Numerical simulation of Erosion in a
pipe
bend
CHANGE
FIGURE
NUMBERS
Kevin John O’Flaherty
Bachelor in Engineering
University of Limerick
Patrick Frawley
'Final Year Project report submitted to the University of Limerick, March 2011
I declare that this is my work and that all contributions from other persons have been
appropriately identified and acknowledged.
Abstract
An abstract, or summary, not exceeding 300 words, single spacing, or one page in
length, should be bound as an integral part of the report, and should precede the main
text. The style of writing for this section is technical and concise, with economical use
of words. It should be written only when almost all section of the report have been
completed.
Students sometimes find it difficult to accept that a statement should be made in the
abstract, knowing that an identical or similar statement appears in the body of the
report. The summary should be regarded as an independent section which is
meaningful when read in isolation from the remainder of the report.
In writing the abstract, therefore, one should look at each completed section of the
report, extract key statements, and present them as concisely as possible.
It is important to include in the abstract any significant findings of the study or
experimentally determined value, the determination of which is a major feature of the
investigation. Comments should be made, wherever possible, to the significance of
the results.
i
Dedication
ii
Acknowledgements
This section is used to acknowledge anybody who has contributed to your project.
iii
Contents List
Table of contents
Abstract ........................................................................................................................... i
Dedication ......................................................................................................................ii
Acknowledgements ...................................................................................................... iii
Contents List ................................................................................................................. iv
Table of contents ....................................................................................................... iv
Table of figures .......................................................................................................... v
Table of tables ............................................................................................................ v
Nomenclature ...............................................................................................................vii
1.
Introduction ............................................................................................................ 1
2.
Literature Review ................................................................................................... 2
2.1.
Solid particle erosion ....................................................................................... 2
2.2.
CFD modelling ................................................................................................ 7
2.3.
Empirical modelling ........................................................................................ 8
2.4.
Design of Experiments .................................................................................... 9
3.
Theoretical Analysis ............................................................................................. 12
4.
Numerical Modelling ............................................................................................ 14
4.1.
Fluent............................................................................................................. 14
5.
Experimental Apparatus ....................................................................................... 16
6.
Experimental Procedure ....................................................................................... 17
6.1.
7.
8.
ICEM ............................................................................................................. 17
Results .................................................................................................................. 18
7.1.
Observed Readings ........................................................................................ 25
7.2.
Analysis of Data ............................................................................................ 27
Discussion ............................................................................................................. 28
iv
9.
Conclusions and Future Work .............................................................................. 29
9.1.
Conclusions ................................................................................................... 29
9.2.
Future Work .................................................................................................. 29
References .................................................................................................................... 30
Appendices ................................................................................................................... 32
Table of figures
Figure 2.1.1 Wall removal at low impact angles (Sherry, 1997) ................................... 2
Figure 2.1.2 Particle impact at 90° causing deformation (Sherry, 1997) ...................... 2
Figure 2.1.3 Particle causing cutting with velocity being reduced to zero
(O'Mahoney, 2006) ........................................................................................................ 3
Figure 2.1.4 Typical particle removal at different angles of attack (Finnie I. , 1995) ... 3
Figure 2.1.5 Particle with a) Hardness greater than 1.2 time the wall hardness and b)
Hardness less than 1.2 times the wall hardness striking a flat surface (Corish, 2007). . 5
Figure 2.1.6 Normalised characteristic equations for different materials at different
angles (Oka, Olmogi, Hosokawa, & Matsumur, 1997) ................................................. 6
Figure 2.1.7 Normalised erosion for ASTM A106b Carbon Steel ................................ 7
Figure 2.3.1 Schematic of the erosion test rig (O'Mahoney, 2006) ............................... 9
Figure 4.1.1 Plot of residuals for 660mm diameter pipe with a 1.75 radius of curvature
for an ASTM A106b Carbon Steel .............................................................................. 15
Figure 6.1.1 divergence graph for ................................................................................ 18
Table of tables
Table 1 Main factors affecting erosion (O'Mahoney, 2006) .......................................... 4
Each student should discuss the contents of the report with his/her supervisor before
starting to write.
v
This section lists the contents of the report (Table of Contents) giving the page
number at which each section starts. Sections preceding the main body of the report
are not seen as part of the report and should be paginated as such (see Section 5,
above). It is usual to start the Introduction at page 1.
It is common for the FYP supervisor to require that the student include a Table of
Figures and a Table of Tables.
vi
Nomenclature
Symbol
𝑝
Description
Units
Plastic flow stress
All symbols used in the text should be defined here, including for example sub- and
super-scripts, Greek symbols and acronyms. Where a symbol represents a physical
quantity the associated units of measurement should be listed. (SI units should be used
whenever possible). Refer to Engineering Tables and Data (Howatson et al., 1991) or
Young (2005) for Greek Alphabet, symbols and units.
vii
Main body (See Section 9)
Note: Do not number more than 2 subsection levels for each chapter, e.g. maximum
numbering 2.3.5. For any other subsections use formatting (such as Bold or Italic) to
distinguish.
1. Introduction
Slurry flow is a major concern costing up to £20 million in the U.K. according to the
Department of Trade and Industry in 2000. Slurry flow can cause a plant to be shut
down for maintenance unexpectedly, creating a predictive equation would allow
proper scheduling to replace parts which would reduce maintenance and inventory
costs. An example is in the production of alumina; particles can be very abrasive and
cause severe erosion requiring the replacement of equipment every couple of days.
Areas such as a 90° bends have higher erosion in concentrated areas and are more
frequently replaced. The aim of this project is to:

Create a C.F.D model of a 90° pipe bend.

Determine the angle of attack of the particles, particle velocity and particle
impact frequency from a C.F.D model using ICEM and FLUENT.

Compare the historical and previous experimental data to the C.F.D
modelling.
The introduction should include a full but concise statement of:
a) The background to the investigation, briefly stating the reasons governing the need
for the investigation. This background should reflect the title of the project.
b) The aims or objectives of the investigation. (The Conclusion section should always
refer back to the objectives you set out)
The introduction should have a flowing, natural, style of writing and should read like
a story.
1
2. Literature Review
This section will give a review of solid particle erosion, method of computational
fluid dynamics (CFD) to predict erosion and empirical modelling.
2.1.
Solid particle erosion
Erosion can occur in two different ways, cutting and deformation erosion. Cutting
erosion is primarily caused by a particle striking a surface at a low angle of attack and
removing material Figure 2.1.1.
Figure 2.1.1 Wall removal at low impact angles (Sherry, 1997)
(need to be redrawn)
Deformation erosion is caused at high angles of attack when particles cause plastic
deformation at the surface Figure 2.1.2.
Figure 2.1.2 Particle impact at 90° causing deformation (Sherry, 1997)
(need to be redrawn)
Figure 2.1.3 is a method of deformation erosion at lower anlges of attack, the particle
velocity reduces to zero during a cutting erosion before the material is removed
resulting in deformation at angles typical between 20-40° (Finnie I. , 1995).
2
Figure 2.1.3 Particle causing cutting with velocity being reduced to zero
(O'Mahoney, 2006)
(need to be redrawn)
Figure 2.1.4 shows the characteristic erosion curve for a typically ductile material
normalised at 90° showing typical erosion at different angles. At low angles, erosion
shown in Figure 2.1.1 occurs,
Figure 2.1.4 Typical particle removal at different angles of attack (Finnie I. , 1995)
(need to be redrawn)
3
There are numerous factors that affect erosion with the principal factors being listed
in Table 1.
Table 1 Main factors affecting erosion (O'Mahoney, 2006)
Particles
Eroding Surface
Hydrodynamics
Size
Hardness
Impact angle
Hardness
Ductility or brittleness
Impact velocity
Shape
Density
State of motion
Density
Particle concentration
Rotation
An equation to predict erosion is vital for industry and previous attempts have been
made by Bitter (1963) and Finnie (1960). Bitter proposed three equations in 1963,
with a separate equation for deformation erosion (equation 2.1.1) at high impact
angles shown in Figure 2.1.2. Equation 2.1.2 deals with the cutting effect of a particle
with a horizontal velocity component after the collision this is shown in Figure 2.1.1
and equation 2.1.3 deals with the cutting effect of the particle when the horizontal
velocity component is zero after the collision, an example of which is shown in Figure
2.1.3.
𝑊𝑑
2.1.1
2
1
𝑀(𝑉
sin
𝛼
−
𝐿)
= 2
𝜍
𝑊𝑐1 =
2𝑀𝐶(𝑉 sin 𝛼 − 𝐾)
√𝑉 sin 𝛼
2
(𝑉 cos 𝛼 −
𝐶(𝑉 sin 𝛼 − 𝐾)
2
√𝑉 sin 𝛼
𝜌)
2.1.2
3
1 𝑉 2 𝑐𝑜𝑠 2 𝛼 − 𝑘1 (𝑉 sin 𝛼 − 𝐾)2
𝑊𝑐2 = 𝑀
2
𝜌
2.1.3
4
Finnie (1960) proposed equation 2.1.4 and equation 2.1.5 by matching up erosion
patterns for ductile materials. Finnie took 𝑝, the plastic flow stress as the factor
affecting erosion the most. Equation 2.1.4 and equation 2.1.5 are used when the angle
of attack is below 18.5° and above 18.5° respectfully. This is due to an assumption by
Finnie that the ratio of vertical to horizontal forces is 2 as they are difficult to measure
in practise.
𝑊=
𝑀𝑉 2
2𝑝
[sin 2𝛼 − 3sin2 𝛼]
𝑊=
𝑀𝑉 2
24 𝑝
cos 2 𝛼
2.1.4
2.1.5
The previous erosion equations proposed by Bitter and Finnie have been specific to
certain angles of attacks, under certain conditions. In 1995, Finnie proved a reflection
of contributions to erosion prediction and determined that typically the velocity
exponent would be around 2.3 to 2.4 (Finnie I. , 1995). This was due to new
technologies at the time as it was possible to more accurately measure velocities
resulting in a finding that a rotational velocity was present resulting in a potential
velocity cubed term so an exponent of 2 was not the case as previously thought.
Hutching (1992) showed the hardness of the particle must be 1.2 times the hardness of
the wall otherwise the particle itself would be deformed, as shown in Figure 2.1.5.
Figure 2.1.5 Particle with a) Hardness greater than 1.2 time the wall hardness
and b) Hardness less than 1.2 times the wall hardness striking a flat surface
(Corish, 2007).
In 1997, Oka et al (1997) proposed a general set of equations with the hardness being
the main factor affecting erosion. The equations, applicable to any material, are
5
shown in equations 2.1.6, 2.1.7 and 2.1.8, provide an estimation of erosion and based
on semi-theoretical model (Oka, Olmogi, Hosokawa, & Matsumur, 1997).
𝐸(∝) = 𝑔(∝)𝐸90
2.1.6
𝑔(∝) = (sin ∝)𝑛1 (1 + Hv(1 − sin ∝))𝑛2
2.1.7
𝐸90 = 𝐾(Hv)𝑘1 (𝑣)𝑘2 (𝐷)𝑘3
2.1.8
Oka et al measured the erosion rate of sand particles striking different materials with
varying hardness. The erosion was normalised at 90° and found that as hardness
increased impact angle causing highest erosion increased as shown in Figure 2.1.6.
Figure 2.1.6 Normalised characteristic equations for different materials at different
angles (Oka, Olmogi, Hosokawa, & Matsumur, 1997)
(need to be redrawn)
For the ASTM A106b Carbon Steel elbow under investigation, the following erosion
curve is produced in Figure 2.1.7.
6
Normalised Erosion
Normalised erosion
2.5
2
1.5
1
0.5
0
0
10
20
30
40
50
60
70
80
90
Angle of attack (°)
Figure 2.1.7 Normalised erosion for ASTM A106b Carbon Steel
Stokes number
𝑆𝑡 =
𝜏𝑝
𝜏𝑓
𝜌𝑝 𝑑𝑝2
𝜏𝑝 =
18𝜇
𝜏𝑓 =
2.2.
𝐿𝑠
𝑉𝑠
2.1.9
2.1.10
2.1.11
CFD modelling
ANSYS Fluent
𝑁𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
𝑅𝑒𝑟𝑜𝑠𝑖𝑜𝑛 =
∑
𝑝=1
𝑚̇𝑝 𝐶(𝑑𝑝 )𝑓(𝛼)𝑣 𝑏(𝑣)
𝐴𝑓𝑎𝑐𝑒
2.2.1
7
Fluent using the following equation to model erosion, outputting units in
𝑘𝑔
𝑚2 𝑠
, the
particle impact frequency. 𝑏(𝑣) is the velocity exponent which can be calculated
using 𝑘2 in equation 2.1.8. 𝐶(𝑑𝑝 ) is a function of particle diameter which was
modified to include 𝐾, (Hv)𝑘1 and (𝐷)𝑘3 from equation 2.1.8.
2.3.
𝑒⊥ = 0.988 − 0.78𝜃 + 0.19𝜃 2 − 0.024𝜃 3 + 0.027𝜃 4
2.2.2
𝑒∥ = 1 − 0.78𝜃 + 0084𝜃 2 − 0.21𝜃 3 + 0.028𝜃 4 − 0.022𝜃 5
2.2.3
Empirical modelling
In 2007, A PhD thesis by Corish (2007) proposed an empirical equation (2.3.1)
applicable to ASTM A106b Carbon Steel, it was found empirically for a mild steel
elbow from erosion testing using a sand blasting rig pictured in Figure 2.3.1 and from
site data from Aughinish Alumina Limited.
𝐶1 + 𝐶2 𝐿𝑖𝑞𝑓𝑙𝑜𝑤𝑅 + 𝐶3 𝑃𝑎𝑟𝑡𝑓𝑙𝑜𝑤 + 𝐶4 𝑃𝑎𝑟𝑡𝑑𝑖𝑎𝑚 + 𝐶5 𝑃𝑎𝑟𝑡𝑑𝑒𝑛𝑠
+𝐶6 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎 + 𝐶7 𝑅𝑂𝐶 + 𝐶8 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎2 + 𝐶9 𝐿𝑖𝑞𝐹𝑙𝑜𝑤𝑅 ∗ 𝑃𝑎𝑟𝑡𝑓𝑙𝑜𝑤
+𝐶10 𝐿𝑖𝑞𝐹𝑙𝑜𝑤𝑅 ∗ 𝑃𝑎𝑟𝑡𝐷𝑖𝑎𝑚 + 𝐶11 𝐿𝑖𝑞𝑢𝑖𝑑𝐹𝑙𝑜𝑤𝑅 ∗ 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎
2.3.1
+𝐶12 𝑃𝑎𝑟𝑡𝑓𝑙𝑜𝑤 ∗ 𝑃𝑎𝑟𝑡𝐷𝑖𝑎𝑚 + 𝐶13 𝑃𝑎𝑟𝑡𝑓𝑙𝑜𝑤 ∗ 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎
+𝐶14 𝑃𝑎𝑟𝑡𝑑𝑖𝑎𝑚 ∗ 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎
An equation for ASTM A106b Carbon Steel Tee was also found empirically given in
equation 2.3.2.
0.2 ∗ (𝐶1 + 𝐶2 𝐿𝑖𝑞𝑓𝑙𝑜𝑤𝑅 + 𝐶3 𝑃𝑎𝑟𝑡𝑓𝑙𝑜𝑤 + 𝐶4 𝑃𝑎𝑟𝑡𝑑𝑖𝑎𝑚 + 𝐶5 𝑃𝑎𝑟𝑡𝑑𝑒𝑛𝑠
+𝐶6 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎 + 𝐶7 𝑅𝑂𝐶 + 𝐶8 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎2 + 𝐶9 𝐿𝑖𝑞𝐹𝑙𝑜𝑤𝑅 ∗ 𝑃𝑎𝑟𝑡𝑓𝑙𝑜𝑤
2.3.2
+𝐶10 𝐿𝑖𝑞𝐹𝑙𝑜𝑤𝑅 ∗ 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎 + 𝐶11 𝑃𝑎𝑟𝑡𝑓𝑙𝑜𝑤 ∗ 𝐸𝑙𝑏𝑜𝑤𝐷𝑖𝑎)
8
Figure 2.3.1 Schematic of the erosion test rig (O'Mahoney, 2006)
(need to be redrawn)
It was found that the elbow diameter and liquid flow rates were the factors most
affecting the empirical erosion with particle density and radius of curvature being the
least influential.
2.4.
Design of Experiments
Traditional experiments require factors to remain constant with one factor varied and
its response recorded. 𝐿𝑘 experiments are required, with 𝐿 being the number of levels
and 𝑘 the number of factors.
To fully model an experiment with the inputs listed in Table 1, 212 experiments
would be required for a two level experiment. To reduce the number of testing
required, design of experiments is utilized, giving a structured method for evaluating
the effects of selected inputs on desired outputs.
For a simple two level and two factor design, 4 experiments would need to be
conducted. In Figure 2.4.1 the two factors, A and B, were varied from low to high as
9
shown in Table 2. Test 1 line shows a low A value while B was varied from low to
high, Test 2 and Test 3 shows a High A value while B was varied from low to high.
Test 2 shows a change in slope, this represents an interaction between A and B; while
Test 3 shows no change in slope, representing no interaction between A and B. The
slope can determine if the interaction between A and B is significant.
20
Response
18
16
Test 2
14
Test 1
12
Test 3
10
8
6
4
2
0
0
0.5
1
1.5
2
2.5
B value
Figure 2.4.1
Table 2 Factors and responses for a two level and two factor experiment
A
B
Response
Low
Low
Test 1
Low
High
Test 1
High
Low
Test 2, Test 3
High
High
Test 2, Test 3
This section should contain an in-depth review of published work relevant to your
investigation. Where a large number of papers are reviewed it is useful to group them
under different aspects of the investigation, that is, to use a separate sub-section for
each aspect. You should compare and contrast the literature reviewed.
10
The important part of this section is your reporting and discussion of the literature. It
is important to distinguish what you have learnt from reading the papers from what
the authors originally said. Your conclusions, on reviewing the literature, should
reinforce the aims or objectives of the investigation given earlier.
11
3. Theoretical Analysis
ANSYS Fluent
𝑁𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
𝑅𝑒𝑟𝑜𝑠𝑖𝑜𝑛 =
∑
𝑝=1
𝑚̇𝑝 𝐶(𝑑𝑝 )𝑓(𝛼)𝑣 𝑏(𝑣)
𝐴𝑓𝑎𝑐𝑒
Fluent using the following equation to model erosion, outputting units in
2.4.1
𝑘𝑔
𝑚2 𝑠
, the
particle impact frequency. 𝑏(𝑣) is the velocity exponent which can be calculated
using 𝑘2 in equation 2.1.8. 𝐶(𝑑𝑝 ) is a function of particle diameter which was
modified to include 𝐾, (Hv)𝑘1 and (𝐷)𝑘3 from equation 2.1.8.
The
This section will require presentation of relevant formulae, equations, etc., leading to
the appropriate theoretical prediction (s). It is essential that all assumptions be clearly
stated. While it is important to present relevant information do not include
unnecessary theory or pages of derivations, particularly if they are from a book or if
they have no bearing on the work in the report. Reference to other work may be made
in this section.
All equations should prepared using a software package, such as Microsoft Equation
Editor or Math Type; and must be numbered consecutively. A two part numbering
system may be used, where the first part designates the chapter. The number should
be aligned with the right margin, e.g. The Reynolds number (Re) is given in Equation
3.1 as:
12
u = velocity
d = characteristic length, in this case diameter
This can then be referenced in the text – see Equation 3.1, or see Eq. 3.1. Frequently,
available theory will not always adequately cover the system under investigation and
in such cases the differences between the theoretical model and test system should be
stated. The representation of a particular system by an approximate model should
wherever possible be justified.
13
4. Numerical Modelling
4.1.
Fluent
A 64-bit Windows 7 computer running Fluent version 12.1.4 was used to model
erosion on the pipe bend. A limit of 512,000 cells were placed on the educational
version.
The geometry was created as a STEP file using a computational aided drawing
package and imported into ICEM. The meshing was created using a max size of 50
(the max it can be is 20 otherwise won’t run in fluent, 50 is too small) and a height of
1 and a height ratio of 1.2. A tetra/mixed mesh was chosen along with a Robust
(Octree) method of meshing. The ICEM file was outputted to Fluent version 6 with a
3D grid dimension. The inlet was defined as a velocity inlet, the outlet was defined as
outflow.
𝑒⊥ = 0.988 − 0.78𝜃 + 0.19𝜃 2 − 0.024𝜃 3 + 0.027𝜃 4
4.1.1
𝑒∥ = 1 − 0.78𝜃 + 0084𝜃 2 − 0.21𝜃 3 + 0.028𝜃 4 − 0.022𝜃 5
4.1.2
Equation 4.1.1 and 4.1.2 are the coefficents of restitution for AISI 4130 Carbon Steel
(Forder, Thew, & Harrison, 1998) and were used for the normal and tangential
components.
Fluent’s erosion model mentioned in equation 4.1.3, can be used to models particle
impact frequency.
𝑁𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
𝑅𝑒𝑟𝑜𝑠𝑖𝑜𝑛 =
∑
𝑝=1
𝑚̇𝑝 𝐶(𝑑𝑝 )𝑓(𝛼)𝑣 𝑏(𝑣)
𝐴𝑓𝑎𝑐𝑒
The particle impact frequency, 𝑅𝑒𝑟𝑜𝑠𝑖𝑜𝑛 is in
𝑘𝑔
𝑚2 𝑠
4.1.3
, giving the particle impact
frequency. 𝑏(𝑣) is the velocity exponent which can be calculated using 𝑘2 in equation
2.1.8. 𝑓(𝛼) is a function of the impact angle which can be calculated in equation
2.1.7 and shown in Figure 2.1.7. 𝐶(𝑑𝑝 ) is a function of particle diameter which was
modified to include 𝐾, (Hv)𝑘1 and (𝐷)𝑘3 from equation 2.1.8. 𝑚̇𝑝 is the mass flow of
the particle and 𝐴𝑓𝑎𝑐𝑒 is the area of the cell face.
14
A standard k-epsilon model with standard wall functions was used to model the
turbulent flow in the pipe bend. A turbulent intensity of 5% and turbulent length scale
estimated at 7% of pipe diameter. An under-relaxation factor of 0.3 was used for
pressure and momentum, with a typical plot of residuals shown in Figure 4.1.1.
Figure 4.1.1 Plot of residuals for 660mm diameter pipe with a 1.75 radius of
curvature for an ASTM A106b Carbon Steel
The particles, modelled using Discrete Phase Modelling, were injected from the inlet
surface. A spread parameter of 1.7 and 20 stochastic number of tries in a to rosinrammler diameter distribution for particles varied from 0.00005m to 0.003m diameter
with a mean diameter of 0.008m.
A 90°
This section will include information on the analysis method used, such as Finite
Element Analysis or Computational Fluid Dynamics, stating version of modelling
software used. The contents must be agreed with the FYP supervisor, but will include
description of models and boundary conditions.
15
5. Experimental Apparatus
Precise details of items under test, and of the testing system, are required. Sketches,
circuit diagrams, and/or CAD drawings are often required in this section. All
equipment should be specified fully (i.e. using model numbers, and reference numbers
if possible) with the exception of minor ancillary equipment such as a metre rule,
protractor etc. This specification may also include the accuracy of the equipment
used.
Always remember that at some future date the experimental results may be subject to
severe scrutiny and the more accurately the system has been specified the less the
doubt concerning the test, and the better the chance of remedial action.
If this section is short, it may be combined with the Experimental Procedure section.
16
6. Experimental Procedure
6.1.
ICEM
The require geometry was created using computer-aided design and imported into a
64-bit version of ANSYS ICEM CFD 12.1. The geometry was created as a STEP file
using a computational aided drawing package and imported into ICEM. The meshing
was created using a max size of 50 (the max it can be is 20 otherwise won’t run in
fluent, 50 is too small) and a height of 1 and a height ratio of 1.2. A tetra/mixed mesh
was chosen along with a Robust (Octree) method of meshing. The ICEM file was
outputted to Fluent version 6 with a 3D grid dimension. The inlet was defined as a
velocity inlet, the outlet was defined as outflow.
6.2.
FLUENT – Divergence test
Concise details of the operations performed should be presented mentioning factors
which are of special significance. Trivial statements however should be avoided, but,
for example, where the order of performing a number of steps is considered to be
important such information should be concisely presented. The writing style should
resemble a recipe in a cookbook.
It is particularly useful to refer to special precautions taken as this can often eliminate
possible doubts in a future enquiry.
The purpose of this section is to define the experimental techniques employed without
ambiguity, and thus in a way which would permit a complete identical “re-test”.
17
7. Results
Figure 6.2.1 divergence graph for
7.1.
Minitab
7.2.
Angle
The
Main Effects Plot for angle
Data Means
14
LiquidFLowRate
PartFlowRate
PartDiam
Point Ty pe
Corner
Center
12
Mean
10
8
750
1000
1250
6
PartDensity
14
9
12
450
PipeDiam
800
1150
ROC
12
10
8
2900
3000
3100
520
590
660
1.75
2.00
2.25
18
Interaction Plot for angle
Data Means
6
9
12
450
800
1150 2900
3000
3100 520
590
660 1.75
2.00
2.25
12
LiquidFLowRate Point Type
750 Corner
10
LiquidFLowRate
1000 Center
1250 Corner
8
12
PartFlowRate Point Type
6 Corner
10
PartFlowRate
9 Center
12 Corner
8
12
PartDiam Point Type
450 Corner
10
PartDiam
800 Center
1150 Corner
8
12
PartDensity Point Type
2900 Corner
3000 Center
10
PartDensity
3100 Corner
8
12
PipeDiam Point Type
10
PipeDiam
8
520 Corner
590 Center
660 Corner
ROC
Residual Plots for angle
Normal Probability Plot
Versus Fits
99
5.0
Residual
Percent
90
50
10
2.5
0.0
-2.5
-5.0
1
-5.0
-2.5
0.0
Residual
2.5
5.0
5
10
Fitted Value
Versus Order
16
5.0
12
2.5
Residual
Frequency
Histogram
8
4
0
15
0.0
-2.5
-5.0
-6
-3
0
Residual
3
6
1
5
10
15 20 25 30 35 40
Observation Order
45
50
19
Pareto Chart of the Effects
(response is angle, Alpha = 0.05, only 30 largest effects shown)
Term
1.859
A EF
BD
E
C
A
BF
AC
ADF
AC E
A BE
ABD
AF
CF
D
DE
CE
EF
BE
ADE
A BF
AD
AC F
F
CD
AC D
ABC
DF
AB
BC
B
F actor
A
B
C
D
E
F
0
1
2
3
4
5
6
N ame
LiquidF Low Rate
P artF low Rate
P artD iam
P artD ensity
P ipeD iam
RO C
7
Effect
Lenth's PSE = 0.838125
Equation for angle
Coded
Constant
LiquidFLowRate
PartFlowRate
PartDiam
PartDensity
PipeDiam
ROC
PartFlowRate*PartDensity
LiquidFLowRate*PipeDiam*ROC
Ct Pt
1.844
-0.057
1.851
0.657
2.108
0.288
-2.124
-6.542
8.766
0.922
-0.029
0.925
0.328
1.054
0.144
-1.062
-3.271
4.734
0.3398
0.3398
0.3398
0.3398
0.3398
0.3398
0.3398
0.3398
0.3398
1.9520
25.80
2.71
-0.08
2.72
0.97
3.10
0.42
-3.13
-9.63
2.43
0.000
0.012
0.933
0.012
0.344
0.005
0.676
0.005
0.000
0.024
𝜃 = 8.76625 + 0.92187𝐿𝑖𝑞𝑢𝑖𝑑𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 − 0.0275𝑃𝑎𝑟𝑡𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒
+ 0.92531𝑃𝑎𝑟𝑡𝐷𝑖𝑎𝑚 + 0.32844𝑃𝑎𝑟𝑡𝐷𝑒𝑛𝑠𝑖𝑡𝑦 + 1.05406𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚
+ 0.11406𝑅𝑂𝐶 − 1.06219𝑃𝑎𝑟𝑡𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 ∗ 𝑃𝑎𝑟𝑡𝐷𝑒𝑛𝑠𝑖𝑡𝑦
− 3.27125𝐿𝑖𝑞𝑢𝑖𝑑𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 ∗ 𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚 ∗ 𝑅𝑂𝐶
UNCODED NEEDS TO GO HERE
20
𝜃 = 8.76625 + 0.92187𝐿𝑖𝑞𝑢𝑖𝑑𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 − 0.0275𝑃𝑎𝑟𝑡𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒
+ 0.92531𝑃𝑎𝑟𝑡𝐷𝑖𝑎𝑚 + 0.32844𝑃𝑎𝑟𝑡𝐷𝑒𝑛𝑠𝑖𝑡𝑦 + 1.05406𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚
+ 0.11406𝑅𝑂𝐶 − 1.06219𝑃𝑎𝑟𝑡𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 ∗ 𝑃𝑎𝑟𝑡𝐷𝑒𝑛𝑠𝑖𝑡𝑦
− 3.27125𝐿𝑖𝑞𝑢𝑖𝑑𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 ∗ 𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚 ∗ 𝑅𝑂𝐶
7.3.
Particle Impact Frequency
Main Effects Plot for particle impact frequency
Data Means
LiquidF Low Rate
P artF low Rate
P artDiam
Point Ty pe
Corner
Center
0.00020
0.00015
Mean
0.00010
0.00005
750
1000
1250
6
P artD ensity
9
12
450
P ipeD iam
800
1150
RO C
0.00020
0.00015
0.00010
0.00005
2900
3000
3100
520
590
660
1.75
2.00
2.25
21
Interaction Plot for particle impact frequency
Data Means
6
9
12
450
800
1150 2900 3000 3100 520
590
660 1.75
2.00
2.25
0.0003
LiquidFLowRate Point Type
750 Corner
0.0002
LiquidFLowRate
1000 Center
1250 Corner
0.0001
0.0003
0.0002
PartFlowRate
PartFlowRate Point Type
6 Corner
9 Center
12 Corner
0.0001
0.0003
PartDiam
450 Corner
0.0001
1150 Corner
0.0003
PartDensity
800 Center
PartDensity Point Type
0.0002
2900 Corner
3000 Center
0.0001
3100 Corner
0.0003
PipeDiam
PartDiam Point Type
0.0002
PipeDiam Point Type
0.0002
520 Corner
590 Center
0.0001
660 Corner
ROC
Residual Plots for particle impact frequency
Versus Fits
0.00010
90
0.00005
Residual
Percent
Normal Probability Plot
99
50
10
1
-0.00010
-0.00005
0.00000
Residual
0.00005
0.00000
-0.00005
-0.00010
0.00010
0.0000 0.0001 0.0002 0.0003 0.0004
Fitted Value
Versus Order
0.00010
6
0.00005
Residual
Frequency
Histogram
8
4
2
0
-0.00008
-0.00004
0.00000
Residual
0.00004
0.00008
0.00000
-0.00005
-0.00010
1
5
10
15
20
25
Observation Order
30
22
Pareto Chart of the Effects
(response is particle impact frequency, Alpha = 0.05, only 30 largest effects shown)
Term
0.0000473
E
A
B
F
EF
C
BE
AB
A EF
AC
BC
AF
BF
CE
ABD
AC D
CF
ABC
A BF
AE
CD
DF
AD
DE
D
BD
ADE
ADF
A BE
AC E
0.00000
F actor
A
B
C
D
E
F
0.00002
0.00004
0.00006
0.00008
Effect
0.00010
0.00012
0.00014
N ame
LiquidF Low Rate
P artF low Rate
P artD iam
P artD ensity
P ipeD iam
RO C
0.00016
Lenth's PSE = 0.0000213045
Coded
Term
Constant
LiquidFLowRate
PartFlowRate
PartDiam
PipeDiam
ROC
PipeDiam*ROC
Ct Pt
Effect
0.000101
0.000093
0.000048
-0.000150
-0.000087
0.000068
Coef
0.000147
0.000051
0.000046
0.000024
-0.000075
-0.000043
0.000034
0.000010
SE Coef
0.000009
0.000009
0.000009
0.000009
0.000009
0.000009
0.000009
0.000050
T
17.01
5.86
5.37
2.76
-8.66
-5.02
3.92
0.21
P
0.000
0.000
0.000
0.011
0.000
0.000
0.001
0.835
𝑃𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝐼𝑚𝑝𝑎𝑐𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 10−3 ∗ (0.1472 + 0.0507𝐿𝑖𝑞𝑢𝑖𝑑𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒
+ 0.0464𝑃𝑎𝑟𝑡𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 + 0.0239𝑃𝑎𝑟𝑡𝐷𝑖𝑎𝑚 − 0.0749𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚
− 0.0434𝑅𝑂𝐶 + 0.0339𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚 ∗ 𝑅𝑂𝐶
Uncoded
Constant
LiquidFLowRate
PartFlowRate
PartDiam
PipeDiam
ROC
PipeDiam*ROC
0.00301632
2.02937E-07
1.54831E-05
6.83001E-08
-4.94718E-06
-0.00131743
1.93866E-06
23
𝑃𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝐼𝑚𝑝𝑎𝑐𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
= (0.00301632 + 2.02937 ∗ 10−7 𝐿𝑖𝑞𝑢𝑖𝑑𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 + 1.54831
∗ 10−5 𝑃𝑎𝑟𝑡𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 + 6.83001 ∗ 10−8 𝑃𝑎𝑟𝑡𝐷𝑖𝑎𝑚 − 4.94718
∗ 10−6 𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚 − 0.00131743𝑅𝑂𝐶 + 1.93866 ∗ 10−6 𝑃𝑖𝑝𝑒𝐷𝑖𝑎𝑚
∗ 𝑅𝑂𝐶
This section will contain a statement of what has been determined, i.e. both evaluated
and observed, as a consequence of performing the test. Thus it will comprise a concise
statement of the calculated results together with other important facts which have
been derived or observed. The results are a dry unaltered record of the facts. In some
cases the discussion of the results can be included with the results – you must discuss
with your supervisor which method he/she prefers.
A statement referring to the magnitude of the difference (not necessarily error)
between theoretical prediction(s) and experimental results should be included.
It is emphasised that one should not consider the experimental results to be in error if
they do not agree with the theoretical predictions presented, for a variety of reasons.
For example:
i) Assumed material characteristics, local temperatures, friction or loss terms etc.,
may well be unrealistic.
ii) The theoretical model may not be identical to the test system etc.
Experimentally derived results should be respected and not automatically considered
to be in error if they are not in agreement with the theoretical predictions. If at all
times the theoretical predictions were considered to be the correct values and
discrepancies attributed to experimental error there would be no point in performing
experimental investigations. The existence of discrepancies is often the fact which
justifies the need for the experimental investigation.
24
7.4.
Observed Readings
This section will contain details of relevant records taken during the investigation. If
the number of readings is large it is advisable to present these in an Appendix to
which reference is made in the main body of the report.
Ensure that units of measurement are associated with all readings or sets of readings.
Sets of readings should be presented in tabular form, with the units appearing in the
column heading only. Each table should be referenced with a number, with the title
appearing above the table, for an example see Table 1 below.
Modulus, E, for various metals.
-
-6 E (GNm-2 or GPa)
Aluminium 23 71
Brass (70 Cu/30Zn) 18 100
Copper 17 130
Iron (pure) 12 206
Nickel 13 207
Zinc 31 110
Steel 15 210
Irrelevant data should not be presented. Graphs should be prepared using a suitable
software package and embedded in the body of the report, and where there is more
than one data set they should be appropriately identified using icons or colour. The
axes should carry a definition of the quantity and associated unit. Experimental results
should be clearly marked by a suitable symbol, and unless the test interval is
sufficiently small there should be no line through experimental data except when
specifically curve-fitting.
Ensure that all figures (graphs, sketches, drawings etc.) have a suitable title. In
general they should be centred and not have text to either side. If plotted using
„landscape‟ format they must be arranged to be read from the right hand side of the
report. They should have a reference number such as Figure 1, which appears below
the figure. When referencing in the text they may be referred to as Figure 1, or Fig. 1.
It is convenient to number figures separately for each Chapter, i.e. Figure 1.1, Figure
2.10 etc. It is good practice to change the format of the figure title text and single line
spacing may be used, for example see Figure 1 below.
25
Each figure should be mentioned in the text and then shown (i.e. do not show a figure
without previously discussing it or referencing it). The figure title should accurately
explain what is shown in the figure.
Figure 1 Change in Temperature due to increasing air velocity, for Test Case 1
26
7.5.
Analysis of Data
Full details, presented as concisely as possible, of calculations based on observed
readings should be given.
The report should therefore not be a record of the actual sequence of calculations
performed, but rather an adequate coverage of the fundamental steps. Intelligent use
may be made of an Appendix, thereby keeping the body of the report to a minimum.
A sample calculation may be included to indicate understanding of the theory. It is
very important that repetitive type calculations should be avoided.
27
8. Discussion
This section involves an assessment of the experimental results and comparison with
theoretical predictions where appropriate. This section allows opportunity for personal
expression and writing style.
An assessment of the significance of the results must be the theme of this section,
since having obtained results it is essential that they be interpreted soundly. It is
therefore the duty of the author to guide the reader towards such a sound
interpretation and consequently all significant aspects must be examined and
commented upon. Whilst the reader most certainly desires to know the author‟s
opinions, it is nevertheless the responsibility of the author to present his
interpretations in a manner which furnishes the reader with sufficient information to
enable him to assess the soundness of the interpretations, and if necessary formulate
others.
A critical analysis of the whole experiment should be made, but without going into
excessive detail. Such statements as “….. the experiment was successful…” are not
sufficient. Possible modifications and/or further work may be suggested. An error
analysis (both absolute and statistical) may be included in this section if not presented
earlier.
28
9. Conclusions and Future Work
9.1.
Conclusions

Oka’s equation can be applied to a 90° ASTM A106b Carbon Steel pipe bend.

An equation to predict velocity for a 90° ASTM A106b Carbon Steel pipe
bend was created

An equation to predict particle impact frequency on a 90° ASTM A106b
Carbon Steel pipe bend was created.

An equation to predict angle of attack on a 90° ASTM A106b Carbon Steel
pipe bend was created.
9.2.

Future Work
To perform erosion testing on a 90° pipe bend with a different hardness
The author should remember that often this is the only section, to which in industry,
some readers refer due to shortage of time. It is therefore extremely important that this
section be well written. The requirement is therefore for a concise statement of the
results which were sought and obtained, and their significance.
The conclusions contain a series of unambiguous statements; each carefully crafted to
make a point and usually presented as a numbered or bulleted list. These statements
must correspond closely with the aims and objectives set out at the beginning of the
report. It must therefore contain the answers to questions which gave rise to the
formulation of the aims of the experiment.
Careful reference must therefore be made to the section which specifies the aims of
the test. Recommendations, where appropriable, may be put forward together with the
conclusions
29
References
Bitter, J. G. (1963). A study of erosion phenomena: Part I. Wear, 5-21.
Bitter, J. G. (1963). A study of erosion phenomena: Part II. Wear, 169-190.
Chauhan, A. K., Goel, D., & Prakash, S. (2009). Solid particle erosion behaviour of
13Cr–4Ni and 21Cr–4Ni–N steels. Journal of Alloys and Compounds, 459–
464.
Corish, J. (2007). Numerical Simulation of Solid Particle Erosion in Long Radius
Elbows. Limerick.
Finnie, I. (1960). Erosion of surfaces by solid particles. Wear, 87-103.
Finnie, I. (1995). Some reflections on the past and future of erosion. Wear, 1-10.
Forder, A., Thew, M., & Harrison, D. (1998). A numerical investigation of solid
particle erosion experienced within oilfield control valves. Wear, 184-193.
Hutchings, I. M. (1992). Tribology: Friction and Wear of Engineering Materials.
London: Edward Arnold.
Lestera, D., Grahamb, L., & Wub, J. (2010). High precision suspension erosion
modeling. Wear, 449-457.
Oka, Y., & Yoshida, T. (2005). Practical estimation of erosion damage caused by
solid particle impact; Part 2: Mechanical properties of materials directly
associated with erosion damage. Wear, 102-109.
Oka, Y., Mihara, S., & Yoshida, T. (2009). Impact-angle dependence and estimation
of erosion damage to ceramic materials caused by solid particle impact. Wear,
129-135.
Oka, Y., Okamura, K., & Yoshida, T. (2005). Practical estimation of erosion damage
caused by solid particle impact, Part 1: Effects of impact parameters on a
predictive equation. Wear, 95-101.
Oka, Y., Olmogi, H., Hosokawa, T., & Matsumur, M. (1997). The impact angle
dependence of erosion damage caused by solid particle impact. Wear, 573579.
O'Mahoney, A. P. (2006). Numerical Simulation of Slurry Erosion using Lagrangian
and Eulerian Techniques. Limerick.
30
Sherry, J. (1997). Numerical Simulation of Solid Particle Erosion in a Control Choke.
Limerick.
Treadgold, T. (2010). Redirection reduce impact of erosion. Process, 6-7.
Wood, R., Jones, T., Ganeshalingam, J., & Miles, N. (2004). Comparison of predicted
and experimental erosion estimates in slurry ducts. Wear, 937-947.
Zhang, Y., Reuterfors, E., McLaury, B., Shirazi, S., & Rybicki, E. (2007).
Comparison of computed and measured particle velocities and erosion in
water and air flows. Wear, 330-338.
Any work which is not the student‟s own must be referenced, to avoid allegations of
plagiarism. For the presentation of references it is required that the UL Harvard style,
as published by the Library & Information Services, be use – this is available at
http://www.ul.ie/~library/referencing/harvard.html for details. Examples, online
tutorials, and information on the use of Endnote are also provided
31
Appendices
Appendix A Excel file showing erosion rate for 90° pipe bends of ASTM A106b
Carbon Steel
Appendices are used to give additional information which is not essential to the
reading of the report but may be required in order to continue with the work, or to
explain in great detail some aspect of the work carried out. As a rule items that are
readily available (e.g. journal and conference papers) are not included as an appendix
except where it is judged to be unusual and not readily available.
Appendices should be named alphabetically (Appendix A, Appendix B, etc.) and
numbered as outlined in Section 5. Examples of material that may be included in
Appendices:
be in main body of the report)
32
33