation of particlemotion:

mp

d~V p

dt¼ ~F D þ~F P þ~F B þ~F A ð5Þ

The above equation consists of

• Drag force:

~F D ¼ CDqf

pd2p

8j~V f � ~V pjð~V f � ~V pÞ ð6Þ

where CD is the drag force coefficient, defined as

CD ¼ 24

ReSð1þ 0:15Re0:687S Þ ð7Þ

where ReS is the particle relative Reynolds number, defined by

ReS ¼qf j~V p � ~V f jdp

lð8Þ

• Pressure gradient force:

~F P ¼ 14pd3

prP ð9Þ

• Buoyancy force:

~F B ¼ 16pd3

pðqp � qfÞ~g ð10Þ


• Added mass force:

~F A ¼ � 1

12pd3

pqp

d~V p

dtð11Þ

Gosman and Ioannides approach [20] is employed to incorporate the effect of the turbulencedispersion on the particle motion. This model takes into account the crossing trajectories andeddy lifetime to calculate the interaction time of particle and the eddy. In this approach, theturbulence is assumed to be isotropic and to possess a Gaussian probability distribution in thefluctuating velocity. The mean of the fluctuating velocities is zero and the standard deviation, q, isgiven by the predicted local turbulent kinetic energy field:

q ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffið2k=3Þ

pð12Þ

The standard deviation and mean velocity are used to sample the fluctuation velocity, u0.In order to accurately predict the particle trajectories an appropriate rebound model describing

the particle–wall collision must be used. At impact, the reflected velocity of the particle is lowerthan the incoming velocity due to energy transfer. This impact signature is described by themomentum-based coefficient of restitution, e. Researchers have shown that the particle incomingangle may have a significant effect on the coefficient of restitution. Forder et al. [12] proposed thefollowing coefficient relationships for perpendicular and parallel velocity components for AISI4130:

eper ¼ 0:988� 0:78hþ 0:19h2 � 0:024h3 þ 0:0027h4 ð13Þ

epar ¼ 1� 0:78hþ 0:84h2 � 0:21h3 þ 0:028h4 � 0:022h5 ð14Þ
Grant and Tabakoff [21] and Sommerfeld [22,23] treated the rebound dynamics of the particles ina statistical sense. Based on experimental data (for 2024 Aluminum and 200 lm sand particles),Grant and Tabakoff postulated the mean values of the coefficients of restitution (eper and epar),which are incoming angle-dependent distributions with angle-dependent standard deviations (rper
and rpar).

eper ¼ 0:993� 1:76hþ 1:56h2 � 0:49h3 ð15Þ

epar ¼ 0:998� 1:66hþ 2:11h2 � 0:67h3 ð16Þ

rper ¼ �0:0005þ 0:62h� 0:535h2 þ 0:089h3 ð17Þ

rpar ¼ 2:15h� 5:02h2 þ 4:05h3 � 1:085h4 ð18Þ

2.2.3. Erosion predictionImpingement information, such as impact speed and impact angle, is gathered as particles hit

the wall of the geometry. Using this information the erosion ratio can be calculated. The erosionratio is defined as the mass loss of the pipe wall due to erosion divided by the mass of particleimpacting the wall. The erosion ratio depends on the particle impact speed and impact angle.According to Ahlert [24] and McLaury [10], the erosion ratio is given by

Table 1

Erosion model empirical constants

Constants Material

Carbon steel Aluminum

a 38.4 )34.79b 22.7 12.3

u 1 5.205

x 0.3147 0.147

y 0.03609 )0.745w 0.2532 1

n 1.73 1.73


ER ¼ AFsV nf ðhÞ ð19Þ

where ER is the erosion ratio (kg/kg), A is an empirical constant, V is the particle impingementspeed, n is an empirical coefficient. Previous studies at the Erosion/Corrosion Research Center atThe University of Tulsa demonstrated that a value of n equal to 1.73 was a representative valuethat fits erosion experiments using various oilfield materials. Thus a value of 1.73 was used in thiswork. Fs is a particle shape coefficient; Fs ¼ 1:0 for sharp (angular), 0.53 for semi-rounded, or 0.2for fully rounded sand particles. While f ðhÞ is the function of the impact angle that is given by

f ðhÞ ¼ ah2 þ bh for h6ux cos2 h sinðwhÞ þ y sin2 hþ z for h > u

�ð20Þ

where u, a, b, w, x, y, and z are empirical constants that depend on the material being eroded. Thesuitable values of the model constants, assuming V has units of ft/s, are provided in Table 1 forcarbon steel [24] and aluminum [10]. In the post-processor, the erosion is visualized as the pen-etration rate profile within the geometry. The penetration rate is defined as the local wall thicknessloss rate caused by erosion. The penetration rate is determined when the local wall mass loss rateis divided by the local cell area and the density of wall material. For this work, the penetrationrate is converted to penetration per mass of sand, to remove the dependence on sand rate.

3. Application of the CFD-based erosion prediction procedure

The CFD-based erosion prediction procedure is applied to simulate the flow field and thuspredict the erosion in an elbow and a plugged tee. In this section, a grid refinement study ispresented. A study on the effect of the number of particles released at the inlet on the maximumerosion is also shown. This section also discusses the influence of particle–wall collision model onparticle’s trajectories and consequently the predicted erosion profile in the geometry.

3.1. Grid refinement study

The CFD-based erosion prediction procedure is applied to predict the erosion in an elbow anda plugged tee (both with 1-in. diameter), as shown in Figs. 1 and 2. In Fig. 1, the elbow is a

Fig. 1. Schematic of standard elbow geometry.

Fig. 2. Schematic of plugged tee geometry.


standard elbow with a curvature ratio ðr=DÞ equal to 1.5. In Fig. 2, the relative plugged lengthðL=DÞ is equal to 1.5. In order to accurately predict the erosion, a grid sensitivity study must beperformed. As an example, the grid refinement study for the elbow is demonstrated. The erosionin the elbow is predicted under the flow conditions as listed in Table 2. The solution options arealso summarized in Table 2. Instead of simulating the actual number of particles that correspondto the specified mass of sand (40 lb/day or 2.08· 10�4 kg/s), CFX tracks a certain number ofparticles to represent the mass of sand. In this section, 100,000 particles were tracked which meansthe mass rate that each sand particle conveys is 2.08· 10�9 kg/s. It is needed to point out that theactual physical properties of sand particles (diameter and density) are used to determine the

Table 2

Summary of flow conditions and solution options

Temperature 298 K

Carrier fluid Air

Fluid velocity 150 ft/s (45.72 m/s)

Sand particle diameter 150 lmSand flow rate 40 lb/day (2.08 · 10�4 kg/s)

Sand volume concentration 0.0042%

Pipe material Aluminum

Turbulence model Differential stress [18]

Differencing scheme QUICK [13]

Particle rebound model Stochastic rebound model [21]


particle trajectories and the mass of each particle is required to calculate the erosion for individualparticle impingements. Since one-way coupling is used the number of particles (or mass flowof particles) does not affect the flow solution and particle trajectories, so concentration effects arenot considered.

The grid refinement process was performed in two steps. The first step was to refine the grid onthe plane that is normal to the flow direction with the axial grid spacing fixed. The second step isto adopt an appropriate mesh of the cross-area plane and to refine the axial direction grid,especially for the elbow curved section. In order to generate structured grids that are compatiblewith the solver, a five-block geometry is built for the elbow, as shown in Fig. 3. In Fig. 3, thelength ratio AB/AC is equal to 2.4. In the first step, the erosion prediction is performed for 9different meshes. The grid number on length AB and AC for each mesh is listed in Table 3. As arepresentative case, the cross-area plane mesh of Mesh No. 5 is plotted in Fig. 4. For all these9 meshes, the grid number of the elbow curved section (DE) is 30 where length DE is shown inFig. 5.

The stochastic particle–wall collision rebound model is used to predict the erosion. 50,000 sandparticles are released randomly at the inlet of the elbow to represent the sand mass flow rate asspecified in Table 2. As a sample, the predicted erosion profile using Mesh No. 5 is shown in Fig.6, where the erosion is in mil/lb (the wall thickness loss per unit mass of sand). Fig. 6 shows thatthe maximum erosion of 11.8 mil/lb (659 lm/kg) occurs at the center area of the elbow section.

The predicted maximum erosion normalized using the coarsest grid (Mesh No. 1) of each meshis shown as Fig. 7. In Fig. 7, the horizontal axis represents the cross-area plane grid densitynormalized with respect to grid density of Mesh No. 1. From Fig. 7, the erosion approaches aspecific value as the grid density increases. The variation of the maximum erosion between MeshNo. 8 and Mesh No. 9 is about 2%, and it is about 20% between Mesh No. 5 and Mesh No. 9. 20%is well within the acceptable tolerance for erosion calculations. So Mesh No. 5 is deemed suffi-cient.

Fig. 3. Five-block elbow.

Table 3

Grid numbers of the cross-area plane meshes

Meshes No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9

N1 3 4 6 8 10 12 16 20 24

N2 5 6 9 12 15 18 24 30 36

Fig. 4. Representative cross-area plane mesh.

Fig. 5. Elbow section mesh.


In the second step of the grid refinement, the erosion is predicted for four different axial gridspacings with the cross-area plane grid spacing fixed. As a combined consideration of predictionaccuracy and computational cost, the cross-area plane Mesh No. 5 is selected in the second step.The axial grid number used on the elbow section curve (DE) is listed in Table 4. It is worth notingthat Mesh No. 5 of Table 3 is equivalent to Mesh No. 11 of Table 4.

The variation of the normalized predicted maximum erosion for each mesh listed in Table 4 isplotted as Fig. 8. The predicted maximum erosion of each mesh is normalized by that of MeshNo. 10. The grid density of the elbow curved section using Mesh No. 10 is defined as 1. Theerosion appears to converge with the increase of elbow curved section axial grid density.

The remaining simulations of this study adopted Mesh No. 5 (No. 11). Identical grid spacing isused in the generation of the mesh of the plugged tee.

Fig. 6. Sample erosion profile of the elbow.

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

1 11 21 31 41 51 61

Cross-Area Plane Grid Density

Nor

mal

ized

Pre

dict

ed M

axim

um

Eros

ion

Fig. 7. Variation of the maximum erosion with the cross-area grid density.

Table 4

Number of grid in the elbow section curve meshes

Meshes No. 10 No. 11 (No. 5) No. 12 No. 13

DE 20 30 40 60


3.2. Particle number independent study

As stated previously, a certain number of particles are used in CFX to represent the given massof sand to calculate the erosion and the mass of each particle is determined by applying the massof sand divided by the number of sand particles used. The erosion on the wall due to individualparticle impacts is related to the mass that each particle represents. In order to insure that astatistically representative set of particle impingements are obtained, the effect of particle numberon the quantity of the predicted erosion needs to be investigated. The purpose of this section is to

11.011.021.031.041.051.061.071.08

1 1.5 2 2.5 3 3.5Elbow Section Axial Grid Density

Nor

mal

ized

Pre

dict

ed

Max

imum

Ero

sion

Fig. 8. Variation of the maximum erosion with the axial direction grid density.


obtain the particle number that is sufficiently large to insure the predicted erosion due to the givenamount of sand is independent of the number of particles simulated.

The erosion prediction procedure is applied to the elbow and the plugged tee for six particlenumbers: 1000, 5000, 10,000, 25,000, 50,000, and 100,000 for the flow conditions and sand volumeconcentration given in Table 2. Figs. 9 and 10 demonstrate how the normalized predicted

0.6

0.7

0.8

0.9

1

0 20000 40000 60000 80000 100000

Number of Particles

Nor

mal

ized

Pre

dict

ed

Max

imum

Ero

sion

Fig. 9. Variation of the predicted maximum erosion with the number of particles in the elbow.

0.5

0.6

0.7

0.8

0.9

1

0 20000 40000 60000 80000 100000

Number of Particles

Nor

mal

ized

Pre

dict

ed

Max

imum

Ero

sion

Fig. 10. Variation of the predicted maximum erosion with the number of particles in the plugged tee.


maximum erosion changes with the input particle number in the elbow and the plugged tee,respectively. The predicted maximum erosion obtained for each particle number is normalized byerosion obtained using 1000 particles in the elbow and the plugged tee. Figs. 9 and 10 demonstratethat the effect of particle number on the predicted erosion is negligible when the particle number isgreater than 50,000, which means 50,000 particles are sufficient to provide statistically represen-tative results. Thus, 50,000 particles were released at the inlet of the elbow and plugged tee for theremaining simulations of this study.

3.3. Effect of particle–wall collision rebound model

The particle rebound model proposed by Forder et al. [12] and the stochastic particle reboundmodel by Grant and Tabakoff [21] are evaluated in a standard elbow and a plugged tee. The flowconditions and sand flow rate are listed in Table 2.

Figs. 11 and 12 show the sample particle trajectories and the erosion rate profile predicted bythe Forder rebound model. Figs. 13 and 14 demonstrate the sample particle trajectories and theerosion profile in the elbow predicted by the stochastic particle rebound model. Ten representativeparticle trajectories are shown in Figs. 11 and 13. As shown in these figures, similar particletrajectories are predicted by the Forder rebound model and the stochastic rebound model in theelbow. From Figs. 12 and 14, a slight difference of the erosion pattern in the elbow as well as themaximum value of the erosion is observed. The maximum erosion predicted by the Forder re-bound model is 13.7 mil/lb (765 lm/kg) that is about 15% greater than the stochastic reboundmodel. In Fig. 12, two antenna-like high erosion regions are observed. Simulations explain thatmultiple impingements of one particle may occur in the elbow section. The antenna-like higherosion region is due to the secondary impingements of the particles that have similar impactangle and incoming speed as the first impingement. This behavior did not occur when the sto-chastic particle rebound model was applied.

For the plugged tee, the sample particle trajectories in Fig. 15 using the Forder rebound modeldemonstrate that the particles become trapped in the plugged section of the tee. Some individual

Fig. 11. Sample particle trajectories in the elbow predicted by the Forder particle rebound model.

Fig. 12. Erosion rate profile in the elbow predicted by the Forder particle rebound model.

Fig. 13. Sample particle trajectories in the elbow predicted by the stochastic particle rebound model.


particles impinge the wall in this section hundreds of times along a recirculation path before theygo to the downstream section. This simulation result is not physical because of the nature of theparticle–wall collision rebound process. The repeating particle impingements result in highlylocalized erosion on the wall near the intersection of the plug, as shown in Fig. 16. The maximumerosion predicted by the Forder rebound model is 30 mil/lb (1675 lm/kg) at the corner of theplugged tee. However, from experimental observations it is anticipated that the maximum erosionoccurs on the surface of the plugged end. When simulations with the stochastic rebound wereconducted, due to variation in particle rebound introduced using the stochastic rebound model,the localized repeating impingements are not predicted (as seen in Fig. 17). The randomly scat-tered particle rebound results in more distributed particle impingements as well as erosion damagein the plugged section. From Fig. 18, the maximum erosion is 5 mil/lb (279 lm/kg) in the plugged

Fig. 14. Erosion rate profile in the elbow predicted by the stochastic particle rebound model.

Fig. 15. Sample particle trajectories in the plugged tee predicted by the Forder particle rebound model.


end of the plugged tee. The simulations in the plugged tee demonstrate that the application of thestochastic particle rebound model is required for the cases that posses strong particle recircula-tion.

4. Experimental validation of predicted erosion in elbow and plugged tee

In order to evaluate the erosion predicted by the CFD-based erosion procedure, the trend of theerosion with respect to the air velocity in the elbow and plugged tee are obtained numerically as

Fig. 16. Erosion rate profile in the plugged tee predicted by the Forder particle rebound model.

Fig. 17. Sample particle trajectories in the plugged tee predicted by the stochastic particle rebound model.


well as experimentally. Erosion predictions and experiments are performed in a standard elbowand a plugged tee with 1-in. diameter for three air velocities: 50, 100, and 150 ft/s. The relativeplugged length ðL=DÞ of the plugged tee is equal to 1.5. For all simulations in this section, the gridspacing of Mesh No. 5 is applied for both elbow and plugged tee. The Reynolds Differential Stressturbulence model and the QUICK (third order) differencing scheme are used to simulate the flowfield. The stochastic particle rebound model is employed in the particle trajectories calculation.50,000 particles are released in the inlet of the elbow and plugged tee to obtain the particle numberindependent solution.

Fig. 18. Erosion rate profile in the elbow predicted by the stochastic particle rebound model.


4.1. Experimental facilities and procedure

Air is used as the carrier fluid for all experimental tests. Erosion tests are performed on test cellsrepresenting an elbow and a plugged tee with 1-in. diameter. The flow is incoming verticallyupward and discharged horizontally. The schematic of the test flow loop is shown in Fig. 19. Thetest cells and specimens of the elbow and plugged tee are shown as Figs. 20 and 21, respectively.The specimens are made of aluminum. The elbow specimen is a 0.25

00 · 0.2500bar that is bent to

match the radius of curvature of the elbow. Specimen 1 of the plugged tee covers the plugged endsurface. Specimens 2–4 have the width of 0.25

00and are placed on the center plane of the plugged

tee test cell. Mass loss measurements are taken for the elbow and plugged tee specimens. The testsin the elbow and plugged tee are repeated three times for each air velocity. 500 g of sand is injected

Fig. 19. Schematic sketch of the test flow loop.

Fig. 20. Test cell and specimen of the elbow.

Fig. 21. Test cell and specimens of the plugged tee.


through the sand injector continuously during a fixed period of time (40 min), which is about 40lb/day. In addition, the local thickness loss was also determined for the elbow specimen andspecimen 1 of the plugged tee by using a profilometer for the case with the air velocity of 150 ft/s.Measurements are taken at seven locations that are evenly distributed along the elbow specimenas well as the center line of the plugged tee specimen 1.


4.2. Experimental data

The mass losses of the elbow and plugged tee specimens are taken for different air velocities,and the average values are summarized in Table 5. From Table 5, it is apparent that the masslosses of specimens 3 and 4 of the plugged tee are negligible as compared to the elbow specimenand specimens 1 and 2 of the plugged tee. For the elbow specimen and specimens 1 and 2 of theplugged tee, the average mass loss and 95% confidence intervals are plotted versus the air velocityas Fig. 22.

4.3. Experimental data and simulations

In this study, the mass loss of the elbow and plugged tee specimens, as listed in Table 3, isconverted to a thickness loss by applying the density of aluminum and assuming the erosion isuniform over the entire specimen surface that is exposed to particles. From Table 3, for the casethat the air velocity is 150 ft/s (45.72 m/s), the average experimental erosion rate of specimen 1 ofthe plugged tee is 0.25 mil/lb (14 lm/kg) which is three times greater than specimen 2 of theplugged tee. From Fig. 18, the maximum erosion predicted by the stochastic particle reboundmodel occurs on the plugged end surface. Fig. 18 also shows that the maximum erosion on theplugged end surface is about two times greater than the maximum erosion at the plug intersectioncorner. This is consistent with experimental data.

Table 5

Average mass loss of the elbow and plugged tee specimens

Weight loss (g) Air velocity (ft/s)

50 100 150

Elbow specimen 0.0019 0.0051 0.0094

Plugged tee specimen 1 0.00137 0.0059 0.0098



Plugged tee specimen 4 0 0.0002 0.0003

Fig. 22. Averaged mass loss and 95% confidence interval of the elbow and plugged tee specimens.


For the case of air velocity equal to 150 ft/s, the measured erosion profile of the elbow specimenand specimen 1 of the plugged tee are compared with predicted erosion profiles, as shown in Figs.23 and 24. From Fig. 23 it is clear that the predictive erosion model is able to accurately predictthe erosion profile for the elbow as well as the location where the maximum erosion occurs. Good

Fig. 23. Comparison of predicted erosion profile with measured erosion profile in the elbow.

Fig. 24. Comparison of predicted erosion profile with measured erosion profile in the plugged tee.


agreement between the predicted erosion profile of the plugged tee and the experimental data isalso observed in Fig. 24. The numerically and experimentally based trends of erosion with respectto air velocity in the elbow and plugged tee are plotted in Figs. 25 and 26 by calculating theaverage erosion for different air velocities. The measured average erosion is determined from theaverage thickness loss based on mass loss measurements. The predicted average erosion ofthe elbow is obtained for the location that corresponds to the elbow specimen used in theexperiment. In Figs. 25 and 26 the predicted average erosion values of the elbow and plugged havesimilar trends as the data, which indicates that the CFD-based erosion prediction procedure isreliable in predicting the trend of erosion.

In Figs. 23–26 it is demonstrated that the predicted erosion in the elbow and plugged tee isover-predicted by an order of magnitude. Good agreement between the predicted and measurederosion profiles as well as the trends of erosion implies that the CFD-based erosion model isaccurate in predicting the flow field, and calculating particle trajectories when the stochastic

0.1

1

10

100

40 60 80 100 120 140 160

Air Velocity (ft/s)

Eros

ion

(mil/

lb)

Predicted Average Erosion of Elbow

Measured Average Erosion of Elbow

Fig. 25. Trend of erosion of the elbow.

0.01

0.1

1

10

100

40 60 80 100 120 140 160

Air Velocity (ft/s)

Eros

ion

(mil/

lb)

Predicted Average Erosion of Plugged Tee

Measured Average Erosion of Plugged Tee

Fig. 26. Trend of erosion of the plugged tee.


particle rebound model is applied. Thus the over-prediction of erosion may indicate that refine-ment of the erosion correlation given in Eq. (19) should be investigated to provide more accurateprediction of the magnitude of erosion.

Simulations based on the stochastic particle rebound model show that the maximum erosionoccurs at the plug end surface of the plugged tee, which is consistent with the experimental datashown in Figs. 22 and 24. The analysis of Figs. 22, 24 and 26 concludes that the application of thestochastic particle rebound model is effective to reasonably estimate the erosion rate and patternin a plugged tee.

5. Conclusion

A CFD-based erosion prediction procedure is presented in detail in this paper. This compre-hensive procedure includes: flow simulation, particle tracking and erosion calculation. Essentialissues, such as grid space and particle number effects, of predicting erosion by applying thisprocedure are discussed. Since classic particle rebound models that can provide reasonable pre-diction in elbows are not suitable for plugged tees, the focus of this paper is to investigate theimpact of a stochastic particle rebound model on erosion of elbows and plugged tees. Further-more, the effectiveness of the CFD-based erosion prediction model is validated against experi-mental data.

Numerical simulations as well as experimental erosion tests are performed in an elbow and aplugged tee with 1-in. diameter. Simulations show that particle rebound model plays an importantrole in determining the motion of particles. The particle rebound model may have a significantimpact on the particle trajectories as well as the erosion profile. For cases where the strong particlerecirculation potentially occurs, such as in a plugged tee, the application of the stochastic particlerebound model is required to acquire realistic simulation results of erosion. Good agreement isachieved between the experimental results and simulations based on the application of the sto-chastic particle rebound model.

This erosion prediction procedure is validated by comparison of the predicted erosion profilesas well as the trend of average erosion with the experimental data in the elbow and plugged tee.Comparisons show that the CFD-based erosion prediction procedure is able to reasonably predictthe erosion profile and satisfactorily capture the trend of erosion with respect to the carriervelocity. However, the quantity of erosion is over-predicted by about one order of magnitude,which suggests that the erosion correlation needs to be re-evaluated in order to accuratelyquantify the erosion. The accurate determination of the empirical constant A in Eq. (19) will becrucial to improve the performance of the predictive erosion model. Currently this work is inprogress in a separate study of the Erosion/Corrosion Research Center at The University of Tulsa.

Acknowledgements

The authors would like to acknowledge the member companies of the Erosion/CorrosionResearch Center at The University of Tulsa for supporting this project.


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