Numerical Investigation of the Elbow Angle Effect on Solid ...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:19 No:01 1

190401-3535-IJMME-IJENS © February 2019 IJENS I J E N S

Rehan Khan 1a), H. H. Ya 2, William Pao3 1, 2, 3 Mechanical Engineering Department, Universiti Teknologi PETRONAS, Tronoh Perak, Malaysia

(a) Corresponding author: [email protected]

Abstract-- Solid particle erosion is predominant in

hydrocarbon production, drilling, and minerals processing

industries. Erosion may be cause by the impact of particles of

various sizes, shape and hardness to the surface at various

speeds and impact conditions. This work pertains

Computational fluid dynamics (CFD) study to characterize the

wear behavior of carbon steel material long radius elbows used

as flow changing devices in pipelines of the hydrocarbon

production industry. Although extensive studies have been

directed to substantiate the association of system parameters

and material erosion rate, accurate prediction of the erosion

severity in flow changing devices is still a challenge. In this

study, CFD with the discrete phase models is adopted to study

the solid particle erosion physics and the erosion severity of

carbon steel long radius elbow with three different angles 90o,

60o and 30o under the impact of sand particles. The simulation

is done with the k–epsilon turbulence model and the simulation

result from the k–epsilon model was validated by comparing

with the experimental results from the previous study. The 60o

and 30o elbow are less prone to erosion wear and maximum

rate appeared in the 90o elbow. The largest erosion zones have

been identified at or near the outlet of the 90oand 60o elbows

and near to the inlet for 30o elbow. Furthermore, the

relationship of curvature angle on erosion, particle trajectory

and turbulence in the elbow pipe has been discussed.

Index Term— Solid particle erosion; Long radius elbow;

discrete phase model; CFD.

I. INTRODUCTION

In hydrocarbon production when particles have to be

transported, flow changing devices i.e. elbow, bends and

tees are inclined to erosion damage because of the high

transport velocity rate required to keep the particle

motion [1]. In this sense, flow changing devices such as

elbows are more likely to wear during the abrasive

particle conveying and considered a weak component of

gathering and transferring pipelines [2]. Despite a simple

geometry configuration, the erosive wear elbows

encounter has emphasized numerous researchers past

decades [3]. Many experimental studies have been

executed to extract the erosion pattern in an elbow

configuration.

Table I summarizes the pertinent literature on erosion

research on solid particles erosion in elbow

configurations. Most of the past studies in solid particle

erosion have been related in the liquid phase for the

standard elbow while few investigations have been

conducted for various elbow angular configuration

[4].Most of the literatures have focused on 900 elbow and

fewer studies have investigated erosion with smaller

angular configuration elbow.

The study of the elbow in erosion research is

significant since it is the common configuration that is

the most influence to erosion failure under industrial

operating conditions [5].The velocity developed

downstream of the elbow forces particles in direction of

the wall. For low Stokes number (liquid-solid flows), the

deviation in particle trajectories before impact is seen due

to fluid flow and particles impact the target surface with

a range of different impact angles. Collective

mechanisms further enhance the erosion in the larger

angle elbow [6]. In the present work, the influential effect

of elbow angular configuration on sand erosion was

studied using computational fluid dynamics simulation . A

semi-empirical erosion correlation is implemented to

quantify erosion severity of elbow geometry

configuration. Furthermore, considering that in long-

range flow pipelines large curvature angle i.e. 90° elbows

can be substitute by elbows configuration with smaller

curvature angle, as 60° and 30°elbows, on which the

limited studied had done in literature. This study

highlights to quantify erosion in elbows geometrical

configurations by adopting of a numerical approach.

Numerical Investigation of the Elbow Angle

Effect on Solid Particle Erosion for Liquid-Solid

Flow

mailto:[email protected]



Table I

Literature in the sand erosion of elbow configuration

S. N Reference Geometry Fluid Particle Measurement

technique

Key Findings

1 Ronald E. Vieira

[7]

Material:

Aluminum

Configuration:

90o Elbow

Gas

Water

Sand

300μm;150 μm

Flow loop with non-

intrusive Ultrasonic Technique (UT)

The 300 μm sand particles generate 3.1 times more metal

removal in comparisonto 150

μm sand particles.

The annular flow regime is

creating more erosion induced damage than pseudo-

slug flow regime conditions

2 Soroor Karimi [8]

Material:

Stainless steel 316

Carbon steel 1018

Configuration:

90o Elbow

Gas Water

Sand; Fine

300μm;25 μm

CFD The CFD over predict the erosion-induceddamage due to

fine particles and not accurately predicts the erosion

intensity and locations in

elbows geometry. 3 JianGuo Liu

[9] Material: Carbon steel

Configuration:

90o Elbow

Water Sand

250 μm

Flow Loop The erosion intensity changes

significantly as velocity changes from 3.5 to 4.0 m/s.

4 Wenshan Peng [10]

Material:

Stainless steel 316

Configuration:

90° elbow and 180° elbow

Water Sand

150 μm

CFD Erosion significantly occurs at the boundary walls of the

flow pipeline near to the elbow exit and the outer side

of the elbow

5 Jukai Chen

[4] Material: Carbon steel

Configuration:

450,600,90°

standard elbow

Water Sand

150 μm

CFD-DEM The maximum locations

oferosion induced damage are closest to exit for all elbows

configurations.

The bend-angle significantly

affects the erosion and alter its

magnitude. 6 Gabriel Chucri

Pereira

[5]

Material:

Aluminum

Configuration:

90o Elbow

Air Sand

150 μm

CFD The wall roughness

significantly affects the erosion and increases its

magnitude.

The specific value of the friction coefficient does not

affect erosion measurement.

II. COMPUTATIONAL FLUID DYNAMIC

SIMULATION

To quantify the erosion intensity and damage in the wide

range of geometries under different flow conditions, erosion

equations should be implemented into CFD codes. Because

of the significance of computational techniques in erosion

quantification, a range of studies has been done by scholars

for complex geometries [4, 5, 8, 10]. For that reason,

erosion computational code was implemented in

Computational Fluid Dynamic (CFD) software such as

FLUENT, CFX, STAR-CCM+. These CFD tools offer the

advancement of computational capabilities in providing

better accuracy of sand erosion rate and suspected erodent

locations.

Generally, each CFD simulation has three main

components: a pre-processing unit, flow physics solver, and

post-processing unit. In the erosion, CFD simulation step

followed shown in Fig 1.

Fig. 1. CFD simulation stages

The Oka CFD based erosion model is considered for this

research and the k–ε model is selected to restrain turbulent

flow. Numerous empirical and semi-empirical erosion



correlations have been published in the literature. Many

experimental and theoretical types of research are

performed for erosion processes and erosion prediction

models are evaluated and developed based on different

parameters. For a ductile material where the erosion varies

with the impact angle and velocity, the Oka erosion model

is more suitable erosion model [11]. In this paper, the

erosion correlation developed by Oka outlined in Equation

1 is adopted which accounts for material characteristic and

geometrical shape. The erosion damage can be related to

other parameters in the form

3)(2)(1))((

9101

k

d

pdk

V

pVk

vHkF

wER

(1)

Where ρw is the density of target material, F(ϴ)

dimensionless function of the impact angle, Hv is the

Vickers hardness of the target material,VP particle impact

velocity,V’ is the impact velocity of the reference

particle,dp is the particle diameter and d’ is the reference

diameter.

A. Turbulence model

In this study,the k–ε turbulence model is implemented to

extract the flow profile. Zhang and Liu [12] identified the

certaintyby comparison of various turbulence correlations

and found that the k–epsilon correlation accurately predicts

flow field in elbows geometry. The k–ε model pertains two

important parameters: turbulent kinetic energy (k) and the

turbulence dissipation rate (ε). Equation 2 represents the

mean kinetic energy.

).''(''.2

'''.2

1''2''

)(

ijE

ju

iu

ije

ije

ju

iu

iu

ijepdiv

kdivt

k

uu

U

(2)

Where Eij is the mean rate of deformation tensor. For high

viscosity, generally, turbulence flow has fewer occurrences.

Such aspect influence to impact velocity and particles

impact angle.

Fig. 2. Schematic of geometry (a) 900 (b) 600 (c) 300

B. Numerical Simulation

Erosion of the low stroke number flow was simulated using

a commercial software package. Assuming that sand

particle was introduced at a steady flow condition entrance

length of 1m and exist length 0.5m was added to the elbow

configuration. The long radius elbow pipe having an inner

radius of 0.0255m and the radius of curvature of a 0.0765m,

schematic of geometric configurations are shown in Fig 2.

The erosion rate and sand trajectory were extracted from the

simulation. The two phases were water as liquid phase and

the sand as the solid phase. The computational mesh was

generated by ANSYS, 524000 elements with an element

size of 0.003 m were intended to assure the quality. To

extract erosion rate and particle trajectories, discrete phase

model (DPM) approach was introduced in simulation

stages. The simulation parameters used to extract the

erosion profile of the elbow configurations are listed in

table II: Table II

Simulation Setup

Simulation Parameters

Target surface material Carbon Steel

Erodent Particle SiO2

Particle Diameter 250 micron

Density 2.65 [g/cm3]

Shape Uniform-sphere

Mass flow rate 230 [kg/hr]

Turbulence Model Realizable k-epsilon

Residuals 1e-5

Turbulent intensities 3.68 %

C. Computational Mesh:

To depict the numerical setup, the entire flow domain was

solved and generated using hexahedral mesh, which gives a



provision of stable and minimization of numerical diffusion

error in the numerical simulations. To capture flow pattern

more accurately near the wall gradual refinement technique

adopted near the vicinity of walls as shown in Fig 3.To

assure the stability of results quality and computation use, a

mesh independence study was performed. The results are

presented in a mesh independence study section.

Fig. 3. Computational Mesh for Elbow configuration

As the numerical approach is adopted to solve the problem,

to ensure its applicability it is important to assess the

validity of the adopted approach. Therefore, Ronald et al.[7]

flow loop test results on a long radius elbow has been used

for validation of flow physics. Fig. 4 shows the agreement

between the flow loop tests and the CFD results. There is a

good agreement in terms of the quantification of erosion

rate and location of highest erosion as outlined in Fig 4. The

trend of the variation of erosion rate over the curvature of

long radius elbow is also captured by CFD. As a result, the

CFD approach with the current simulation arrangement is

considered being suitable to the problem of quantification

of the erosion rate on different elbow geometric

configuration types.

D. Mesh independence study

Three mesh resolutions were analyzed for this study to

adjudge the mesh independence. All three meshes were

hexahedral and generated with the ANSYS pre-built

meshing module. For the k–epsilon turbulence models

refinement of the grid is important to assure that y + value

less than 1 in the first element is not outside the laminar

layer and away from the wall, parameters for the mesh is

listed in Table 3. The erosion rate was quantified from three

grid sizes, producing slight differences from mesh to mesh

as presented in Fig 5. As the difference in the quantified

erosion rate from mesh 2 and mesh, 3 was less than 2%, the

mesh 2 was in good agreement for minimizing run-time and

memory use. Based on the study, the numerical simulations

of the current study were performed considering the mesh

2.

Fig. 4. Simulation and experimental [7] erosion rate vs. bend curvature

angle for 900 elbow

Fig. 5.Numerical erosion rate vs. bend curvature angle for 900 elbows for three mesh resolutions.



Table III

Mesh independence statistics

III. RESULTS AND DISCUSSION

The results and discussion are outlined with erosion

pattern and particle trajectories for three elbow

geometric configurations in first section. Thereafter the

numerical erosion rate under liquid-solid flow along the

curvature angle for various elbow configurations is

investigated. Then the effects of elbow curvature angle

on flow field are presented.

A. Erosion profile and erodent particle trajectories

Fig. 6, Fig. 7 and Fig.8presentstheextracted erosion

profile, erosion contour, and erodent particle path in

three elbow configuration for carrier fluid velocity of

2m/s, 3m/s and 4m/s with particle diameters of 250

microns. In low Stokes number flow, i.e. liquid-solid

flow the dynamics of particles depends on carrier fluid

flow. Consequently, the erosion region depends on the

collective impact and a path followed by erodent

particles towards wall surface of the elbow.

Fig. 6, Fig. 7 and Fig.8shows that particle collision with

wall generates erosion profile under liquid-solid flow

condition; the erosion rate with 900curvature is

considerably larger than the 600 and 300 curvature

configuration. The large erosive zone generated due to

the impact of particles transported at high speed to the

outer wall surface with high impact angles. Fig. 6, Fig. 7

and Fig.8displays that consideration of curvature angle

escalates the maximum erosion rate and erosion region.

Also, consideration of curvature angle causes numerous

particles-wall impacts and leads to narrow particle

cluster region created in 900 bends, a cluster region will

resulted in narrow erosion crater on the elbow wall

surface. Thus large curvature angle maximizes the

erosion in the liquid-solids flow. Fig. 9 shows the

trajectories of particles. Fig. 9(a), Fig. 9(b) and Fig.9(c)

comparisons clearly show that curvature angle alters

particle trajectories. Particle dynamics leads to a more

catastrophic impact to the wall surface of 900elbows as

the particle disintegrates more walls mass compared to

600 and 300 and turnout in an increase of the erosion rate.

B. Influence of the curvature angle and flow speed on

the erosion rate

Fig 9 depicts, the erosive region is affiliated to the path

of the erodent particle in the carrier fluid and the

trajectory of the particles is preeminent per flow

conditions. Altering the curvature angle of the elbow

will alter the flow conditions and leads to the maximum

erosion location. Fig. 9 shows the erosive wear in elbow

due to sand particles resulted in the disintegration in the

outer wall surface. As illustrated by the particle tracks,

the particles are inclined to the rotation motion when the

elbow configuration is changed to 300 the erosion

location is shifted to location B at the elbow inlet side.

The erodent particles will cause more percussion the

wall in region B at inlet side for 300elbows whereas for

900and 600elbow configuration the more particles collide

the wall in region A at elbow outlet sides as shown Fig.

9. The maximum erosion rate for 900 in Fig. 10 reflects

reduction with increasing carrier fluid velocity. The

maximum erosion rate gets going to reduce for the

carrier fluid velocity is 4 m/s in 90°, 60°, and30° elbows

and when the carrier fluid velocity is 3 m/s the maximum

erosion rate appears for

Mesh Study

Mesh 1 2 3

No of cells 356900 524000 876000

No of the node

on k

5 8 12

Erosion

rate(Maximum)

(mm/year)

1.306 1.334 1.356



Fig. 6. Erosion contour 90o elbow at different flow velocity (a) 2m/s, (b) 3m/s, and (c) 4m/s

(a)

(b)

(c)

(a)



Fig. 7. Erosion contour 60o elbow at different flow velocity (a) 2m/s, (b) 3m/s, and (c) 4m/s

(a)

(b)

(c)



Fig. 8. Erosion contour 30o elbow at different flow velocity (a) 2 m/s, (b) 3m/s, and (c) 4m/s

(a)

(b)

(c)



Fig. 9. Erosion contour and particle trajectory for 3m/s flow velocity: (a) 900 elbow ; (b) 600 elbow and; (c) 300 elbow

all three elbow configurations as shown in Fig 10, 11 and

12. The maximum erosion rate of 90° elbow is 0.95

mm/year located in Ө = 5° and 60° elbow is 0.55 mm/year

at Ө = 0°. The simulation results show that the maximum

erosive zone of large curvature angle elbows configuration

i.e. 90° and 60°are located at or adjacent to the exit wall and

the reduction in erosion rate is observed for low curvature

angle i.e. 30° with a maximum erosion rate of 0.22 mm/year

located in Ө = 25° near the inlet.

Figs. 10, 11 and 12 shows the erosion rate of bend under

different flow velocities and the wall thickness loss of the

bend along the bend section curvature angle θ with the

maximum erosive region of the various elbow geometrical

configurations. Figure 10, it can be seen that for 90° elbow

(a) (b)

(c)



when 0°<θ<40° the more erosive zone induced at the outer

surface of the bend leads to a considerable wall thickness

loss, and for 40°<θ<80°, the small erosive zone is created at

the outer surface and no erosive zone developed for

80°<θ<90°. Figure 11, it can be seen that in 60° elbow for

0°<θ<20° high erosive wear disintegrate outer surface wall

of the bend, and for 20°<θ<50°, the less erosive wear

induced at the outer wall of the bend and no surface

disintegration can be seen for 50°<θ<60°, In Figure 12, for

30° elbow with curvature angle of 0°<θ<10° the erosive

wear in elbow wall is zero and for 10°<θ<30°, the outer

wall erosion rate of the is the considerable large, which is

the most likely to cause wear and tear and cause bend wear

failure.Note that for curvature angle from 0° to 90°, erosion

and particles impact the outer wall surface of elbow

geometrical configuration. From this simulation study, it is

clear at the exit of 90° and 60° elbow, particle motion are

primarily suspected for altering erosion pattern. This can be

observed in Fig 9.By comparing 900, 600 and 300 elbow

erosion rate results the maximum erosion rate in 600elbow

is 42% less than 900 elbow and in 300elbowit's 76.8% less

compared to 900elbow. As a result, taking all the above

under consideration, the replacement of 900elbow with 600

and 300 elbow is recommended for suitable cases.

C. Relationship of the curvature angle and turbulence

intensity

Fig. 13 and 14 illustrates that turbulent intensity also leads

to increase particle impact and erosion at the outer surface

of the elbow curvature. The high intensity turbulent flow at

downstream of 90° elbow escalates motion of particles in

the radial directions and results in more impact induced to

the outer wall surface. It turns out to be a narrow erosive

region. This means that apart from the drag force,

turbulence intensity contributes to altering particle

trajectories in 90°, 60°,and 30° elbows. Based on analysis

turbulence weigh more in 90° and 60° elbow at the

downstream and for 30° elbow high turbulence occurrence

at the upstream. Fig. 13 and 14 illustrate the turbulent

intensity contours in the outlet and inlet of the elbows

configuration. The turbulent intensity contours suggest that

the contraction in the blue zone and the enlargement in the

red and yellow zone signify the maximization of turbulent

intensity. This means an excessive turbulence turn out in

90° and 60° elbow exit sections.

Fig. 10. Numerical erosion rate vs. bend curvature angle for 900 elbows for three flow velocities





Fig. 13. Turbulent intensity contours in the outlet (a) 900 elbow; (b) 600 elbow and;(c) 300 elbow.

(a) (b) (c)



Fig. 14. Turbulent intensity contours in the inlet (a) 900 elbow ; (b) 600 elbow and;(c) 300 elbow.

IV. CONCLUSIONS

This work pertains erosion study of carbon steel long radius

elbow pipe under liquid-solids flow using computational

fluid dynamics.Numerical results show that the curvature

angle has an influence on the particle dynamics and the

wear profile of the elbow. The adopted erosion model

developed by Oka to be an accurate model for

quantification of the erosion rate under liquid-solids pipe

flows. This paper highlights the numerical investigation to

decouple the relationship of elbow curvature angle and

erosion rate. The following conclusions can be summarized

based on the results extracted in this study:

1. The results reveal that the severe erosion occurrence is

downstream of the 900 and 600 elbows. Since, in the

300elbow the locations of maximum erosion are shifted

to upstream and the curvature angle significantly

influences the maximum erosion rate.

2. In 900 and 600 curvature angle elbow, a sand particle

concentration region induced on the outer surfaces of

the elbow towards downstream generates an erosion

crater on the elbow near or at the outlet side.

3. When the curvature angle is changed to 300, the

particle trajectories changes and the particle

concentration region shifted to upstream and cause

more destructive impact to the outer surface at the inlet

side.

4. In presence high curvature angle elbow, the high

turbulence due to flow driven at exists affects particles

trajectories and induces more collisions to the outer

wall surface and leads to alter the erosion pattern.

5. The effect of curvature angle on erosion in the elbows

geometrical configuration shows that 90° elbow pipe is

more prone to erosion than 60° and 30° elbows. A

reduction in the 90° curvature angle to 30° seems to

reduce the maximum erosion rate up to 76.8%.On the

other hand, the use of 60° curvature angle reduces the

maximum erosion rate up to 42% .Thus, to replace

large curvature-angle elbows with less curvature-angle

(e.g. 30° and 60°) elbow is recommended for suitable

cases.

ACKNOWLEDGMENT

The authors acknowledge the support given by the

Universiti Teknologi PETRONAS for this research.

AUTHOR’S CONTRIBUTIONS

Rehan Khan: Literature study, data analysis and the

simulations analysis of the research and also participated in

writing the manuscript.

H. H. Ya and William Pao: Provided the research topic,

guided to the route of research and numerical study.

Ethics

This article pertains an original research. There are no

ethical issues ensue after the publication of this manuscript

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