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Wear 261 (2006) 715–729

Numerical and experimental investigation of the relative erosion severitybetween plugged tees and elbows in dilute gas/solid two-phase flow

Xianghui Chen a,∗, Brenton S. McLaury b, Siamack A. Shirazi b

a Alion Science & Technology, 8502 “A” N. 128th E. Ave., Owasso, OK 74055, USAb Department of Mechanical Engineering, University of Tulsa, 600 South College Avenue, Tulsa, OK 74104, USA

Received 29 April 2005; received in revised form 12 January 2006; accepted 24 January 2006

Available online 28 February 2006

Abstract

Elbows, that are integral part of piping systems, are vulnerable in erosive environments. Plugged tees are used in industrial practice to replace

elbows when erosion is expected. However, it remains unclear that plugged tees reduce erosion. Thus, this paper investigates the relative erosion

severity betweenplugged teesand elbows for dilutegas/solid two-phaseflow where thepressureis close to the atmospheric pressure. A computational

fluid dynamics (CFD) based erosion prediction model was applied to predict the relative erosion severity. Experimental tests were conducted to

verify the simulation results obtained for gas/sand flows. The ratio of erosion at the end of the plugged section to that in an elbow was found to

approach a constant value for a range of conditions. A correlation is presented that provides the ratio of erosion of the outer downstream corner of

the plugged tee to that in an elbow. The significant effect of sand loading on the relative erosion severity was discussed. The influence of phase

density (e.g. water/sand flow) was preliminary explored.

© 2006 Elsevier B.V. All rights reserved.

Keywords: Solid particle; Erosion; Plugged tee; Elbow; CFD; Gas–solid flow

1. Introduction

Erosion caused by entrained solid particles in piping systems

is a concern for many industrial practices. Elbows, that are an

integral part of pipingsystems,are vulnerable in erosive environ-

ments. Wang’s study [1] shows that increasing the elbow radius

is an effective way to reduce the sand erosion damage. When it

is unfeasible to use a long radius elbow due to space considera-

tions, plugged tees are usually put in service rather than standard

elbows to reduceerosion.As sketchedin Fig.1, the physical con-

figuration of plugged tees dictates that plugged tees are subject

to erosion damage when solid particles are present. Therefore,

knowledge of the relative erosion (severity) between plugged

tees and elbows provides a guideline for appropriate application

of these two geometries. The relative erosion is defined as the

maximum erosion in the plugged tee divided by the maximum

erosion in the elbow.

∗ Corresponding author. Tel.: +1 918 274 9398; fax: +1 918 274 9399.

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

Elbows are a typical subject of erosion studies primarily

because of the broad applications and susceptibilities to erosion.

For instance, erosion in elbows was experimentally analyzed

by different investigators [2–7]. Several empirical correlations

and mechanistic models were developed to calculate erosion

in elbows for gas/solid and gas/liquid/solid flows [3,5,7,8].

Recently, the computational fluid dynamics (CFD) approach has

been widely applied for erosion prediction in elbows [1,9–14].

Erosion studies in plugged tees are rare in the literature, except

preliminary discussions found in references [3,7,10]. Thus, very

limited informationis available in the literature regardingthe rel-

ative erosion between plugged tees and elbows. Bourgoyne [3]

compared measured erosion between plugged tees and elbows

for gas/solid flow with high sand volume concentrations (about

0.12%). As will be discussed in this paper, Bourgoyne’s obser-

vations based on high sand loadings are very different from the

findings of this study for dilute gas/solid flow.

Thus, the purpose of this study is to provide deeper under-

standing of the relative erosion between plugged tees and the

elbows with the primary focus on dilute air/sand flows. A com-

putationalfluid dynamics (CFD)based erosion prediction model

was applied to numerically predict erosion in plugged tees and

0043-1648/$ – see front matter © 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.wear.2006.01.022

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716 X. Chen et al. / Wear 261 (2006) 715–729

Nomenclature

a empirical constant in Eq. (10)

A empirical constant in Eq. (9)

b empirical constant in Eq. (10)

B body force vector (N)

C D drag coefficientd p particle diameter (m)

D pipe diameter (m)

epar particle impingement restitution coefficient in

tangential direction

eper particle impingement restitution coefficient in

normal direction

EE original prediction of end region

Ef E prediction of end region due to the first impinge-

ment

ESC original prediction of side and corner region

Ef SC prediction of side and corner region due the first

impingement

EASC prediction of side and corner region with adjusted

particle recirculation

ER erosion ratio defined by Eq. (9) (kg/kg)

f (θ ) particle impact angle and pipe material properties

dependent correlation

F A added mass force (N)

F B buoyancy force (N)

F D drag force (N)

F P pressure gradient force (N)

F S particle shape coefficient

I unity matrix

L plugged section length of the plugged tee

L0 particle terminal distance (m)

mp mass of particle (kg)

n empirical constant used in Eq. (9)

p pressure (Pa)

r elbow radius (m)

Re Reynolds number

u fluid velocity fluctuation components (m/s)

U fluid velocity vector (m/s)

V p particle velocity vector (m/s)

V 0 particle impingement speed (m/s)

w empirical constant in Eq. (10)

x empirical constant in Eq. (10)

y empirical constant in Eq. (10) z empirical constant in Eq. (10)

Greek letters

α contribution factor of particle recirculation

impingements

εpar standard deviation of epar

εper standard deviation of eper

µ fluid viscosity (Pa s)

θ particle impingement angle (◦)

θ 0 empirical particle impingementangle in Eq. (10)

(◦)

ρ fluid density (kg/m3)

σ surface tension (Pa m)

Φ stress tensor (N)

Fig. 1. Schematic sketch of the plugged tee and elbow.

elbows for a broad range of flow conditions. Additionally, exper-

imental erosion tests were conducted in air to evaluate the sim-

ulation results. Based on simulations and experimental data, the

relative erosion between two regions of the plugged tees and

elbows are discussed. Further experiments were performed to

preliminarily investigate the sand volume concentration effect

on the relative erosion severity. The influence of fluid properties

is also discussed via the CFD erosion simulations in plugged

tees and elbows in water/sand flow. Bourgoyne’s observations

of erosion for water/sand flow qualitatively support the CFD

erosion predictions.

2. CFD prediction

2.1. CFD-based erosion prediction model

This paper describes only the framework of the erosion pre-

diction model. Further details are given by Chen et al. [10].

Predicting erosion by employing this model is a three-step pro-

cess: the continuous carrier fluid flow field simulation; particle

tracking using a Lagrangian approach; and erosion calcula-

tion using information on particle impingements on the wall.

The single-phase CFD-based erosion prediction model is imple-

mented in the commercially available CFD code, CFX-4. Thestringent assumption of this model is that particle–particle inter-

actions are negligible. This assumption implies that the model

is designed for dilute systems.

The first step is to solve the continuous carrier fluid flow

equations. The continuity and momentum equations employed

by CFX-4 are given in Eqs. (1) and (2), respectively [15]:

∂ρ

∂t +∇ · (ρU ) = 0 (1)

∂(ρU )

∂t

+∇ · (ρU ⊗ U ) = B +∇ · (−ρu ⊗ u + Φ) (2)

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X. Chen et al. / Wear 261 (2006) 715– 729 717

where the stress tensor, Φ, is given by

Φ = −p

ρI +

µ

ρ

∇ U + (∇ U )

T

(3)

After obtaining the flow field, the particle trajectories are sim-

ulated. Assuming particles not to affect the flow field, one-way

coupling between sand particles andthe carrier fluid is applied in

the current model. It is noted that the one-way coupling methodis suitable only for low solid loading. Clift et al. [16] proposed

the governing equation of particle motion in the fluid based on

Newton’s second law:

mpdV p

dt = F D + F P + F B + F A (4)

F D, F P, F B and F A represent the drag force, pressure gradient

force, buoyancy force and added mass force, respectively. Chen

et al. [10] gave full descriptions of these forces.

Once a particle impinges the pipe wall, the accompanied

energy lost during the impingement process must be taken into

account to determine the reflected particle trajectory. Grantand Tabakoff [17] performed sand particle impingement experi-

ments on aluminum specimensin the wind tunnelwhere thesand

particle diameter is 200m and the air velocity is 110–170 m/s.

The experimental data indicates that the restitution coefficient

is dominantly affected by the particle impact angle, θ . Grant

and Tabakoff treated the particle rebound dynamics of the parti-

cles in a statistical sense and postulated the mean values of the

coefficients of restitution (epar and eper) and the corresponding

standard deviations (εpar and εper):

epar = 0.998 − 1.66θ + 2.11θ 2 − 0.67θ 3 (5)

eper = 0.993 − 1.76θ + 1.56θ 2 − 0.49θ 3 (6)

εpar = 2.15θ − 5.02θ 2 + 4.05θ 3 − 1.085θ 4 (7)

εper = −0.0005 + 0.62θ − 0.535θ 2 + 0.089θ 3 (8)

Chen et al. have demonstrated the significance of applying the

concept of stochastic particle rebound.

Impingement information, such as impact speed and impact

angle,is gathered as particleshit thewall. Using this information,

the erosion ratio can be calculated. The erosion ratio is defined

as the mass loss of the pipe wall due to erosion divided by the

mass of particles impacting the wall. According to Ahlert [18]

and McLaury [19], the erosion ratio is given byER = AF sV n0 f (θ ) (9)

where ER is the erosion ratio (kg/kg) and V 0 is the particle

impingement velocity; A is a material dependent coefficient. For

the carbon steel, A is a function of the material Brinell hardness,

B. F s is a particle shape coefficient; F s = 10 for sharp (angular),

0.53 for semi-rounded, or 0.2 for fully rounded sand particles;

n is an empirical constant and takes the value of 1.73; and f (θ )

is particle angle dependent function which is determined by

f (θ ) =

aθ 2 + bθ, for θ ≤ θ 0

x cos2 θ sin(wθ ) + y sin2 θ + z, for θ > θ 0(10)

Table 1

Erosion model empirical constants

Empirical constant Material

Carbon steel Aluminum

A 1559B−0.59 ×10−9 0.388×10−7

θ 0 15◦ 10◦

a 38.4 −34.79b 22.7 12.3

w 1 5.205

x 3.147 0.147

y 0.3609 −0.745

z 2.532 1

n 1.73 1.73

The relevant empirical constants in Eqs. (9) and (10) are sum-

marized in Table 1. Divided by the pipe material density and

the local grid cell area, the erosion ratio can be converted to the

local wall thickness loss or the so-called local penetration.

2.2. CFD prediction of the relative erosion between

plugged tees and elbows

As previously discussed, long radius elbows are more erosion

resistant than standard radius (r / D = 1.5) elbows. In industrial

practice, plugged tees rather than standard radius elbows are

applied in an erosive environment if space is not available for

long radius elbows. Thus, it is meaningful to make comparisons

of erosion between plugged tees and elbows. The physical con-

figurations of plugged tees and elbows are sketched in Fig. 1.

A plugged length, L, of 1.5 D is used in this study. By applying

the above described CFD-based erosion prediction procedure,

erosion predictions were performed in plugged tees and elbowsfor the flow conditions tabulated in Table 2. It should be noted

that the sand volume concentration for these flows is less than

0.0015%. Thus, the flows are considered as dilute gas/sand flows

to which the CFD-based erosion prediction model is applicable.

As a sample, detailed predictions in the 0.0254 m diameter

plugged tee and elbow are presented for air flow with a mean

velocity of 45.72 m/s and a sand diameter of 150m. A sample

of predicted particle trajectories (of 10 particles) is shown in

Fig. 2. As expected, the majority of the particles released at the

pipe inlet impinge the inlet projected area of the plugged tee and

the elbow. For this flow condition, the particle inertia dominates

the particle motion. As shown in Fig. 2(a), particle recirculationcharacterizes the particle motion in the plugged tee. As will be

discussed, the potential consequence of particle recirculation is

concentrated erosion at a certain area of the plugged tee. In prac-

tice, the cap (the end surface) of the plugged tee can be made

with a desired thickness. It is also more economical to make the

Table 2

Simulation matrix of erosion prediction in plugged tees and elbows

Pipe diameter (m) 0.0254, 0.0508, 0.1016, 0.2032

Air velocity (m/s) 15.24, 30.48, 45.72

Particle diameter (m) 50, 100, 150, 220, 300

Sand flow rate (kg/s) 3.0e-4

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718 X. Chen et al. / Wear 261 (2006) 715–729

Fig. 2. Predicted sample particle trajectories in the plugged tee and elbow.

end surface thicker than the other sections of the plugged tee.

Hence, two regions in the plugged tee are defined (see Fig. 3(a))

to clarify the erosion in the corresponding regions: end region

and side and corner region. The predicted erosion patterns are

presented in Fig. 3. It should be noted that erosion is given as

penetration (mm/kg), which represents the pipe wall local thick-

ness loss per unit mass of sand loading. Fig. 3(a) indicates that

themaximum erosion occursat theend surface of theplugged tee

(end region). Considerable erosion is also observed at the side

and corner region. As shown in Fig. 3(b), high erosion occurs

in regions corresponding to the downstream projection of the

inlet area for on the elbow. For this sample case, the maximum

penetration of the plugged tee (in the end region) is about half

of that in the elbow, which means the relative erosion between

the plugged tee end region and the elbow is about 0.5.

For the flow conditions listed in Table 2, the maximum pene-

trations were determined from the simulation results for the end

region and side and corner region of the plugged tees, respec-

tively. Dividing these maximum penetrations by the maximumpenetration in the elbows yields the relative erosion for both the

end region and side and corner region of the plugged tee. The

results are presented in Figs. 4–7 for four pipe diameters as a

function of particle diameter. It is clear that therelative erosion in

the end region is strongly affected by the pipe diameter and par-

Fig. 4. Predicted relative erosion between the plugged tee and the elbow with

0.0254 m diameter.

ticle diameter. Depending on the actual flow conditions, a peak

value of the relative erosion appears. The trends of the relative

erosion in the end region also tend to converge to a constant of

0.5 as the particle diameter becomes sufficiently large. Similar

Fig. 3. Predicted erosion pattern in the plugged tee and elbow of air/sand flow.

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X. Chen et al. / Wear 261 (2006) 715– 729 719


0.0508 m diameter.

trends of the relative erosion of the side and corner region can

be observed, but typically approaches a smaller value than the

end region as the particle diameter increases. This information is

very useful since erosion occurring at the side and corner region

determines the service life of the plugged tee.

3. Experimental study

3.1. Description of experimental set-up

Air was used as the carrier fluid and was near standard condi-

tions in the test cell. As schematically shown in Fig. 8, air with

theinjected sand flows vertically upwardinto the test section andwas discharged horizontally. Erosion tests were performed on

test cells representing a plugged tee and an elbow with 25.4 mm

diameter, as shown in Fig. 9. The relative plugged length of

the plugged tee ( L / D) is 1.5, and the elbow radius (r / D) is

1.5. Elbow and plugged tee specimens are made of aluminum.

Specimen 1 of the plugged tee covers the plugged end surface.

Specimens 2–4 have a width of 6.4 mm and are placed on the

center plane of the plugged tee test cell. The elbow specimen

is a 6.4 mm× 6.4 mm bar that was bent to match the radius of

curvature of the elbow and is also place along the center plane.

Sand was injected through the sand injector at a constant rate

during each test.


0.1016 m diameter.

Experiments of mass loss measurements indicate that erosion

of specimens3 and4 of theplugged teeis negligible as compared

to specimens 1 and 2 of the plugged tee and the elbow specimen.

Thus, local thickness loss measurement of specimens 1 and 2 of

the plugged tee and the elbow specimen was measured to obtain

the relative erosion between both regions of the plugged tee (end

region and side and corner region) and the elbow. Local thick-

ness loss profiles were measured using a profilometer (shown in

Fig. 10). The accuracy of the profilometer is ±0.1m.

Before and after the test, the specimen surface profiles were

recorded by the profilometer at the same location. The differ-

ence of these two surface profiles determines the local thickness

loss provided that a measurement reference is given. “V ”-shapedscratchesare drawn on the specimensurface. The cross-sectional

profile (depth and shape) of the scratches are recorded by the

profilometer. It is assumed that the bottom of a scratch does not

erode, so the bottoms of the scratches serve as the profilometer

measurement reference locations. Due to the highly sensitive

nature of the local thickness measurement, the surface profiles

before and after the test must be taken at the identical location to

yield meaningful thickness measurements. Thus, two scratches

(major scratch and minor scratch) with a certain angle were

introduced on the specimen surface for each measurement (see

Figs. 11 and 12). The surface profiles were taken across these

two scratches with the profilometer reading line perpendicular

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720 X. Chen et al. / Wear 261 (2006) 715–729


0.2032 m diameter.

to the major scratch. Thus, the measurement location can beuniquely located using the distance between two scratches. In

the experiment, the uncertainty of the measurement location is

about ±2.54× 10−5 m. As shown in Fig. 11(a), measurements

were taken along the centerline from the bottom (flow discharge

side) toward the top of specimen 1 of the plugged tee. As shown

in Fig. 11(b), measurements were taken along the center line for

Fig. 8. Schematic of experimental set-up for erosion test.

both edges of specimen 2. For the elbow specimen, measure-

ments were made at seven locations in 10◦ increments along

the elbow specimen curve starting 20◦ downstream of the elbow

inlet, as seen in Fig. 12.

3.2. Experimental erosion test

Simulation results shown in Figs. 4–7 reveal that the particle

diameter is the dominant factor that affects the relative erosion

between the plugged tees and elbows. Thus, experimental ero-

sion tests were conducted to primarily validate particle diameter

effects. In the current study, three different average particle size

groups were used: 50–75, 125–175 and 212–275 m. The aver-

ageparticlediameters of these groupsare about 65,150, and250,

respectively. Thegas velocity was 45.72 m/s. The test conditions

are summarized in Table 3.

As a sample, the profilometer measurement of specimen 1

of the plugged tee is presented in Fig. 13 f or the case of parti-cle diameter = 150m. From Fig. 13, the maximum erosion is

40m/kg. Experiments show that the joint corner of specimen 2

of the plugged teeexperiences high erosion. Note that specimens

1 and 2 of the plugged tee correspond to the end region and side

and corner region of the plugged tee, respectively. For the elbow,

the maximum penetration is detected at measurement location

Fig. 9. Test cell and specimens of the plugged tee and elbow.

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X. Chen et al. / Wear 261 (2006) 715– 729 721

Fig. 10. Profilometer and surface profile measurement.

Table 3

Conditions of experimental erosion tests in the plugged tee and elbow

Pipe diameter (m) 0.0254

Mass of sand injected (kg) 1.0

Test time (min) 80

Fluid velocity (m/s) 45.72Sand volume concentration (%) 5.1e-4

Particle diameter (m) 65, 150, 250

5 which is about 60◦ downstream of the elbow inlet. Using the

measured maximum penetrations in specimens 1 and 2 of the

plugged tee and the elbow specimen, the relative of both the end

region and side and corner region are obtained.

4. Results analysis

4.1. Validation of simulation results

In Fig. 14(a), experimental data shows that the relative ero-

sion between the plugged tee end region and the elbow is almost

a constant having the value of 0.5. For sufficiently large particle

sizes (greater than 150m), the relative erosion is accurately

predicted. While for smaller particle sizes, the relative ero-

Fig. 12. Measurement locations and scratches of the elbow specimen.

sion is over-predicted. Careful analysis of the simulation results

(including erosion pattern and particle deposition rate) indi-

cates that particle recirculation intensity becomes stronger with

decreasing sand size, which results in more concentrated ero-

sion in the end region of the plugged tee. When particle sizeincreases, the erosion on the end surface is more uniformly

distributed. This analysis suggests that there is better agree-

ment between experimental and simulated results when erosion

caused by the particle recirculation is negligible. The parti-

cle recirculation seems to be numerically exaggerated in the

simulations for small particle sizes, which results in the over-

predictions of the relative erosion. The comparisons in Fig. 14

and the discussions are made based on the experimental data

and simulation results obtained for the plugged tee and elbow

with 0.0254 m diameter. Figs. 4(a)–7(a) consistently show that

the relative erosion between the end region of the plugged tee

and the elbow approaches a constant value of about 0.5 whenthe particle diameter becomes sufficiently large. Meanwhile, a

particle diameter dependent peak value of the relative erosion is

observed in Figs. 5(a)–7(a). Following the previous argument,

the peaks may be due to the unrealistic predictions of the particle

recirculation.

Fig. 11. Measurement locations and scratches of specimens 1 and 2 of the plugged tee.

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722 X. Chen et al. / Wear 261 (2006) 715–729

Fig. 13. Sample measurements to obtain local thickness loss on specimen 1 of the plugged tee using profilometer.

Excellent agreement is observed in Fig. 14(b) between the

experimental data and simulations. One question that may arise

here is why the over-prediction shown in Fig. 14(a) for small

sand sizes does not appear in Fig. 14(b). The predicted erosion

patterns for relevant flow conditions were carefully examined.

Fig. 14. Predicted and measured relative erosion between the plugged tee and

the elbow.

The predicted maximum erosion at the side and corner region

is located exactly at the joint corner, which is consistent with

experimental results. Erosion at the corner is primarily caused

by the first impingement of the particles. Thus, the predictions

in Fig. 14(b) are free of the numerical discrepancy of particle

recirculation that is included in Fig. 14(a). Again, it is pointed

out that this discussion is based on the numerical and exper-

imental results and observation of the erosion obtained in the

plug tee and elbow with 0.0254 m diameter and an air velocity

of 45.72 m/s. Figs. 5(b)–7(b) show that the relative erosion is

not a monotonic function of the particle diameter. Depending

on the actual flow conditions, the maximum erosion of the side

and corner region may be detected in the plugged section of the plugged tee rather than at the corner. For instance, Fig. 15

shows the predicted erosion pattern for the flow with air velocity

of 45.72 m/s, particle diameter of 50m, in 0.0508 m diam-

eter pipe. It can be deduced that the localized erosion in the

Fig. 15. Numerical exaggeration of particle recirculation causes localized ero-

sion in the plugged section of the plugged tee.

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X. Chen et al. / Wear 261 (2006) 715– 729 723


0.0254 m diameter due to first impingement of particles.

plugged section (not on the end surface) is due to the same

particle recirculation that is responsible for the over-predictions

of erosion on the end surface. Thus, exaggerated particle recir-

culation also results in the irregularity of the trends shown in

Figs. 5(b)–7(b).

4.2. Development of a simplified model

The particle recirculation characterizes the particle motion in

the plugged section of plugged tees. Fig. 14(a) shows that the

numerically exaggerated particle recirculation predictions result

in over-predicted erosion in the plugged tees. The first impinge-ment of particles and impingements resulting from recirculation

are two contributors to erosion in plugged tees. The contribution

due to each must be distinguished if it is deemed that particle

recirculation in the plugged section is being exaggerated in the

simulations. Figs. 16–19 present the relative erosion that is due

to the particle first impingement only.

Figs. 16–19 indicate that the relative erosion due to the first

impingement of particles is a monotonic function of the par-

ticle diameter and is weakly affected by the gas velocity. As

shown in Figs. 16(a)–19(a), the relative erosion of the end region

increases with the particle diameter and becomes a constant

value of 0.5 when the particle is sufficiently large. This constant

Fig. 17. Predictederosionbetweenthe plugged teeand theelbow with 0.0508 m

diameter due to first impingement of particles.

is also observed in Figs. 4(a)–7(a). More importantly, this con-

stant value is experimentally confirmed, as shown in Fig. 16(a).

The difference between the measurement and simulations is con-

tributed by particle recirculation. It is clear that the contribution

of particle recirculation decreases with increasing particle diam-

eter. Figs. 16(a)–19(a) show similar trends of the relative erosion

between the plugged tee end region and the elbows. Based on

these findings, it is recommended in this study that the relative

erosion between the end region of plugged tees and elbow is a

constant having the value of 0.5.

From Figs. 16(b)–19(b), the relative erosion due to the first

impingement of particlesfor theside andcorner regiondecreaseswith increasing particle diameter and approaches a constant

value that is diameter dependent. In order to effectively account

for the contribution of the particle recirculation on erosion in

the side and corner region, an empirical particle recirculation

impingement contribution factor is introduced. The purpose

of this contribution factor is to adjust the amount of erosion

resulting from particle recirculation, since the effect is being

over-predicted. A combination of the experimental and predicted

results of relative erosion between the plugged tee end region

and the elbow are used to determine this factor. The experiments

show that a constant value of 0.5 can be used for the relative

erosion for all particle sizes of interest. Predicted deviations

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724 X. Chen et al. / Wear 261 (2006) 715–729



examining the end region and the elbow from this constant areused to determine the particle recirculation contribution factor

as follows:

α =0.5 − Ef

E

EE − Ef E

(11)



where EE is the prediction shown in Figs. 4(a)–7(a); Ef E is the

prediction due to the first impingement of particles, as shown in

Figs. 16(a)–19(a). The particle recirculation contribution factor

indicates the ratio of actual erosion due to particle recirculation

to the overall predicted erosion of particle recirculation. Particle

recirculation in the plugged section results in erosion both in

Fig. 20. Relative erosion between the plugged tees (side and corner region) and the elbows.

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X. Chen et al. / Wear 261 (2006) 715– 729 725

the side and corner, and the end regions. Statistically, the par-

ticle recirculation contribution factor should be similar. Thus,

it is assumed that the end and side and corner regions have the

same particle recirculation contribution factor. Thus, the over-

predicted erosion due to particle recirculation in the side and

corner region can be approximately compensated by α. The rel-

ative erosion in this region is adjusted using α:

EASC = Ef

SC + α(ESC − Ef SC) (12)

where EASC is the adjusted relative erosion, ESC the prediction

presented in Figs. 4(b)–7(b), and Ef SC is the prediction due to

first particle impingement, as presented in Figs. 16(b)–19(b).

The gas velocity has little influence on the adjusted relative ero-

sion, which is also demonstrated by experimental data listed in

Table 4. Thus, the average value of the results obtained from Eq.

(12) f or three velocities can be used to represent the adjusted

relative erosion which is plotted in Fig. 20. It is clear that the

relative erosion between the side and corner region of plugged

tees to elbows strongly depends on theparticle diameter and pipediameter. As shown in Fig. 20, the trends can be closely corre-

lated by the following simplified model in the dimensionless

form:

EASC =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩−

0.0526 ln

L0

d p+ 0.4404

ln

ln

106d p

D

+ 3.6964

L0

d p

−0.0852

, d p < 65m

−

0.0994 ln

L0

d p+ 0.1054

ln

ln

106d p

D

+ 4.0 × 10−5 L0

d p+ 1.9268, d p ≥ 65m

(13)

where L0 (m) is the distance for a particle to reach its ter-

minal velocity in stagnant atmospheric air. L0 is determined

in the current study by using the simplified particle motionequation:

mpdV p

dt = F D + F A = −

πd 2p ρCD|V p − U |

8(V p − U )

−mp

2

dV p

dt (14)

where U = 0 and C D is the drag coefficient. Chen et al. [10]

describe how to determine C D.

Good agreement is observed in Fig. 20 between the adjusted

predictions obtained by using Eq. (12) and the predictions from

Eq. (13). Similar trends of relative erosion between the pluggedtees (side and corner region) and the elbows are also observed

for different pipe diameters. Apparently, the CFD results based

on Eq. (12) and the predictions by the proposed model (Eq. (13))

for the diameter of 0.0254 agree very well with the experimen-

tal data. Fig. 20 suggests that the introduction of the particle

recirculation impingement contribution factor is a reasonable

approximation method to account for erosion due to particle

recirculation in the plugged tees. It should be noted that the

recommended value of 0.5 for the end region and Eq. (13) are

strictly applicable to gas/sand flows where the carrier fluid prop-

erties are comparable to the atmospheric air and dilute gas/solid

systems.

5. Discussion

5.1. Particle tracking in the plugged tees

Good agreements between predictions and data shown in

Fig. 14 suggest that the flow field is reasonably predicted in

both the plugged tee and the elbow. However, the discrepancy

in Fig. 14(a) for small particles implies that particle track-

ing in the plugged tee needs to be improved. Particle tracking

is determined by the particle motion governing equation and

the particle-wall rebound model provided that the carrier fluid

flow simulation is sufficiently accurate. In the current study,

the stochastic particle rebound model by Grant and Tabakoff

[17] and the non-stochastic particle rebound model by Forder

et al. [20] are compared to investigate the effects of the parti-

cle rebound model on the particle tracking and resulted erosion.

The non-stochastic particle rebound model by Forder et al. is

expressed as follows:

epar = 1 − 0.78θ + 0.84θ

2

− 0.21θ

3

+ 0.028θ

4

− 0.022θ

5

(15)

eper = 0.988 − 0.78θ + 0.19θ 2 − 0.024θ 3 + 0.0027θ 4 (16)

For the air/sand flow with air velocity of 45.72m/s and sand

diameter of 50m, the predicted particle trajectories in the

plugged tee by the stochastic and non-stochastic models are

compared in Fig. 21. As shown in Fig. 21(a), severe particle

recirculation in the plugged section is predicted by the non-

stochastic model. Some particles recirculate repeating almost

identical paths more than one hundred times. These repeating

impingements at the same location cause highly localized ero-

sion in the plugged tee. The unrealistic particle recirculation

predictedby the non-stochastic particle rebound modelis greatly

improved by the stochastic model, as shown in Fig. 21(b). Theexplanation is that the particle rebound process is literally an

event of stochastic nature. However, the particle rebound mod-

els show little effect on particle tracking and predicted erosion

in the elbows where no particle recirculation impingements are

expected. Fig. 22 shows that the non-stochastic particle rebound

model gives predictions that drastically differ from experimental

results. The predictions are substantially improved by applying

the stochastic particle rebound model.

In spite of the significant improvement resulting from the

application of the stochastic particle rebound model, discrepan-

cies still exist in Fig. 14(a). It is noted that one-way coupling is

used for particle tracking and the predictions assume no particle

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726 X. Chen et al. / Wear 261 (2006) 715–729

Fig. 21. Sample particle trajectories in the plugged tee predicted by the stochastic and non-stochastic particle rebound models.

interactions. The discrepancies shown in Fig. 14(a) suggest that

these embedded assumptions may not suitable for the plugged

tees even when the sand loading is very low since considerableparticle recirculation occurs. It is expected that the predictions in

the plugged tees can be further improved by considering the par-

ticle interactioneffects in the particle motiongoverning equation

and using two-way coupling particle tracking.

5.2. Sand volume concentration effects

The simulations and experimental data were obtained from

air/sand flow with very low sand volume concentration,

0.0005%. These results show that erosion in plugged tees

is less than but comparable to erosion in elbows. However,

based on experiments with high sand loadings, Bourgoyne [3]

stated that erosion in plugged tees is less than in elbows by

two orders of magnitude. In order to verify the influence of

sand volume concentration, further experimental erosion tests

were conducted in both the plugged tee and the elbow with

0.0254 mm diameter with three different sand volume concen-

trations where thehighest oneis comparable to theconcentration

used by Bourgoyne. The test conditions and results are shown in

Table 4.

Fig. 22. Effects on particle-wall reboundmodel on the predictedrelative erosion

between the plugged tee (end region) and the elbow.

From Table 4, it is clear that the relative erosion severity is

strongly affected by the sand volume concentration. High sand

volume concentration results in reduction of erosion in boththe plugged tee and the elbow due to strong particle to particle

interactions. However, the reduction of erosion in the plugged

tee is more drastic than in the elbow. It is also observed that

under high concentrations,the erosion on specimen 1 is even less

than on specimen 2 of the plugged tee, which is the opposite to

low concentration experiment. These observations may suggest

two particle interference zones (see Fig. 23) in the plugged tee.

One is near the end surface where the reflected particles interact

with impinging particles. The second zone is at the joint sec-

tion of the two pipes where the incoming particles collide with

the outgoing particles from the plugged section due to parti-

cle reflection, gravity, and flow recirculation. These two particle

interference zones result in negligible erosion on the wall of theplugged section. Thus, the erosion reduction of the plugged tee

is more strongly affected by the sand volume concentration than

the elbow. In depth investigations of particle interaction in both

the plugged tees and elbows for high sand volume concentra-

tions are needed to better understand the erosion phenomena

under such conditions.

Table 4

Effects of sand loading on the relative erosion severity

Region Air velocity

(m/s)

Sand volume

concentration (%)

Relative erosion

(plugged tee/elbow)

End 30.48 7.5e-4 0.534

End 45.72 5.0e-4 0.517

End 30.48 6.0e-3 0.048

End 45.72 4.0e-3 0.051

End 30.48 5.0e-2 0.011

End 45.72 3.3e-2 0.010

Side and corner 30.48 7.5e-4 0.095






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X. Chen et al. / Wear 261 (2006) 715– 729 727

Fig. 23. Schematic of sand particle interference in the plugged tee.

5.3. Fluid property effects

The above analysis and developed simplified model are made

based on the experimental data and simulation results obtained

from air/sand flow. CFD simulations of erosion were performed

forwater/sandflow to illustrate how thefluid properties affect the

relative erosion severity between the plugged tees and elbows.

Figs. 24 and 25 present predicted sample particle trajectories

and erosion patterns in both the plugged tee and the elbow

for the case of water velocity of 3 m/s and sand diameter of

150m.

As compared to Fig. 2(b), Fig. 24(b) shows that particles

closely follow the flow streamlines in the elbow, due to the

high drag force exerted on the particles by water. Particles

are also driven by the inertia force to cross the flow stream-

lines and impinge the elbow at the exit region. This causes the

maximum erosion to occur at the exit region of the elbow, as

shown in Fig. 25(b). Further simulations of erosion in elbows

for water/sand flow reveal that the location of maximum erosion

in the elbow is weakly influenced by flow parameters including

Fig. 24. Predicted particle trajectories in water.

Fig. 25. Predicted erosion pattern in the plugged tee and elbow of water/sand flow.

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728 X. Chen et al. / Wear 261 (2006) 715–729

flow velocity, pipe diameter and particle diameter. These obser-

vations were experimentally confirmed by Blanchard et al. [2].

Flow streamline redirection is more drastic in plugged tees than

in elbows. As seen in Fig. 24(a), more particles deviate from

the streamlines and impinge the plugged tee at the joint corner

of the plugged tee. Comparing Figs. 21(a) and (b), greater ero-

sion is observed at the joint corner of the plugged tee than at

exit region of the elbow. Erosion was predicted for water/sand

flow in both plugged tees and elbows using pipe diameters and

particles diameters listed in Table 2. Simulations consistently

show that plugged tees experience greater erosion than elbows.

The predictions are qualitatively supported by Bourgoyne’s [3]

observations that when only liquid (i.e. water) and sand are

present, the plugged tee is less resistant than the long radius

or short radius elbows.

Particle motion and resulting erosion in both plugged tees

and the elbows are primarily determined by two mechanisms:

drag force and particle inertia. Particle inertia dominates the

particle motion with low density and viscosity fluid (e.g. air).

The redirection of the fluid in the plugged tees has little effecton the particles. Consequently, the particles directly impinge

the end surface of the plugged tee before they pass through the

plugged tee geometry transition. When the fluid density and

viscosity increase, the drag force exerted on particles by the car-

rier fluid has greater effect on particle motion. Consequently,

fewer particles impinge the end surface of the plugged tee and

more particles tend to impact the joint corner. Drag force is the

dominant mechanism for water/sand flow. The particle impinge-

ments primarilytake place at thejointcorner with greater erosion

than in the elbow. Similarly, in air/sand flow, the effect of drag

force increases when the particle diameter decreases, which

results in increasing erosion at the joint corner of the pluggedtees (side and corner region). This analysis is confirmed by

Fig. 20.

6. Conclusion

This study concerns the relative erosion severity between

plugged tees and standard elbows (r / D = 1.5). A CFD-based ero-

sion prediction model was applied to predict erosion in plugged

tees and elbows for a wide range dilute air/sand flows. Exper-

imental erosion tests were conducted in the plugged tee and

elbow with 0.0254 m diameter to validate the simulation results.

Both simulations anddata show that considerable erosion occurs

at the end and side and corner regions of the plugged tees.Based on the analysis of the CFD simulations and experimen-

tal data, a constant value of 0.5 is recommended for relative

erosion severity between the end region of plugged tees and

elbows. A simplified model in dimensionless form was devel-

oped to predict the relative erosion severity of the side and

corner region. It is shown that the sand loading significantly

affects the relative erosion severity. Experiments under high

sand volume concentration indicate that erosion in plugged

tees is about two orders of magnitude less than erosion in

elbows.

This study demonstrates that the relative erosion severity is

significantly affected by the carrier fluid properties. Simulations

in water/solid flows indicate that plugged tees experience greater

erosion than elbows. Bourugoyne’s [3] experimental observa-

tions qualitatively confirm the numerical simulations. Thus, the

fluid properties of an erosive environment must be carefully

examined to determine whether to adopt plugged tee to redirect

the flow. Further investigation should be conducted to incorpo-

rate fluid properties in the simplified model for the prediction of

relative erosion severity.

Acknowledgement

The authors would like to express their gratitude to the

member companies of the Erosion/Corrosion Research Cen-

ter (ECRC) at The University of Tulsa for supporting this

study.

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