Erosion of natural gas elbows due to rotating particles in turbulent gas-solid flow

Accepted Manuscript Erosion of natural gas elbows due to rotating particles in turbulent gas-solid flow Mohammad Zamani, Sadegh Seddighi, Hamid Reza Nazif PII:

S1875-5100(17)30043-4

DOI:

10.1016/j.jngse.2017.01.034

Reference:

JNGSE 2051

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 29 November 2016 Revised Date:

29 January 2017

Accepted Date: 30 January 2017

Please cite this article as: Zamani, M., Seddighi, S., Nazif, H.R., Erosion of natural gas elbows due to rotating particles in turbulent gas-solid flow, Journal of Natural Gas Science & Engineering (2017), doi: 10.1016/j.jngse.2017.01.034. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Reverse motion of two kind of rotational particles.

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Erosion of Natural Gas Elbows due to Rotating Particles in Turbulent GasSolid Flow

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Mohammad Zamani a, Sadegh Seddighi *a, Hamid Reza Nazif b Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

b

Department of Mechanical Engineering, Imam Khomeini University, Ghazvin, Iran

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a

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* To whom correspondence should be addressed. Email: [email protected]

Abstract

This work investigates the erosion of an elbow pipe due to the gas-solids turbulent pipe flow using computational fluid dynamics (CFD) with special attention to the effect of particle rotational motion on

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erosion. The gas-solid flow is solved by employing two-way coupled Eulerian-Lagrangian approach while enhanced wall treatment is used for modeling the flow behavior close to the walls and in boundary layer. Effects of key erosion parameters such as gas velocity, particle diameter and particle mass flow rate on the erosion rate was evaluated and discussed. Simulation results are verified with experimental data with

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concept of percent bias. Results show that the erosion rate is strongly affected by the particle rotation. The particles rotation has a considerable effect on the particle motion path and consequently the erosion

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pattern of the elbow. Particle trajectories show that particles have reverse motion due to rotation which plays a significant role on erosion pattern due to the more collision to the elbow wall. Keywords: Erosion, Gas-solid flow, Solid particle rotation, Turbulent flow, Computational fluid dynamics (CFD)

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1. Introduction Erosion due to solid particles is a major problem in many industrial applications, particularly in the field

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of oil and gas. For instance, Jordan [1] reported the importance of erosion rate in the sizing of lines, analyzing pipe failures, and limiting production rates in multiphase gas or oil transportation. Elbows as the most vulnerable parts of transportation pipelines, are at the risk of failure due to the presence of sand particles in the turbulent flow. Erosion is a main cause of damage and shorter life time for pipelines in oil

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and gas transportation routes. The damages done by erosion to the hydrocarbon transportation lines may affect the safety of the people, have negative environmental impacts and increases the maintenance costs

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[2, 3]. Thus it is critical to find the erosion bottlenecks in hydrocarbon transportation lines and generate predictive erosion models with high accuracy in order to prevent potential failures and improve the weak points.

The existence of solid particles in gas or liquid pipelines such as sand particles is known to be a major cause of erosion. Elbows are particularly more prone to erosion where the impact of solid particles remove

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parts of the elbow materials. In addition, sudden change in the flow direction in elbows leads to considerable changes in particle distribution in the flow and consequently higher erosion rate. For example

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Lin et al showed that the erosion rate of 90° elbows is 50 times bigger than in straight pipes [4]. Erosion have been studied vastly in the literature including examples of experimental elbow erosion due to

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solid-gas flow. Bikbaev et al. [5, 6] found that the erosion rate increases with increase in gas inlet velocity and increase in the ratio of bending radius over branch diameter (r/d). Chen et al. [7] found a constant ratio between the erosion rate in a plugged Tee with one end closed to and erosion rate in the elbow. They also studied the effect of solids loading and distribution of solid particles on erosion rate Chen et al. [7] concluded that the erosion in elbows was about two orders of magnitude larger than that in plugged tees. Fan et al. [8] made experimental and numerical study on a new method for protecting the elbows from erosion in solid-gas flows. They suggested that the utilization of fixed ribs is an efficient approach for reducing the erosion of bends in gas-particle flows. Chen et al. [9] experimentally studied the validity of 2

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erosion models which are using computational fluid dynamic (CFD). They concluded that the stochastic tracking improves the accuracy of modeling the erosion rate and erosion pattern. Islam et al. [10] using Aluminum oxide particles found the erosion of API X-42 Steel to increase when particle velocities

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increase. They found that the particle with low impact and high velocities lead to higher failure rate. In addition, the increase in particle impact angle reduces the erosion rate. Levy et al. [11] studied the effect of particle shape on erosion rate and found that the particles with sharp edges erode more pipe mass than

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the spherical particles.

Considering most of previous experiments such as [5, 6, 9, 12] did not report comprehensive erosion

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information in bends, recent efforts are focusing on 3-dimensional erosion profiles such as Kesana et al. [13] and Vieira et al. [14] who used 16 ultrasound sensors to study erosion distribution in various locations of an elbow. Bozzini et al. [15] evaluated bend erosion-corrosion for the passivating and actively corroding alloys in a flow of gas, particles and two unmixable liquids using key parameters for erosion as flow velocity, particulate content and gas volume fraction. They concluded that the gas volume fraction

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has little impact on erosion–corrosion of the duplex stainless steel. Nicolici et al. [16] used CFD with Eulerian-Lagrangian approach for calculating the erosion in a gas-solid flow assuming one-way coupling. The main aim of the study by Nicolici et al. [16] was to find the properties of impact of particles on the

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outer wall of the elbows such as velocity, angle and frequency of the impact. They also studied the effect of particle size, particle density and fluid viscosity on the erosion rate. They also concluded that the

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increase in flow velocity leads to the increased particle outreach and consequently higher eroded area in the pipe. Zhang et al. [17] studied the location of maximum erosion in addition to the effects of flow velocity, the direction of the bend and the elbow angle on erosion. They also compared the spatial distribution of particle-wall interaction to erosion pattern focusing on the maximum eroded location. One of the conclusions by Zhang et al. [17] was that the location of the maximum erosion part is highly dependent on the flow velocity. They found that the increase in slurry velocity leads to that the maximum erosion location shifting downstream while the impact force is increasing. Duarte et al. [18] numerically

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investigated the effect of particle mass concentration on erosion of an elbow. They found that even in low and medium particle mass concentrations, effect of particle collision on penetration ratio (the ration of eroded mass of wall to the mass of solid particles) cannot be ignored. They also found that the penetration

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ratio decreases with increase in particles mass concentration. This phenomenon which is also experimentally observed is called cushioning effect. However the effects of the particle rotation on erosion models are lacking in the literature.

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The aim of this work is to model the erosion rate in gas pipelines in order to optimize the design of transportation lines in addition to predict the erosion damage. The numerical investigations in this work

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are based on CFD using Eulerian-Lagrangian approach. The results are verified with experimental data on erosion.

The major forces on the solids particles are assumed to be drag forces, inertial forces, gravity forces and buoyancy forces. Virtual mass force and pressure gradient force are ignored due to the high density ratio between the solids and fluid. The particle rotation is considered in particle motion equation in addition to

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the particle angular momentum equation. The turbulence is modeled using realizable k-ε model while enhanced wall model is used for modeling the flow behavior close to the walls and in boundary layer. Stochastic tracking is used for modeling the particle dispersion due to the turbulence. Discrete Random

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2. Theory

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Walk is used to model the interaction between vortices and particles.

The Eulerian-Lagrangian method, which is chosen in this work for modeling the two-phase flow, relies on solving Navier-Stokes equations for the gas phase as the continuous phase while the dispersed phase (particles) are modeled using Lagrangian tracking approach. Realizable k-ε (RKE) [19] is chosen for turbulent flow modeling since it is found more accurate for extreme curvatures in the direction of the flow as well as flows with large rotation and large separations [19]. Thus this work used RKE model to simulate the turbulent flow near the wall and in the elbow. 4

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2.1 Gas phase model The continuous phase (gas in this work) is modeled using the Navier-Stokes equations. The steady state

=0

+



+

+

is static pressure,

(2)

is volume force,

below:

=

+

(3)

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is turbulent viscosity found as below [20]

=

!" #

(4)

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RKE model used for turbulence modeling in this work, equations below are used [19].

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! + $

# + $

where

+

#

=

!

% +

is the

is the gas effective viscosity which is found from equation

source term for dispersed phase and

where

+

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where ρ shows gas density, ui is velocity component,

(1)

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=−

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equations used in this work are written as below:

=

&*

(

% +

#

+

computed from:

5

&'

+

(

!

#−

+ )' − # +

"

#"

! + √-#

+

'

(5)

*

(6)

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+

= max 10.43,

6 8,6 = 6+5

1 = 2

! #

, = 92

,

+

(7)

is the average rate of strain tensor,

'

and

*

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where in RKE equations, ! is turbulence kinetic energy, # is turbulence kinetic energy dissipation rate, represent the effects of dispersed phase on turbulent flow

structure. σ= and σ> are turbulent Prandtl numbers for ! and #. G> shows the production of kinetic energy

)' =

"

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The constants used in RKE model.

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due to average velocity gradient found as below:

C" = 1.9 , σ> = 1.0 , σ= = 1.2 turbulent viscosity computed as described in equation (4). strain and rotation rate (

(9)

in RKE model is a function of the average

,Ω ) and turbulence variables (!,#) in contrast to other models which use

is computed from the following equation:

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constants.

(8)

CD + C E

!F

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=

1

+Ω Ω #



(10)

Where coefficients CD and CE is computed from: +

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CD = 4.04 , CE = √6 cos K , K = L cosM+ √6N , N=

F

' '

(11)

L

2.1.1 Streamline curvature Correction model

In general, two-equation turbulence models have less accuracy when modeling streamline curvature and system rotation compared to straight streamlines [21]. Thus in order to increase the accuracy RKE model when considering the effects of streamline curvatures, the production term is modified with a multiplier. 6

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In this article, a modified equation is used for the production term for two equation turbulence models offered by Smirnov and Menter [21] based on Spalart and Shur [22] and shur et al. [23] as below: R QS

= 1+

P+

2T ∗ V1 − 1 + T∗

PL $WX

M+

Where variables T ∗ and T̃ are found from following equations:

T̃ = 2Ω ' ab c a

1

[ + \# ]S [$

S

P+

(12)

(13)

Ω + # ]S

S

^ Ω_Q ] 8

1 ` [

(14)

represents the Lagrangian derivative of the strain rate tensor components and the second term

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Where

'

Z−

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T∗ =

P" T̃

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OPQ

in brackets indicates the measurement of system rotation. Also Ω ' is vorticity tensor and computed from the following relationship: 1 2

−

+ 2#] ΩPQ ]

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Ω'=

(15)

` in equation (14) is computed from the relationship given by Smirnov and Menter [21]: [

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` = Ω[L , [ " = dW [

"

, 0.09e" ,

"

=2

(16)

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constants of equation (12) is presented from experimental results of Smirnov and Mentor [21]: P+

= 1.0 ,

P"

= 2.0 ,

PL

= 1.0

(17)

In streamline curvature correction model, production term in turbulence equations is modified as below. )' → )' . OP

Where OP is multiplying factor found using following equation:

7

(18)

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OP = dW g0 , O`P − 1 h O`P = dW idjX OPQ

R QS , 1.25

(19)

, 0k

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In order to prevent over-production of the eddy viscosity with destabilizing curvature and numerical stability causes, OP is limited between zero (intensive convex curvature) and 1.25 (intensive concave curvature) Depending on the streamline curvature.

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2.1.2 Low-Reynolds number approach

The k-ε turbulence model assumes that the flow is turbulent in the whole solution domain. However, the

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low Reynolds number region near the wall needs to be modeled more accurately in this work. Enhanced wall treatment method is used to simulate the flow near the wall. This method solves the flow with a twolayer approach dividing the flow field to two areas of near wall region affected by viscosity and a fully turbulent region [24]. The classification criteria of these two layers is the turbulence Reynolds number that is defined by Ren =

on√'

. The parameter p is the distance of the element centers from the wall. When

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Ren > rsn ∗ = 200 , flow region is fully turbulent and for Ren < rsn ∗ the area is affected by viscosity. For the near wall region affected by viscosity, Wolfstein [24] suggested using one-equation k-ε model.

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Near wall turbulent viscosity is calculated by:

,"uRn P

=

v √!

(20)

Where the length scale v is computed using following equation[25]: v =p

u

w

1 − exp −rsn ⁄C

(21)

Sine both one-equation model and realizable k-ε model are solved over the whole flow domain, the turbulent viscosity of enhanced wall treatment method in different flow regions is computed from blending turbulent viscosity of both models with a blending function z* as proposed by Jongen [26]: 8

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, {

= z*

+ 1 − z*

,"uRn P

(22)

where blending function is found as below: rsn − rsn ∗ 1 1 + tanh 2 C

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z* =

(23)

According to the definition, blending function is zero very close to walls and is equal to one far from the

|∆rsn | WT$WXℎ 0.98

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C=

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walls. C specifies the width of the blending function and is obtained from [26]:

(24)

In the near wall region affected by viscosity, the conservation equation for turbulence kinetic energy(k) retained while turbulence kinetic energy dissipation rate (ε) calculated as below: ƒ

' …„ u†

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#=

(25)

where the length scale v* is found as [25]:

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v* = p

u

w

1 − exp −rsn ⁄C*

(26)

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The constants of length scale equations found from [25]:

u

w

=‡

L… ˆ

, C = 70 , C* = 2

u

w

(27)

In order to ensure correct results for the flow when using low Reynolds approach, this work improved the grid so as to achieve p Š < 1 in the first element near the wall.

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2.2 Dispersed phase model The motion of particles is modeled using Lagrangian approach where the interaction between particles is ignored due to the low concentration of solid particles. The particle path is found from integration of the

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balance of the forces on the particles where inertial forces balance other forces.

The main focus of this paper is the effect of particle rotation on erosion and therefore two cases of with and without particle rotation is used as described below.

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2.2.1 Particle motion without particle rotation

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The balance of forces on the particle is used to calculate the particle velocity vector, ‹ , as shown below: Œ‹ = •a + •Ž + • Œ$

(28)

The drag force on the particle, FD, found as below:

‹ −‹ •P

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•a =

(29)

where ‹ is flow velocity, •P is particle relaxation time found as below [27]:

where

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•P =

Π18

"

24 a Re•

is particle density, Œ is particle diameter, C‘ is drag coefficient, and

(30)

is the fluid kinematic

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viscosity. The particle Reynolds number is found as below: Re• =

Œ |‹ − ‹ |

(31)

The C‘ is found from the study by Morsi and Alexander [28] as below: a

= W+ +

W" WL + Re• Re• "

The gravity forces in Eq. (28) as below: 10

(32)

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(33)

Where S is the ratio between density of particle to the density of the fluid. The other forces in Eq. (28)

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shown by • including Saffman force, virtual mass force and pressure gradient force. The Saffman lift force is negligible in this work because it is important only for low Reynolds numbers and sub-micron particles. Virtual mass force and pressure gradient force become important only when fluid density becomes larger than the particle density. Since the particle density in this work is around 2200 times larger

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than fluid density, these Virtual mass force and pressure gradient force are small enough to be ignored as

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well. 2.2.2 Particle motion with particle rotation

Particle rotation which is a natural aspect of particle motion is shown in this work to have considerable impact particle path and on erosion. The influence of the particle rotation on particle motion is more pronounced for large particles with large inertial momentum. When considering the particle rotation, Eq.

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(28) is changed to Eq. (34) while the equation for angular momentum is shown in Eq. (35). Œ‹ = •a + •Ž + •_“ + •b“ + • Œ$

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‹ =• ”

Œe ‹ Œ$

(34)

(35)

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Where •_“ shows the rotational lift force of Magnus force which is calculated as below [29]. 1 •_“ = C 2

|‹ − ‹ | –‹ × ‹ − ‹ ‹| |–

_“

where Ap is projected area of particles and

_“

(36)

is the rotational lift coefficient which is correlated to the

particle Reynolds number and particle rotational Reynolds number as below valid for rs• ≤ 2000 [30]. _“

= 0.45 +

Re™ − 0.45 s Re

11

ž.Ÿ _ ž.ƒ MD.Dš›œ_ •

(37)

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where •b“ refers to shear lift force. The available equations (see [31-33]) mainly focus on linear shear flows and low Reynolds numbers which is different from flow conditions in this work. Also the relation given by Mei et al. [34] is valid for medium Reynolds numbers gives that the shear lift force is less than

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rotational lift force for particle with high angular velocity [35]. Thus the shear lift force is not considered in this work due to the lack of a clear understanding of this force in conditions relevant to this work. ¡

In Eq. (35), • refers to inertial momentum of particle found from • = ›D

Π2 2

š

‹ ‹

™ ¢– ¢–

(38)

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‹ = ”

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‹ is the momentum of the particle found as below [36]. particle and ”

Œ š. e ‹ is angular velocity of

By replacing Eq. (38) in Eq. (35), an ordinary differential equation can be found for particle angular momentum which should be solved when particle rotation is considered. š

‹ ‹

™ |– |–

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Œe ‹ Œ • = Œ$ 2 2

‹ = + £ × ‹ − e ‹ . where –‹ is the relative angular momentum found from – "

(39)

™

is rotational drag

coefficient found as below [37]:

=

12.9

Re™

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™

D.š

+

128.4 20 ≤ Re™ ≤ 1000 Re™

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where Re™ is rotational Reynolds number found from Re™ =

(40)

‹‹ | o¤ ¥ „ |¦ ¤

.

2.3 Coupling between phases Correct calculation of particle path and erosion distribution requires through modeling of interaction between continuous and dispersed phases [38]. continuous phase affects the motion of dispersed phase through drag force and eddies. On the other hand, dispersed phase can also affect the continuous phase

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which is typically modeled by adding the source terms in the flow equations. Depending on the particle volume fraction, the interaction between the phases is categorized as below [39]: •

One-way coupling: When particle volume fraction is generally less than order of 10-06 (very low

•

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mass loading cases - φ≪1), only the gas phase affects the dispersed phase.

Two-way coupling: When particle volume fraction of surpasses 10-6 (intermediate mass loading cases - φ≈1, both dispersed phase and continuous phase affect each other.

Four-way coupling: When particle volume fraction passes 10-3 (high mass loading cases - φ≫1),

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•

in addition to the mutual effects of both phases on each other, the effects of interaction between

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particles become considerable.

Crowe et al. [40] also introduced Momentum coupling parameter for investigating the relationship among phases. Momentum coupling parameter addresses the importance of communication between the phases by comparing drag force of dispersed phase with the continuous phase momentum flux. By defining Mass

below equation [40]:

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loading (φ) and momentum stokes number (St ª«ª), the momentum coupling parameter is calculated from

Пª«ª =

φ 1 + St ª«ª

(41)

τ® ¯ [

(42)

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where momentum stokes number computed as:

$]Q] =

τ® is particle characteristic time and found from following equation: τ® =

Π18

"

(43)

Mass loading and momentum stokes number are the key parameters in defining the type of interaction between phases. Mass loading is defined as the mass flow rate of dispersed phase over the mass flow rate of continuous phase. 13

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In this work, the effects of particle phase on continuous phase is evaluated. For inlet flow velocity of 27 m/s with particle diameters of 300 µm, the volume fraction of particles is 2.26*10-5 and the number of particles is 1200 particles. Based on Sommerfeld [39], Since the particles volume fraction is of 10-5 order

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of magnitude, the effects of particles on turbulence is shown in this work to be very small. Also since the particles volume fraction is smaller than 10-3, particles do not affect each other.

Based on Crowe et al. [40] Since in this work the particle mass loading is very low (0.014 ≤ φ ≤ 0.063)

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and momentum stokes number of flow is high (26.56 ≤ $]Q] ≤ 260.82), the momentum coupling parameter and so the source terms related to the effects of dispersed phase on turbulent flow structure have

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very low value. So it can be concluded that one-way coupling is the proper approach for modeling the interaction between the dispersed and continuous phases. Nevertheless, this work considered the two way coupling to keep the effects of dispersed phase on continuous phase. Discrete phase source terms and effect of discrete phase on gas phase is investigated in results section.

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2.4 The particle-wall interaction

Lost momentum of particles is calculated by a rebound model after the collision with the wall. since after colliding particles lose energy after the collision with the wall, the rebound velocity is affected quickly. This effect has a significant role on particle tracking. Different rebound model are developed to

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considerate particle-wall interaction [41-43]. In this study, the model by Grant and Tabakoff [42] is used for interaction between particles and wall. In this model, it is assumed that the return of particles after the

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impact is a stochastic phenomenon and is affected by size and shape of the particles. The normal and tangential restitution coefficients that represent alteration in particle velocity after hitting the wall are found as below respectively:

sS = −

-S °

S

= 0.998± − 1.66± " + 2.11± L − 0.67± ˆ

14

(44)

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s =

-

°

= 0.993± − 1.76± " + 1.56± L − 0.49± ˆ

Where ± is the particle impacting angle to the wall,

(45)

and - particle velocity are particle velocity before

directions. Figure 1 shows mechanism of particle impacting on the wall.

2.4 Erosion models

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and after hitting the wall respectively. The parameters n and t show vertical and tangential velocity

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Various erosion models such as [44-50] developed to prevent erosion from flow of solid particles using data obtained from experimental results. Generally, erosion models are developed for special experimental

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conditions. Since the erosion is a complicated phenomenon which is affected by various parameters, there is lack of a general erosion model that can predict erosion for different conditions in an exact way. In erosion models which use CFD, the information of particle impacts on the wall is stored. Then the particle impact information is used in an erosion model which calculates the eroded mass from the walls and the

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erosion rate. In previous studies models were used to predict the erosion rate without considering particle rotation [7, 9, 14, 51-57]. In this work, the effect of particle rotation on the accuracy of three erosion model of DNV [45], Zhang et al. [46] and Oka et al. [47, 48] is studied.

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2.4.1 DNV erosion model

Det Norske Veritas (DNV) [45] suggested a prediction erosion model based on experimental and

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numerical data for different geometries such as elbows, plugged tees and reducers. For steel pipes, the model is expressed by following equations: ²r = 2.0 × 10M³ ´• ".› • ± œ

• ± = µC ± ¶+

where ± is the impact angle. The values of C are listed in equation (48).

15

(46) (47)

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C+ = 9.370 , C" = −42.295 , CL = 110.864 , Cˆ = −175.804

(48)

Cš = 170.137 , C› = −98.398 , C· = 31.211 , Cœ = −4.170 2.4.2 Zhang et al. erosion model

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Zhang et al. [46] suggested the erosion ratio, ²r, as a function particle impact angle, • ± , to be as below: ²r = 2.17 × 10M· ¸¹

MD.š³

•b Œ ´• ".ˆ+ • ±

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• ± = 5.4± − 10.11± " + 10.93± L − 6.33± ˆ + 1.42± š

(49) (50)

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where ± is the impact angle, F» d is the particle shape factor and BH is the Brinell hardness of the wall

material. For SS316, the value of BH is 178.9. F» d is found from analysis of samples of materials in

electron microscopes [14, 46]. The value of F» d for particles with diameter of around 150 microns is 0.53 and for particles with diameters of 300 microns is 1.

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2.4.3 Oka et al. erosion model

Oka et al. [47, 48] suggested an erosion model taking into account more parameters such as particle diameter, reference diameter of the particle, reference particle impact velocity, the wall density and

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Vickers hardness of the material as the following equation:

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²r = 65 × 10M³

{

¹-

MD.+"

%

´• ' Œ ( ´∗ Œ∗

D.+³

• ±

(51)

Where particle impact angle function • ± is found as: • ± = sin ±

S¾ V1

+ ¹- 1 − sin ± ZS„

(52)

This angle function is based on two erosion mechanism. The first term on the right hand of equation (52) illustrates plastic deformation and the second term illustrates cutting action [55]. Values of Oka et al. [47, 48] erosion model parameters are given in following equation:

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! = 2.3 Hv

D.DLœ

,

X+ = 0.71 Hv

D.+ˆ

,

For SS316: Hv = 1.83 GPa

X" = 2.4 Hv

MD.³ˆ

(53)

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3. Case description This work takes the geometry and conditions given in Vieira et al. [14] to verify the modeling used in this work. Vieira et al. [14] used 16 ultrasonic transducer to measure the eroded mass in 16 locations of a

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standard elbow. The elbow is made of stainless steel 316 with r/d of 1.5. The gas velocity varies in the range of 11-27 m/s with solids flow rate of 103-256 kg/day. Two particle diameters of 150 and 300

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microns were used. Table 1 shows the experimental conditions of the 11 experiments in Vieira et al. [14]. In general the particle rotational motion is an integral part of the particle motion and cannot be ignored. The study of Vieira et al. [14] which aimed for erosion predictive models included two major experimental parts of: 1) erosion from particle impacts on the wall, and 2) erosion from particle impacts on the bends.

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The first part of the experiments by Vieira et al. [14] used direct impact testing to evaluate the erosion. In their work particles entered the flow after the compressor and the distance that particles pass from the particle feed until the impact was small. Therefore, particles were expected to have a rotational motion

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due to the eddies in the main flow.

The second set of experiments by Vieira et al. [14] was about erosion in bends. In this part, even though

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the length of the pipe was large enough to damp the rotation, the existence of several bends before the test section lead to enhancement of particle rotation and generation of instant particle rotation. Also Vieira et al. [14] used their experiments to improve the model by Oka et al. [47, 48] where Vieira et al. [14] suggested the equation (54) modifying the angle function of Oka et al. [47, 48] using the experimental fitting values of n1 to n3. What is expected to be the main cause of model improvement in Vieira et al. is that the generation of instant particle rotation improved the impact angle.

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• Â =

1 sin  O

S¾

1 + ¹- Sƒ 1 − sin Â

S„

(54)

It should be noted that measuring the particle rotation is typically not performed due to large number of

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particles and the difficulty of non-intrusive measurement of particle rotation. Deng et al. [58] also concluded that not only the particles are rotating, but also particle rotation has a considerable impact on the erosion rate. Dos Santos et al. [59] found the inclusion of particle rotation of importance for large

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particles due to their frequent collision with walls. Lei et al. [60] also considered the particle rotation in their work using Newton’s kinetic equation.

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Erosion modeling in this work consists of the following four steps: Modeling the gas flow as the continuous phase Particle tracking Modeling the erosion

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Verification of erosion using the experimental results

4. Description of CFD method

4.1 Grid study

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The model geometry generation and simulations are performed as described in this section.

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The elbow has a diameter of 76.2 mm where the flow enters from a 1000 mm pipe (length=13D). Flow leaves the vertical pipe to a 90° elbow with r/D=1.5 and then to a horizontal pipe with 600 mm (8D) horizontal pipe. Figure 2 shows the geometry of the studied elbow and the mesh generated in this work for modeling the low Reynolds flow. Since the erosion is highly dependent on the low Reynolds flow modeling close to the wall, enhanced wall treatment is used to model the boundary layer and flow close to the wall accurately. The mesh size close to all can be evaluated using dimensionless wall distance or y+ (A non-dimensional wall distance for a wall-bounded flow) which is a measure to specify whether the cell is 18

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located in viscous sub layer, buffer layer or fully turbulent region. It can be defined as p Š =

∗ nÃ

Ä

Where

u∗ is the friction velocity at the nearest wall, yÇ is the distance to the nearest cell to wall and È is the local kinematic viscosity of the fluid. For using enhanced wall treatment model, the wall adjacent to the first

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cell size must be small enough to achieve p Š in order of 1. To achieve this purpose, it was determined that 34 nodes with a successive ratio of 1.15 on line G is enough (See Figure 2(c)). As seen in Figure 2, the mesh undergoes a gradual resizing to achieve fine cells close to the walls while avoiding sudden cell size variations which can cause false fluctuations in the results. Figure 3 shows p Š value along the outer wall

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of pipe centerline. As it can be seen, p Š value is less than 1 around the pipe. Mesh independence study is

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given in Table 3 based on the amount of maximum erosion rate The number of elements, CPU running time to the convergence (system specifications that simulations are executed on it have been shown in Table 4) and maximum erosion rate for each meshes are listed in Table 3. In all cases, the number of nodes near the wall is kept constant. It is observed that changing the number of elements even up to 4 times of primary mesh have a negligible effect on the amount of erosion. So it can be concluded that the

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grid size at the middle of the pipe does not have much effect on the amount of erosion. However to reduce the computational costs and the uniformity of the near wall elements with middle of the pipe, mesh number 3 shown in Table 3 is appropriate and was selected to perform the simulations.

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4.2 Numerical set-up

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The gas-phase momentum Navier-Stokes equation is discretized using finite volume approach. The flow is assumed to be steady state while the flow is viscous with the same temperature in the flow field. The gravity is considered in the calculations. The specifications of the gas and solid particles are shown in Table 2. The fields of pressure and velocity are connected using SIMPLE method. The momentum equation, nonlinear convective terms and viscose terms are discretized using 2nd order discretization. The global residual for flow convergence is set as 5e-6. This convergence is sufficient to guarantee that the fluid velocities and continuity equations balance will not change anymore.

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The particles get their motion from the flow where some of the particles follow the streamlines and collide with the walls and generate the erosion. In particle tracking, the information about the particles collision with the wall such as velocity, impact angle, location and intensity of impact are calculated. The particle

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dispersion due to the turbulence is modeled using stochastic tracking discrete random walk [27] which is used to model the interaction between particles and eddies assuming particles pass through a series of turbulent structures in the flow. The interaction between particles and eddies leads to the change in

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particle path. Further assumptions on particle tracking model are found below:

The interaction between particles is negligible due to low particle concentration

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The particles are not affecting the gas flow due to the low mass loading There is no slip between particles and the continuous phase

Chen et al. [9] and Zhang et al. [17] showed that for the particle numbers of more than 20000, the erosion rate is independent from particle numbers. In this work it is found that for particle numbers of more than

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10000, the erosion rate becomes independent of the particle numbers. However, to ensure a sufficient number of particles, 30,000 particles were considered in simulations.

4.3 Boundary conditions

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The simulations are performed using average flow velocity of 11-27 m/s leading to Reynolds number of 7.33×105 - 1.72×106 showing a fully turbulent flow regime. Since the turbulent flow are intrinsically

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unstable, flow properties must be accurately averaged before being used in the erosion model. Solid particles are injected homogenously with the same velocity from entrance of the geometry. The boundary conditions are shown in Figure 2(a). The velocity inlet boundary condition is imposed in entrance of the elbow while pressure outlet boundary condition (with a gauge pressure of 0 Pa) is implemented in the exit of the elbow. At the pipe walls, the no-slip condition is applied. Turbulence intensity and hydrodynamic diameter are assumed to be 5% and 76.2 mm respectively based on experimental data [14].

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5. Results and Discussion In this section, the results and discussion is presented firstly for two-phase flow validation. Thereafter the

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coupling between phases and particles behavior are investigated. Then the effects of particle rotation on erosion is presented. Finally, the effects of flow velocity, particle diameter and particle mass flow rate on erosion is shown.

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5.1 Two-phase flow validation

In order to show the reliability of the simulations performed, validation of two-phase flow model of this

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work is performed using the experimental data by Kliafas and Holt [61]. Kliafas and Holt [61] studied very dilute gas-solid flow with the mass loading of 9.5×10-5. The validation performed for the case with gas velocity of 52.19 m/s corresponding to the Reynolds number of 3.47×105 and particle diameter of 50 µm with particle density of 2990 kg/m3. Figure 4 shows comparison between the experimental and numerical results of gas and particle streamwise velocity in three section of 0° , 15° and 30° in bend. As

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seen, the numerical results are in good agreement with experimental data and shows similar quantitative and qualitative trends as experimental data for both gas and particle phases.

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5.2 Investigating coupling between phases

Mass loading and Stokes number of each case is shown in Table 1. The particles have little time to

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respond to the fluid velocity changes when stokes is much more than unity and the particle velocity has a small change during its motion through the bend. Figure 5 shows the flow behavior in the elbow for oneway and two-way coupling for flow velocity of 27 m/s (highest gas velocity in this work) and particle diameters of 300 µm. As seen the effect of particle phase on the continuous phase is negligible and there is no significant changes in the velocity distribution. Figure 6 shows the area weighted average of the dispersed phase momentum and turbulent source terms for 10 cross sections of the bend for 300 µm particles and flow velocity of 27 m/s. As seen, the source terms have a very small value and therefore two-

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way coupling assumption does not vary the results. Nevertheless, as mentioned in Theory section this work considered the two way coupling to keep the effects of dispersed phase on continuous phase.

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5.3 Behavior of particles Figure 7 shows behavior of gas and particle velocity for flow velocity of 27 m/s and particle diameters of 300 µm. As seen from the velocity profiles of particle and main flows, before the bend particles follow the main flow due to the momentum they got from the flow. However, when approaching the bend,

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particles deviate from the gas flow due to the large stokes number and particle rotation. Thus for the 30 and afterward, particles can be seen to have a different velocity profile than the gas flow.

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Figure 8 shows the stokes number, defined in Eq. (42), of the flow for 300 µ particles with the inlet velocity of 27 m/s. The stokes number, by means of comparing particle inertial and drag forces, shows to what extent the particles follow the fluid flow, particularly curvilinear motion of the solid particle. For instance, for a particle in an eddy, when Stokes number is much larger than unity (which is the case in this

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work), particles are not that sensitive to gas phase fluctuations. In such case, the particle with high momentum, do not get trapped in eddies. For large Stokes numbers, the inertial forces dominate the drag forces and therefore the particles have enough momentum to flow across eddies, leading to that the solid

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particles deviate from the main flow streamlines and impact the outer wall.

5.4 Effect of particle rotation on erosion rate

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5.4.1 Bias of prediction models from experimental data

The simulations performed based on Table 1 and the results are compared to experimental results [14] as seen in Table 5. CFD results have been reported as area weighted average for transducers surfaces in 45° and 47°. For comparing the modeled and measured experimental values, the percent bias is defined which shows the inclination of modeling results to the experimental results. The smaller inclination value shows a better agreement between model and experiment and the optimum inclination value is zero [62]. The percent bias is calculated as below: 22

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ÊËÌÍ» = R

R

− Ï b ] × 100

∑S¶+ Ï ¥R

R

(55)

and Ï b ] show the measured and modeled value. As seen in Table 6, the percent bias has an

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where Ï ¥R

∑S¶+ Ï ¥R

average of 80.5, 48.9 and 47.3 for DNV [45] , Zhang et al. [46] and Oka et. al. [47, 48] erosion models respectively when particle rotation is ignored. The numerical study by Vieira et al. [14] showed that the percent bias of DNV [45], Zhang et al. [46] and Oka et al [47, 48] erosion models are 70.5, 39.4 and 25.2

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respectively for cases studied in this work. The difference in results between this work with Vieira et al. study [14] is due to difference in turbulence model and specially mesh that used for considering the near

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wall treatment. Vieira et al. [14] used RSM turbulence model that is stronger model than k-ε model due to more rigorous and realistic approach which can capture anisotropy effects with the cost of increasing computing costs. Also Vieira et al. [14] used enhanced wall treatment method with a mesh capable of providing an average y Š value of around 30 for the first grid point from the wall. As noted in this study,

for having near wall approach, it is important to improve the grid so as to achieve y Š < 1 in the first

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element near the wall in order to ensure correct results. The main aim of this study is investigating the effects of particle rotation on erosion rate. The percent bias of erosion models presented in Table 6 shows that When the particle rotation is included in the modeling, the percent bias decreases to around 29.3, -

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54.3 and -65.6 for DNV [45] , Zhang et al. [46] and Oka et al. [47, 48] erosion models respectively which is a considerable improvement in the modeling. Thus the DNV [45] model with considering particle

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rotation has minimum deviation from experimental results and is optimal model for erosion prediction. The results also show that Zhang et al. [46] and Oka et. al. [47, 48] erosion models over predict erosion rate from experimental data compared to when the particle rotation is included in the modeling which is conservative model for designing pipelines in a safe way. It should be noted that there is not any completely accurate erosion model available and thus the deviation reported in this work is a reasonable accuracy for erosion.

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5.4.2 Erosion pattern and particle trajectories

Figure 9 and Figure 10 show the modeled erosion pattern, particle concentration and particle trajectory in two cases of with and without particle rotation for flow velocity of 23 m/s and particle diameters of 300

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µm respectively. The high Stokes number calculated in Table 1 shows that the motion of particles is independent from fluid flow and particle paths do not follow streamlines. Thus the erosion region is exclusively due to the collision of particles with upper surface of elbow. Figure 9(a) and Figure 10(a)

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show that while both cases of with and without particle rotational motion generates a symmetric V-shape erosion pattern due to the fully developed gas flow, the erosion rate with particle rotational motion is

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considerably larger than the case that this motion is not considered. The highest erosion occurs when particles with high speed at the pipe center collide the outer wall with high impact angles. By comparing Figure 9(a) and Figure 10(a) it becomes clear that consideration of particle rotation increases the maximum erosion rate from 2E-04 kg.mm-1 to 7.2E-04 kg.mm-1. Also consideration of particle rotation improves the modeling quality at the end of the elbow while erosion in the end of bend can be modeled

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accurately only when considering particle rotation. Figure 9(b) and Figure 10(b) show the concentration of particles in bend. The accuracy of erosion modeling improves with consideration of particle rotation due to that the lift forces stemmed from particle rotational motion leads to the increased number of particles

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impacting with the wall and thus causes that a zone with greater particle concentration be occurred in bend. Therefore, the erosion pattern modeled more accurately. Particle rotation also provides a pressure

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gradient around the particle which produces a rotational lift force. When particle rotation is not considered in the modeling, the value of maximum particle concentration is 55 kg.m-3 while with particle rotational motion it decreases to 35 kg.m-3. Although the maximum particle concentration decreases with considering particle rotation, but due to rotational lift force, a larger scale particle concentration zone will be created on the inner and outer surfaces of the elbow and so causes a large scale erosion scar on the elbow. Thus consideration of particle rotation enhances the erosion rate in gas-solids flow. Figure 9(c) and Figure 10(c) show the trajectories of particles. By comparing Figure 9(c) and Figure 10(c), it becomes clear that when the particle rotation is included in the modeling, the particle trajectories changes 24

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dramatically compared to when the particle rotation is not taken into account. Particle rotational motion will cause more destructive collisions to the wall since the rotating particle erodes more mass form wall compared to irrotational particles and thus particle rotation leads that the erosion rate increases

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dramatically. In addition, for irrotational particles a particle free zone is created due to mechanism of particle motion while with particle rotation there is not any particle free zone.

Figure 11 shows mean particle velocity distribution in different elbow sections for flow velocity of 23 m/s

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and particle diameters of 300 µm. As seen, mean particle velocity decreases during its motion along the elbow in both cases of with and without particle rotation but mean particle velocity distribution is different

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from each other. when the particle rotation is not to be considered, shown in Figure 11(a), particle velocity is zero in the most part of sections 30, 45 and 60 degrees close to the inner wall. However, when the particle rotation is considered, shown in Figure 11(b), these regions does not exist. These difference between particle velocity distributions in two cases of with and without particle rotation occurs because of different particle trajectories that was mentioned earlier (see Figure 9(c) and Figure 10(c)).

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It is known that rotation of particle in presence of flow velocity gradient near the wall causes rotational lift force. As a result, fewer particles with high velocity approach the wall and we expect a large percentage of particles flowing in the middle of the pipe to fully turbulent region. As the particles flow separation being

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driven to the middle of the pipe, a reverse motion will be occurred in particles trajectories. Figure 12 shows the reverse motion of two kind of rotational particle for flow velocity of 23 m/s and

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particle diameters of 300 µm. Generally, the rotational motion of the particles is irregular. The blue arrows show trajectory of particle 1 and the red arrows show trajectory of particle 2. As seen, reverse motion of particle 1 causes three impact to the wall while reverse motion of particle 2 causes two impact to the wall in elbow. Although the next particle collisions to the wall is not as destructive as the initial impact, it plays a significant role on erosion pattern.

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5.4.3 Erosion distribution along elbow centerline

Figure 13 shows erosion distribution along elbow centerline predicted by DNV [45], Zhang et al. [46] and Oka et al. [47, 48] models for flow velocity of 23 m/s and particle diameters of 150 µm. Figure 14 also

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shows erosion distribution along elbow centerline for velocity of 27 m/s and particle diameters of 300 µm. As seen, in the presence of particle rotational motion, the maximum erosion rate occurs at an angle of 47° in addition to the significant increase in erosion rate. When particles rotation is not considered, two

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significant peaks at angles of 47° and 61° can be seen in the diagram due to the particle trajectories. when the rotating motion of the particles is not considered, particles collide directly at two elbow angles.

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Figure 15 shows the comparison between accuracy of erosion prediction models along the elbow centerline in case of considering particle rotational motion for both particle diameter of 150 and 300 µm. As seen, when particle rotation is included in modeling, Zhang et al. [46] and Oka et al. [47, 48] models strongly overpredict erosion rate for both particle diameters of 150 and 300 µm while DNV [45] model is in good agreement with experimental data. For 150 µm particles, DNV [45] model overpredicts erosion

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rate while for 300 µm particles DNV [45] model underpredicts erosion rate.

5.5 Effect of flow velocity and particle diameter on erosion rate

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Figure 16 shows the modeled and measured [14] erosion rate for particles of 150 and 300 µm diameter for different flow velocity. The modeled values for both diameters agree well with the experimental results.

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In addition, as expected the increase in flow velocity and particle diameter leads to a higher erosion rate. Since the velocity of the particles is a function of carrier fluid velocity and when carrier fluid increases, the impact velocity and impact energy of the particles to the wall and so the erosion rate increases. Also it can be concluded from Figure 16(a) and Figure 16(b) that erosion caused by 300 µm particle is double of 150 µm particle. Larger inertia force for 300 µm particle, causes that particles hitting directly to the elbow and causing severe erosion. For smaller particles as 150 µm, both the secondary flow effect and the inertia force paly considerable role on particles. So the direct impacts to the wall will be lower in this case and erosion occurs with lower value. 26

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5.6 Effect of particle mass flow rate on erosion rate Figure 17(a) to Figure 17(d) show the erosion distribution along elbow centerline for different particle mass flow (dÐ = 103, 154, 192, 452 ! . ŒWp M+ ) for flow velocity of 15 m/s and particle diameters of

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300 µm with DNV [45] erosion model. To better understand the impact of the mass flow rate on erosion, erosion rate is reported according to the missed wall thickness per a year (mm.year-1). As seen, numerical results are in acceptable agreement with experimental data.

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Figure 17(e) shows changes of erosion profile versus different particle mass flow rate to investigate the effect of increasing particle mass flow rate on erosion rate. As seen, erosion rate increases with the

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increase in particle mass flow rate. It is clear that when mass flow rate increases, more solid particles will hit to the elbow at a time and higher erosion rate occurs.

Figure 18 shows the modeled maximum erosion rate for different particle mass flow rate. As seen, in both

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cases with and without particle rotation, maximum erosion rate increases linearly with increase in mass flow rate. However, when particle rotation is considered, the slope of maximum erosion change due to increase in particle mass flow rate is higher and is in a better agreement with experimental data. So the

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6. Conclusion

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effect of mass flow rate on erosion rate is more pronounced in this case.

This work investigated the two-phase gas-solids flow and the corresponding erosion of pipe bend using computational fluid dynamics. The erosion of a standard stainless steel elbow due a gas-solid flow is studied using Eulerian-Lagrangian approach. In general, the modeled erosion results agree well with the experimental data. Simulation results show that the particles rotation has a considerable impact on the particle motion path and consequently the erosion pattern of the elbow. The model produced in this work shows to be a reliable model for predicting the erosion in addition to flow field in gas-solids pipe flows.

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A major highlight of this paper has been the numerical investigation of the particle rotation effects on the erosion rate. Three erosion prediction models were used to predict erosion rate on the elbow in two case of with and without particle rotational motion. Based on results found in this work, following conclusions

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can be made: (1) When particle rotation is ignored in the modeling, the percent bias has an average of 80.5, 48.9 and 47.3 for DNV [45], Zhang et al. [46] and Oka et al. [47, 48] erosion models respectively while

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when the particle rotation is included in the modeling, the percent bias decreases to around 29.3, 54.3 and -65.6 for DNV [45], Zhang et al. [46] and Oka et al. [47, 48] erosion models respectively

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which is a considerable improvement in the modeling.

(2) DNV [45] model with considering particle rotation has minimum deviation from experimental results and is optimal model for erosion prediction. For 150 µm particles, DNV [45] model overpredicts erosion rate while for 300 µm particles DNV [45] model underpredicts erosion rate. Also Zhang et al. [46] and Oka et al. [47, 48] erosion models overpredict erosion rate from

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experimental data compared to when the particle rotation is included in the modeling for both particle diameters which is conservative model for designing pipelines in a safe way. (3) In the presence of particle rotation, a large scale particle concentration zone created on the inner

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and outer surfaces of the elbow due to that the rotational lift force causes a larger scale erosion

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scar on the elbow than when particle rotation is ignored. (4) When the particle rotation is included in the modeling, the particle trajectories changes dramatically. Particle rotational motion causes more destructive collisions to the wall due to the type of particle impact on the wall leading dramatic increase in erosion rate. Also in the case that particle rotation is not taking to account, a particle free zone is created due to mechanism of particle motion while with particle rotation there is not any particle free zone.

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(5) In presence of particle rotation, the particles flow separation being driven to the middle of the pipe and a reverse motion will be occurred in particles trajectories. The reverse motion of particles causes several collisions to the wall. Although the next particle collisions to the wall have not the

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destructive power of the initial impact but play a significant role on erosion pattern.

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Haugen, K., et al., Sand erosion of wear-resistant materials: Erosion in choke valves. Wear, 1995. 186: p. 179-188.

53.

McLaury, B., et al. Solid particle erosion in long radius elbows and straight pipes. in SPE annual technical conference and exhibition. 1997. Society of Petroleum Engineers.

54.

Nøkleberg, L. and T. Søntvedt, Erosion of oil&gas industry choke valves using computational fluid dynamics and experiment. International Journal of Heat and Fluid Flow, 1998. 19(6): p. 636643.

56.

SC

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55.

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39.

Parsi, M., et al., A comprehensive review of solid particle erosion modeling for oil and gas wells and pipelines applications. Journal of Natural Gas Science and Engineering, 2014. 21: p. 850-873. Peng, W. and X. Cao, Numerical simulation of solid particle erosion in pipe bends for liquid–solid flow. Powder Technology, 2016. 294: p. 266-279.

57.

Peng, W. and X. Cao, Numerical prediction of erosion distributions and solid particle trajectories in elbows for gas–solid flow. Journal of Natural Gas Science and Engineering, 2016. 30: p. 455470.

58.

Deng, T., M.S. Bingley, and M.S. Bradley, The influence of particle rotation on the solid particle erosion rate of metals. Wear, 2004. 256(11): p. 1037-1049. 32

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dos Santos, V.F., F.J. de Souza, and C.A.R. Duarte, Reducing bend erosion with a twisted tape insert. Powder Technology, 2016. 301: p. 889-910.

60.

Xu, L., et al., Numerical prediction of erosion in elbow based on CFD-DEM simulation. Powder Technology, 2016. 302: p. 236-246.

61.

Kliafas, Y. and M. Holt, LDV measurements of a turbulent air-solid two-phase flow in a 90 bend. Experiments in Fluids, 1987. 5(2): p. 73-85.

62.

Gupta, H.V., S. Sorooshian, and P.O. Yapo, Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration. Journal of Hydrologic Engineering, 1999. 4(2): p. 135-143.

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Table captions Table 1: experimental conditions of eleven gas-sand erosion test [14].................................................... 35

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Table 2: Properties of air, particles and pipe material............................................................................. 36 Table 3: Mesh study .............................................................................................................................. 37 Table 4: system specifications ............................................................................................................... 38

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Table 5: Comparison of CFD predictions and measurements [14] for gas-sand flow in 76.2 mm standard elbow, 150 µm and 300 µm sand size ..................................................................................................... 39

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Table 6: Percent bias of erosion models in two case of with and without particle rotation ....................... 40

34

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Table 1: experimental conditions of eleven gas-sand erosion test [14]

11 15 23 27 11 15 15 15 15 23 27

VμmZ 150 150 150 150 300 300 300 300 300 300 300

Particle mass flow rate dÐ

Mass loading K

254 237 257 206 288 103 154 192 452 227 256

0.048 0.033 0.023 0.016 0.055 0.014 0.021 0.027 0.063 0.020 0.020

Vkg. day M+ Z

V−Z

Momentum stokes number $]Q] V−Z

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26.56 36.22 55.54 65.20 106.26 144.90 144.90 144.90 144.90 222.18 260.82

Transducer angle V°Z 45 47 47 45 45 47 47 47 47 47 47

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Vm. s M+ Z

Particle diameter Œ

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1 2 3 4 5 6 7 8 9 10 11

VGas

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Table 2: Properties of air, particles and pipe material

RP

1.8 × 10Mš kg. mM+ s M+

u

7990 kg. mML

Œ

RP Ôu

2650 kg. mML

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RP Ôu

150 μm , 300 μm

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1.2 kg. mML

E

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RP

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Table 3: Mesh study 1

2

3

4

5

Number of nodes on J

12

20

28

36

44

Total number of cells

900,000

1,600,000

2,400,000

3,200,000

4,100,000

3 hr and 32 min

3 hr and 55 min

25.19

26.79

CPU time

1hr and 51 min 24.94

4 hr and 15 min

8 hr and 35 min

26.12

26.83

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Maximum erosion rate mm. year M+

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Mesh type

37

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Table 4: system specifications Intel(R) Core(TM) i7-6700HQ CPU @ 2.60GHz 12.0 GB

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Processor RAM

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Table 5: Comparison of CFD predictions and measurements [14] for gas-sand flow in 76.2 mm standard elbow, 150 µm and 300 µm sand size Erosion models Exp. Data [14]

DNV model [45]

Zhang et al. model [46]

Oka et al. model [47, 48]

(mm.year )

1

7.05E-05

6.5

1.86E-05

2.27E-05

3.90E-05

4.43E-05

3.68E-05

6.06E-05

2

1.53E-04

13.2

3.28E-05

9.78E-05

6.41E-05

1.79E-04

9.46E-05

2.58E-04

3

3.86E-04

36.2

1.01E-04

4.80E-04

1.90E-04

6.78E-04

2.85E-04

1.05E-03

4

7.19E-04

54.0

2.20E-04

5.82E-04

3.69E-04

8.02E-04

5.32E-04

1.33E-03

5

1.61E-04

16.9

1.59E-05

5.73E-05

7.01E-05

1.36E-04

5.04E-05

1.45E-04

6

3.93E-04

14.7

5.16E-05

2.47E-04

1.85E-04

6.98E-04

1.55E-04

6.53E-04

7

3.94E-04

22.1

5.12E-05

2.46E-04

1.70E-04

6.96E-04

1.52E-04

6.65E-04

8

2.76E-04

19.3

5.10E-05

2.47E-04

1.70E-04

6.78E-04

1.52E-04

6.61E-04

9

3.55E-04

58.5

4.56E-05

2.54E-04

1.75E-04

6.25E-04

1.35E-04

6.44E-04

10

9.71E-04

80.3

1.96E-04

6.93E-04

5.86E-04

1.70E-03

5.69E-04

1.63E-03

11

1.39E-03

129.6

3.07E-04

1.14E-03

8.71E-04

2.72E-03

7.75E-04

2.59E-03

With particle rotation (mm.kg-1)

Without particle rotation (mm.kg-1)

With particle rotation (mm.kg-1)

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-1

Without particle rotation (mm.kg-1)

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-1

With particle rotation (mm.kg-1)

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(mm.kg )

Without particle rotation (mm.kg-1)

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Table 6: Percent bias of erosion models in two case of with and without particle rotation Percent bias of erosion models(%) Exp. Data [14]

DNV model [45]

Zhang et al. model [46] Without With particle particle rotation rotation

(mm.year-1)

Without particle rotation

With particle rotation

1

7.05E-05

6.5

73.6

67.8

44.6

37.1

2

1.53E-04

13.2

78.5

36.0

58.1

-16.9

3

3.86E-04

36.2

73.8

-24.3

50.7

-75.6

4

7.19E-04

54.0

69.4

19.0

48.6

5

1.61E-04

16.9

90.1

64.4

56.4

6

3.93E-04

14.7

86.8

7

3.94E-04

22.1

87.0

8

2.76E-04

19.3

81.5

9

3.55E-04

58.5

87.1

10

9.71E-04

80.3

79.8

11

1.39E-03

129.6

77.9

47.8

14.0

38.1

-68.6

26.1

-172.0

-11.5

26.0

-84.9

15.5

68.6

9.9

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-77.6

60.5

-66.1

37.5

56.8

-76.6

61.4

-68.7

10.5

38.4

-145.6

44.9

-139.4

28.4

50.7

-76.0

61.9

-81.4

28.6

39.54

-75.0

41.4

-67.8

17.9

37.33

-95.6

44.2

-86.3

48.9

-54.3

47.3

-65.6

TE D 80.5

With particle rotation

37.1

29.3

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Average:

Without particle rotation

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(mm.kg-1)

Oka et al. model [47, 48]

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Figure captions Figure 1: Schematic of particle impact to the curved wall according to Grant and Tabakoff [42]. .......... 43

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Figure 2: Schematic of geometry and mesh used for CFD simulations, (a) Schematic of geometry, (b): Cross-sectional view of mesh, (c): Near wall view of mesh, (d): Side view of mesh ............................... 44 Figure 3: Dimensionless wall distance along the outer wall centerline. .................................................. 45

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velocity of 27 m/s and particle diameter of 300 µm to evaluate effect of dispersed phase on the continuous phase. .................................................................................................................................................... 47 Figure 6: Value of discrete phase source terms in two-way coupling for flow velocity of 27 m/s and particle diameter of 300 µm. .................................................................................................................. 48

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Figure 7: Particle and gas velocity distribution for flow velocity of 27 m/s and particle diameter of 300 µm. ........................................................................................................................................................ 49 Figure 8: Contour of stokes number for flow velocity of 27 m/s and particle diameter of 300 µm. ......... 50

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Figure 9: CFD modeled (a): erosion pattern, (b): particle concentration, (c): particle trajectory without particle rotation for flow velocity of 23 m.s-1 and particle diameter of 300 µm. ....................................... 51

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Figure 10: CFD modeled (a): erosion pattern, (b): particle concentration, (c): particle trajectory with particle rotation for flow velocity of 23 m.s-1 and particle diameter of 300 µm. ....................................... 52 Figure 11: Mean value contour of particle velocity: (a): without particle rotation, (b): with particle rotation for flow velocity of 23 m.s-1 and particle diameter of 300 µm. ................................................... 53 Figure 12: Reverse motion of two kind of rotational particles. ............................................................... 54

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Figure 13: Comparison of erosion distribution in two case of with and without particle rotation along the elbow centerline for dp=150 µm and VGas=23 m.s-1, (a): Zhang et al. [46] model (b) Oka et al. [47, 48] model (c): DNV [45] model. ................................................................................................................. 55

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Figure 14: Comparison of erosion distribution in two case of with and without particle rotation along the elbow centerline for dp=300 µm and VGas=27 m.s-1, (a): Zhang et al. [46] model (b) Oka et al. [47, 48] model (c): DNV [45] model. ................................................................................................................. 56

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Figure 15: Comparison between accuracy of erosion prediction models along the elbow centerline for case of considering particle rotation, (a) dp=150 µm and VGas=23 m.s-1, (b) dp=300 µm and VGas=27 m.s-1.

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.............................................................................................................................................................. 57 Figure 16: Comparison of experiment measurements [14] with CFD predictions, (a): dp=150 µm, (b): dp=300 µm. ............................................................................................................................................ 58 Figure 17: Predicted erosion profile by DNV model [45] with considering particle rotation along the elbow centerline for different particle mass flow rates. (a): mp = 103 kg. day − 1, (b): mp =

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154 kg. day − 1, (c): mp = 192 kg. day − 1, (d): mp = 452 kg. day − 1 , (e): comparison of different

particle mass flow rates erosion profile. ................................................................................................. 59

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Figure 18: Changes of maximum erosion rate for different particle mass flow rate. ............................... 60

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Figure 1: Schematic of particle impact to the curved wall according to Grant and Tabakoff [42].

43

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600 mm Pressure outlet

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1.5 D D=76.2 mm

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D

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Velocity inlet

(b)

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Figure 2: Schematic of geometry and mesh used for CFD simulations, (a) Schematic of geometry, (b): Cross-sectional view of mesh, (c): Near wall view of mesh, (d): Side view of mesh

44

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Figure 3: Dimensionless wall distance along the outer wall centerline.

45

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Figure 4: Two-phase flow validation.

46

(b)

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(c)

(d)

Figure 5: Comparison of flow behavior in the bend between one-way and two-way coupling for flow velocity of 27 m/s and particle diameter of 300 µm to evaluate effect of dispersed phase on the continuous phase. 47

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Figure 6: Value of discrete phase source terms in two-way coupling for flow velocity of 27 m/s and

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particle diameter of 300 µm.

48

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Figure 7: Particle and gas velocity distribution for flow velocity of 27 m/s and particle diameter of 300 µm.

49

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Figure 8: Contour of stokes number for flow velocity of 27 m/s and particle diameter of 300 µm.

50

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Without particle rotation

(b)

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Figure 9: CFD modeled (a): erosion pattern, (b): particle concentration, (c): particle trajectory without particle rotation for flow velocity of 23 m.s-1 and particle diameter of 300 µm.

51

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(b)

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(c) Figure 10: CFD modeled (a): erosion pattern, (b): particle concentration, (c): particle trajectory with particle rotation for flow velocity of 23 m.s-1 and particle diameter of 300 µm.

52

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Without particle rotation

(a)

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(b) Figure 11: Mean value contour of particle velocity: (a): without particle rotation, (b): with particle rotation for flow velocity of 23 m.s-1 and particle diameter of 300 µm.

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Figure 12: Reverse motion of two kind of rotational particles.

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(b)

(c)

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Figure 13: Comparison of erosion distribution in two case of with and without particle rotation along the elbow centerline for dp=150 µm and VGas=23 m.s-1, (a): Zhang et al. [46] model (b) Oka et al. [47, 48] model (c): DNV [45] model.

55

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(b)

(c)

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Figure 14: Comparison of erosion distribution in two case of with and without particle rotation along the elbow centerline for dp=300 µm and VGas=27 m.s-1, (a): Zhang et al. [46] model (b) Oka et al. [47, 48] model (c): DNV [45] model.

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(b)

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Figure 15: Comparison between accuracy of erosion prediction models along the elbow centerline for

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case of considering particle rotation, (a) dp=150 µm and VGas=23 m.s-1, (b) dp=300 µm and VGas=27 m.s-1.

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(a)

(b)

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Figure 16: Comparison of experiment measurements [14] with CFD predictions, (a): dp=150 µm, (b): dp=300 µm.

58

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(b)

(d)

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(e)

Figure 17: Predicted erosion profile by DNV model [45] with considering particle rotation along the elbow centerline for different particle mass flow rates. (a): mÐÖ = 103 kg. day M+, (b): mÐÖ = 154 kg. day M+ , (c): mÐÖ = 192 kg. day M+ , (d): mÐÖ = 452 kg. day M+ , (e): comparison of different particle mass flow rates erosion profile.

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Figure 18: Changes of maximum erosion rate for different particle mass flow rate.

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Erosion of Natural Gas Elbows due to Rotating Particles in Turbulent GasSolid Flow

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Mohammad Zamani a, Sadegh Seddighi *a, Hamid Reza Nazif b Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

b

Department of Mechanical Engineering, Imam Khomeini University, Ghazvin, Iran

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* To whom correspondence should be addressed. Email: [email protected]

Highlights

The erosion of elbow pipes due to the gas-solids turbulent pipe flow is investigated.

•

Particle rotational motion leads to dramatic increase in erosion rate.

•

The maximum erosion rate occurs at an angle of 47°.

•

The particle reverse motion caused by particle rotation affects erosion.

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1