Proceedings of the 7th World Congress on Mechanical, Chemical, and Material Engineering (MCM'21)
Prague, Czech Republic Virtual Conference – August, 2021
Paper No. ICMIE 110
DOI: 10.11159/icmie21.110

Numerical Simulation of the Erosion Phenomenon at the Knee Tube at
Different Angles Using DOE Method
Ayed Alshammari1, Faramaz Djavanroodi2, Esam Jassim3
Prince Mohammad Bin Fahd University
Khobar, Saudi Arabia
201500404@pmu.edu.sa; fdjavanroodi@pmu.edu.sa
2
Prince Mohammad Bin Fahd University
Khobar, Saudi Arabia
ejassim@pmu.edu.sa

Abstract This numerical study is considered to investigate the erosion in the pipeline systems affected by different parameters such as
elbow angle and type, mass flow rate, pipe radius, and wall materials using Computational Fluid Dynamics (CFD). the gravity effect has
been considered along the Y-direction. The Standard k-ε model has been selected for turbulence, and standard wall functions have beenused for near-wall treatment. Discrete phase modelling (DPM) is selected to model the secondary phase (sand particles). The continuous
phase is crude oil, and the discrete phase is sand. The particle characteristics were selected based on the region of Saudi Arabia.
Validations are conducted based on the maximum erosion rate at different inlet velocities and particle sizes. Four different elbow angles
included 90, 60, 45, and 30 degrees and two types of elbow included sharp and smooth elbow was used to study the behaviour of theerosion rate. The roughness height is selected to introduce the wall material; considering that, each material has a specific roughness
height. Therefore, the recognition of every material in this study is done by roughness height. Three parameters of the mass flow rate,
tube radius, and roughness height are considered as input parameters to perform the DOE. The DOE study showed that the pipe radius
has the most effect on the erosion rate. The reason rate in the Generic models for different angles with curvature(5D) 90°,60°,45°,30°
are 5.6 × 10−10 , 2.7× 10−10 , 1.5 × 10−9 , 3.96 × 10−10 respectively.
Keywords: Erosion - CFD – Elbow - DOE – DPM

1. Introduction

Piping is an operation in the industry that results in the transfer of various fluids from one point to another. Usually, inthe industry, the fluid flow is not pure and always carries some particles. When particles, such as sand, are dissolved in thefluid in a pipe, there is a possibility of erosion and tear on the pipe wall. However, when there is a sudden change in the
tube's direction, such as the knees, this undesired phenomenon could be augmented. The presence of impurities andparticles such as sand in the fluid flow in a pipe has always been associated with many problems and difficulties.
The movement of these particles and the background fluid flow cause destructive phenomena such as wear andcorrosion inside the pipes. This damage is more noticeable on the surface of the pipe's inner body particularly, inregions that have change in the direction of flow. Elbow joints in pipes are one of the main areas affected by wear
inside pipes. The target of researches were to investigate the factors, which affect the erosion rate. M. Zamani et al. [1]focused on various key parameters, including gas flow velocity, solid particle diameter, and particle mass flow rate. Theirnumerical work showed that the particles' rotational motion strongly influences the wear rate in the elbows. In somenumerical studies, researchers mainly focus on the effect of the geometric parameters of bends or elbows in pipelines [2, 3].
As researchers moved toward simulating the phenomenon of erosion using the DPM model in Fluent software, they
were challenged how to quantify the erosion rate based on the mathematical formulation. Oka et al. [4] focused on the effectof pipe material on the amount of wear rate produced. S. Lain et al. [5] also combined the Eulerian-Lagrange perspectivewith the erosion model proposed by Oka et al. They tried to study the effects of wall roughness, particle impact and massload applied on the penetration ratio as a measure of the intensity of wear at one elbow of transmission lines. Finnie et al. [6]simulated the mechanism of material destruction of wear-induced surfaces in the range of transition from malleable to brittle.

ICMIE 110-1

They focused on the behaviour of abrasive particles without considering corrosion. Maclaury et al. [7] proposed a model for
determining the rate of wear in slurry or dense gas flows.

2. Mathematical Model

Four different models are used to calculate the erosion damage caused by solid particle impact. These models use thefollowing parameters to calculate the erosion:•Particle impact velocity,•Particle impact angle,•
Mechanical properties of materials.
Each model proposes a correlative equation between impact parameters and erosion damage caused by solid particle
impact.
1. The Finnie Erosion Model state that the erosion of ductile metals varies with impact angle and velocity according tothe below equation [12]:𝑛𝑛𝐸𝐸𝐸𝐸 = 𝑚𝑚𝑘𝑘𝑘𝑘 𝑓𝑓(∝)(1)

Wherem : Mass flow rate of the particles
k = Empirical Constant,n = Velocity index
f(α) = Impact Angle Function

2. Oka Erosion Model proposes an equation for estimating erosion damage for any impact conditions and materials. The
size, shape, and properties of particles, impact velocity, and angle are the main parameters that affect erosion mechanisms
and damage to materials. The material parameters are mechanical properties such as material hardness. The erosion rate (ER)is determined as [12]:
ER= 𝐸𝐸90 �𝑉𝑉𝑉𝑉𝑟𝑟𝑟𝑟𝑟𝑟𝑘𝑘2��

𝐷𝐷𝐷𝐷𝑟𝑟𝑟𝑟𝑟𝑟

�

𝑘𝑘3

𝑓𝑓(∝)𝑚𝑚(2)WhereE90= reference erosion ratio at 90º impact angle
V= particle impact velocity
Vref= reference velocity
d and dref= particle diameter and particle reference diameter, respectively
k2 and k3= velocity and diameter exponents, respectivelyf(∝)= impact angle function
3. McLaury proposed a model for predicting the erosion rate of sand particles in water. The McLaury erosion rate (ER)is determined by [12]:WhereA = Empirical constant
V : Particle impact velocity
n : Velocity exponentf(α) = Impact Angle Function

𝐸𝐸𝐸𝐸 = 𝐴𝐴𝑉𝑉 𝑛𝑛 𝑓𝑓(∝)𝑚𝑚ICMIE 110-2(3)

4. The erosion rate (Generic model) is defined as [12]:Where𝑚𝑚̇𝑝𝑝 : Mass flow rate of the particles
f(α) : Impact angle function
𝑣𝑣𝑝𝑝 : Particle impact velocity
n : Velocity exponent𝐶𝐶�𝑑𝑑𝑝𝑝 �: Particle diameter function

𝐸𝐸𝐸𝐸 =𝑁𝑁 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

�

𝑃𝑃=1

𝑚𝑚̇𝑝𝑝 𝐶𝐶�𝑑𝑑𝑝𝑝 �𝑓𝑓(∝)𝑣𝑣𝑝𝑝𝑛𝑛
𝐴𝐴𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓(4)

3. Numerical Model

The Erosion in elbows due to sand particles is simulated by ANSYS Fluent software. The results are compared withexperimental and numerical results [7]. The pipe material is Stainless Steel 316. The recognition of every material in thesoftware is done by three different parameters of hardness, density, and roughness height. four erosion rate models (Generic,Finnie, McLaury and Oka models) of ANSYS Fluent are used to validate the present results. To study the effect ofgeometrical parameters on erosion, different angles of elbow are modelled. Design modeler software is used tomodel the desired geometries. Table 1 shows the simulated geometries in this study.
Table 1 Simulating Geometries

Elbow angle(degree)
30
45
60
90

Elbow curvature
diameter
5D
5D
5D
1.5D

Downstream
pipe length
1.8m
1.8m
1.8m
1.8m

Upstream
pipe length
3.5m
3.5m
3.5m
3.5m

Internal diameter
pipe (D)
0.15m
0.15m
0.15m
0.15m

3.1. Validation
To validate the present model, at first the particles diameters are modelled by constant size and finally the actual
distribution of particle size is simulated by implementing Rosin-Rammler's expression. Table 2 shows the boundary
conditions of the simulations which were used in the previous study and which we used in the present work. Different values
were examined to achieve good agreement with the reference paper's experimental and numerical results. The velocity-inlet
and pressure-outlet boundary conditions were used to specify the flow at inlet and outlet boundaries, respectively.
Table 2 Boundary Conditions

Case
1

Inlet: VelocityInlet (m/s)
11Particle Size(μm)
150

ICMIE 110-3

Sand Flow
Rate (kg/s)
0.00294

Outlet:Pressure-Outlet (Pa)0211315
415
515
623
*Rosin-Rammler expression

300
150300
PSD(177)*PSD(177)*

0.00333
0.002740.001190.00274
0.0029700000

After we set the boundary conditions, we investigate different velocity and sand particles size to match the results inreference paper's experimental and numerical results. Table 3 shows the results of reference paper's experimental andnumerical results.
Table 3 Previous Experimental and Numerical Simulation For 90° Elbow
CaseGas
Velocity(m/s)

Sand Size(μm)

Experimental

NumericalPercent
Bias %

1

11150

6.5

7.07

8.77

211300

16.9

20.65

22.19315150

13.2

14.49

9.77

415300

14.7

17.05

15.99

515

PSD(177)

13.2

12.63

-4.32

623

PSD(177)

36.2

37.78

4.36

There results of present work in four different erosion model based on ansys software are presented in table 4. Also thedifference between the present work and reference paper’s experimental work at investigated and show the percentage oferror between the simulation and the experimental work to find the best model give us the least percentage of error. According
to table 4 the the best two models give least percentage of error and more results close to the experimental work are the oka
model and generic model. Also we noted when we use the Rosin-Rammler's sand particles distribution the simulation results
become more accurate and close to the experimental work so the Rosin-Rammler's distribution enhance and improve thesimulation results.
Table 4 show the results of the present work

CaseGas
Velocity(m/s)

Sand Size(μm)

Generic
Model

Percent
Bias %Oka
Model

Percent
Bias %

FinnieModel

Percent
Bias %

McLaury
Model*

Percent
Bias %

1111507.179.34

6.68

2.69

9.57

32.07

11.78

44.82

211300

13.23

27.73

11.38

48.5

15.02

12.5

17.31

2.36

3

15

150

16.33

19.16

14.05

6.04

18.75

29.6

18.02

26.74

4

15300

13.28

9.66

12.39

18.64

13.42

9.53

12.86

12.52

5

15

PSD(177)

12.79

3.11

12.78

3.18

1.55

88.25

15.27

13.55

623

PSD(177)

37.45

3.33

37.43

3.28

41.09

11.9

3.28

90.94

* McLaury model is proposed only for predicting the erosion rate of sand particles in water.

3.2. CFD Modelling

ICMIE 110-4

The results of considered cases are represented and analysed. The effect of different angles and radius of elbows isinvestigated. Steady and Pressure-Based solver simulates the tube, also the gravity effect has been considered along the Ydirection. The Standard k-ε model has been chosen as the turbulence model, and standard wall functions have been used fornear-wall treatment. The continuous phase is crude oil with a density of 870 kg/m3 and viscosity of 0.00072 kg/m-s, and thediscrete phase is sand with a density of 6650 kg/m3. Mean, Max and Min diameters of sand particles are 2.4mm, 3mm, and1.5mm, respectively. The particle characteristics (like density and diameter) were selected based on the region of Saudi
Arabia. [9]. For all cases, crude oil enters the pipe at a speed of 10 m/s, and sand is injected from the inlet. the non-slip
condition has been applied to the wall. Table 5 shows the results of the erosion rate of different elbow’s angles while wekeep the curvature constant which is 5D. In all angels the Oka modes shows give grater erasion rate than Generic model.

Table 5 Maximum erosion rate for different elbow angles with two erosion rate models ( Oka and Generic )OkaAngle
Generic(kg/m2s)(degree)(kg/m2s)9060
4530

4. Design of Experiments (DOE)

5.6 × 10−10
2.7× 10−10
1.5 × 10−9

3.96 × 10−10

9.2× 10−8

5.2× 10−8
1.94 × 10−7
5.44 × 10−8

Design of Experiments (DOE) is a set of measures that are performed using process modelling and related variables andlead to increased production efficiency. A set of different parameters that affect the outcome of a particular process isanalysed to obtain the best possible values for the production of an optimal product. Therefore, the purpose of DOE is, firstly,
which input factors or parameters will have a significant impact on the output result or product of the process, and secondly,
how much of these input factors or parameters should be used to achieve the desired output result or product.
Three parameters of input mass flow rate [10], tube radius [11], and roughness height [13] are considered input
parameters to perform the DOE. The DOE was performed by the Central Composite Design (CCD) method. Also, the CCD
method uses the Auto Defined type. The interval of change of the simulated input parameters is shown in table 6.
Table 6 Range of Input Parameters

Input parameter
Tube radius
Mass flow inlet
Roughness height

Max value
40 in
200 kg/s5mm

Min value
4.5 in
100 kg/s
0.0015mm

Figure 1 shows the effect of mass flow rate and roughness height on the erosion rate (Generic model) at 4.5in tube
radius. As it is obvious, the roughness height has more effect on the erosion rate compare to the mass flow rate. At highroughness heights, the mass flow rate has more effect on the erosion rate. By increasing the mass flow rate, the erosion rate
decreases, since a higher mass flow rate provides more impact kinetic to abrasive particles and leads to a lower erosion rate[14]. According to figure 1 if the roughness height decreases this will leads to a lower erosion rate. Figure 2 shows the erosion
rate (Oka model) changes as a function of mass flow rate and pipe radius at 0.0011512mm roughness height. The mass flowrate parameter has a small effect on the erosion rate except for large tube radiuses.

ICMIE 110-5

Fig. 1: Response surface of the Generic model in terms of two parameters of mass flow inlet and roughness heightFig 2: Response surface of Oka model in terms of two parameters of mass flow inlet and tube radius

ICMIE 110-6

5. Conclusion

In this study, the effect of different erosion models and types of the elbow on erosion rate was investigated. Threeparameters, the mass flow rate, the pipe radius, and the roughness height, were selected to do the DOE study. Lots of reliable
results can be concluded from these current CFD simulations. First, it can be noticed that by increasing the fillet curve radiusof the pipe knee, the erosion rate decreases. Another important issue is that the effect of three different input parameters ofmass flow rate, pipe diameter, and pipe wall roughness height, on the erosion rate is studied using the DOE method. The
pipe radius has the most impact on the erosion rate. Also, four different erosion rate equations have been investigated. Okaand Generic models present the best results in terms of erosion rate study.

References[1] Mohammad Zamani, Sadegh Seddighi, Hamid Reza Nazif, Erosion of natural gas elbows due to rotating particles inturbulent gas-solid flow, Journal of Natural Gas Science and Engineering, 2017.
[2] Wee Siaw Khur, Yap Yung Jian, CFD study of sand erosion in pipeline, Journal of Petroleum Science and Engineering,
2018.
[3] V. Kannojiya, S. Kumar, Assement of Optimum Slurry Pipe Design for Minimum Erosion, Mechanical and Industrial
Engineering Department, Indian Institute of Technology.
[4] M.A. Habib, H.M.Badr, R.Ben-Mansour, M.E.Kabir, Erosion rate correlations of a pipe protruded in an abrupt pipecontraction, International Journal of Impact Engineering 34 (2007) 1350-1369.
[5] Iain Finnie, Some reflections on the past and future of Erosion, Wear 186-187 (1995) l-10.
[6] B.S. McLaury, Predicting Solid Particle Erosion Resulting From Turbulent Fluctuation in oil Field Geometries (Ph.D.
dissertation), Department of Mechanical Engineering, The University of Tulsa, Tulsa, USA, 1996.
[7] Y.I. Oka, K. Okamura, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact Part 1: Effectsof impact parameters on a predictive equation, Wear 259 (2005) 95–101.
[8] Abolkhair, Yahya Mohammed Sheikh, The Statistical Analysis of the Sand Grain Size Distribution of A.I.- Ubaylah
Barchan Dunes, Northwestern Ar-Rub-Alkhali Desert, Saudi Arabia[9] American Petroleum Institute, API 5L: Specification for Line Pipe, 49 CFR 192.113[10] F. Madani Sania , S. Huizingab , K.A. Esaklulc , S. Nesic, Review of the API RP 14E erosional velocity equation:
Origin, applications, misuses, limitations and alternatives[11] Pathegama Gamage Ranjith, Yong Liu, Jianping Wei and Xiaotian Liu. Effect of abrasive mass flow on the abrasive
acceleration and erosion rates of abrasive gas jets, © Springer-Verlag GmbH Austria, part of Springer Nature 2019[12] ANSYS Fluent, 12.0/12.1 Documentation, Users Guide Manual, Ansys Inc., 2009 Available:
https://www.ansys.com//media/ansys/en-gb/presentations/2018+scottish+innovation+conference+presentations/2018ansys-innovations-erosionmodeling-sabrina-hafid.pdf?la=engb&hash=3A3666DAA3FA78FF471EC8969E8756CB698AECEC[13] Farshad, Fred F., and Herman H. Rieke. "Surface roughness design values for modern pipes." SPE Drilling &Completion 21.03 (2006): 212-215.

ICMIE 110-7