stress and deformation analyses of pipe tees using i

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STRESS AND DEFORMATION ANALYSES OF PIPE TEES
USING I-DEAS PROGRAM
Thongchai SRINOPHAKUN
Department of Chemical Engineering, Faculty of Engineering,
Kasetsart University, Bangkok 10903
THAILAND
Pracha HATTAKITJUMREON
Chemical Engineering Practice School, Department of Chemical Engineering,
King Mongkut’s University of Technology Thonburi, Bangkok 10140
THAILAND
 To whom all correspondence should be addressed.
 Tel. 66-2-9428555 ext. 1214
 Fax. 66-2-5792083
 E-mail: [email protected]
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ABSTRACT - This research presents the finite element analysis of stress in pipe tees
under fluid flow with I-DEAS program. The main objectives of the research are to
predict stress distribution and deformation of pipe tees and to investigate the effect of
fluid flowrate and gas-liquid ratio to the stress of pipe tees. The research was divided
into three parts, namely fluid flow simulation, solid structure simulation, and
sensitivity analysis. The simulation results showed a very good agreement with the
results from theoretical calculations. The highest value of stresses occurred at the
intersecting area of the tee junction. von Mises stresses at this area were 216.39 MPa
and 221.95 MPa for F tee and impact tee, respectively. These values exceeded the
yield strength of the pipe tee material, which indicated yielding of the intersecting
area. The highest displacements at the intersecting area were 0.59 mm for the F tee
and 0.68 mm for the impact tee. According to the sensitivity analysis, stresses in the
pipe tees were slightly increased with increasing fluid flowrate or decreasing gasliquid ratio.
Keywords
:
Branch Flow / Deformation / Finite Element / I-DEAS / Stress
Analysis / Pipe Tee
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บทคัดย่อ -
งานวิจยั นี้ เป็ นการวิเคราะห์ทางไฟไนต์เอลิเมนต์โดยใช้โปรแกรม I - D E A S
โดยมีวตั ถุประสงค์เพื่อหาความเค้นและการเปลี่ยนรู ปของท่อรู ปตัวทีและตัวเอฟซึ่ งเกิดจากความดัน
และการไหลของของไหลภายในตัวท่อ
นอกจากนี้ยงั ศึกษาผลกระทบของอัตราการไหลและสัดส่ วนระหว่างก๊าซและของเหลวที่มีต่อความเ
ค้นที่เกิดขึ้นในตัวท่ออีกด้วย
งานวิจยั ได้ถูกแบ่งออกเป็ น
การจาลองการไหลของของไหลในท่อ
3
ส่ วน
คือ
การจาลองโครงสร้างของตัวท่อเพื่อหาความเค้น
และการแปรผันคุณสมบัติการไหลเพื่อศึกษาการเปลี่ยนแปลงของความเค้นที่สภาวะการไหลต่างๆกั
น
หลังจากโปรแกรมทาการประมวลแล้วพบว่าผลลัพธ์ที่ได้จากโปรแกรมมีความใกล้เคียงกับค่าที่ได้จ
ากการคานวณทางทฤษฎีมาก
ค่าความเค้นสู งสุ ดเกิดขึ้นที่รอยต่อของท่อบริ เวณทางแยกของท่อรู ปตัวทีและตัวเอฟ
โดยที่บริ เวณดังกล่าวมีค่าความเค้น von Mises เท่ากับ 216.39 เมกะปาสคาล สาหรับท่อรู ปตัวเอฟ
และ 221.95
เมกะปาสคาล สาหรับท่อรู ปตัวที
นี้มีค่าสู งกว่าค่าความแข็งแรงของวัสดุ ( y i e l d
เนื่องจากค่าความเค้น v o n M i s e s
S t r e n g t h )
ที่ใช้ทาตัวท่อ
ดังนั้นจึงสามารถสรุ ปได้วา่ ท่อรู ปตัวเอฟและตัวทีมีแนวโน้มที่จะเกิดการครากหรื อการเปลี่ยนรู ปอย่
างถาวร ซึ่ งค่าการเคลื่อนตัวที่บริ เวณรอยต่อของท่อรู ปตัวเอฟและตัวทีมีค่าเท่ากับ 0.59 มิลลิเมตร
และ 0.68 มิลลิเมตร ตามลาดับ นอกจากนี้จากการแปรผันคุณสมบัติการไหลต่างๆกัน พบว่า
ค่าความเค้นของท่อมีค่าสู งขึ้นเมื่ออัตราการไหลของของไหลมีค่าเพิ่มขึ้นหรื อเมื่ออัตราส่ วนของก๊า
ซต่อของเหลวมีค่าลดลง
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คาสาคัญ (Keywords) : การไหลบริ เวณทางแยก / การเปลี่ยนรู ป / ไฟไนต์เอลิเมนต์ / โปรแกรม
I - D E A S
/
การวิเคราะห์ความเค้น / ท่อรู ปตัวที
1. INTRODUCTION
Unocal Thailand Co., Ltd. explores for and develops natural gas resources
in the Gulf of Thailand. Natural gas and condensate are transported through pipeline
circuits from many offshore fields such as Erawan, Satun, Platong, Kaphong, etc.
Inside these pipelines, there is the multiphase fluid flow consisting of natural gas,
condensate, salt water, and mud. Since the major components in the stream are natural
gas, condensate, and water, the flow therefore can be simplified as a two-phase fluid
flow (gas and liquid). The ratio of gas per liquid volumetric flowrate is defined as gas
liquid ratio, GLR.
In the production platform, the two-phase stream is sent to separators A
and B before being forwarded to downstream processes. F tee is previously used to
split the two-phase flow into these separators as shown in Fig 1.
Figure 1. Two-phase flow splitting using F tee.
Nevertheless, the GLRs. of the inlet stream between two separators are
not the same such that the GLR of separator A is less than that of separator B. This is
because the density of liquid is much more than the gas density. Therefore, the gravity
force drags the liquid into separator A before heading to separator B. This problem
affects significantly the downstream processes and the productivity of the plant.
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It was found that this problem could be solved by replacing the F tee with
impact tee as shown in Fig 2. By this way, the GLR in both separators is almost the
same and the productivity is increased because the two-phase flow can be passed to
each separator at the same amount [1]. However all liquid and gas would directly
strike this impact tee wall and yield high stress around the impacted area. The fatigue
of the tee wall is generated and may lead to the cracking propagation of the tee.
Figure 2. Two-phase flow splitting using impact tee.
This research therefore focuses on the stress and deformation analysis of
F tee and impact tee due to the flow of fluid stream. Moreover, the research also
investigates the effect of inlet GLR and fluid flowrate on the stress and deformation of
the tee.
There are few studies concerned with the stress and cracking phenomena
by fluid flow within the pipe. Sritham [1] studied the pressure and flow distribution of
ERAWAN pipeline circuit. PIPESIM was used to formulate the two-phase flow
model in pipeline. Then, CFD technique with PHOENICS program was utilized to
establish the pipe tee model. The result shows the flow and pressure profile of fluid in
the pipe, which indicates that for splitting of two-phase flow, the impact tee is better
than the F tee.
Thampanitchawong,[2] studied the corrosion phenomena in pipeline
system with multiphase flow simulation model. Corrosion model was constructed and
PHOENICS was used to simulate and display the flow pattern within the pipe.
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Mochizuki, et al.,[3] analyzed the residual stress in the pipe welded joints
using finite element method. The pipe joint had an X-shaped groove and the sequences of
welding passes were changed. The optimum welding sequence was determined from the residual stress
distribution.
2. GOVERNING EQUATIONS FOR FLOW SIMULATION
In this research, the study of fluid and solid part was performed in 3
dimensions with the powerful software named I-DEAS software (Master Series 7) [4].
The time-averaged Navier-Stokes equations, for mass, momentum and energy are
respectively as ;
 U j 
x
 0
(2.1)
j
U i   U j U i 
P


 

t
x j
x i x j

 eff

 U j H 
H 



t
x j
x j

eff

 U i U j


 x
x i
j

 H

 x
 j

  S Ui



  S H


(2.2)
(2.3)
This equation system is for the Reynolds stress model of an
incompressible, Newtonian fluid with the eddy viscosity. The effective viscosity and
effective coefficient of diffusion for energy part are given by:
 eff
   t
(2.4)
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eff

t


Pr
Pr t
(2.5)
The turbulence viscosity for the fixed viscosity and k- two-equation
model are; respectively,
 t  0 . 01 V m L t
(2.6)
k2
 C 

(2.7)
t
These last two quantities are computed from their own differential
equations. For turbulent flow at solid walls, logarithmic wall functions are used to set
wall shear stress, heat transfer and boundary conditions for k and .
3. OPERATING CONDITION AND GEOMETRY DESCRIPTION
This research used the data of natural gas production processing from
Unocal Thailand Co., Ltd. and some information provided by Sritham [1]. All
physical properties and operating conditions in this work are concluded in Table 1.
Table 1. Physical properties and operating conditions of fluid within the pipe tees.
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The dimension of pipe tees and material properties are shown in Table 2
and Figure 3.
Table 2. Dimensions and material properties of F tee and impact tee .
Figure 3. Dimensions of F tee and impact tee.
4. FINITE ELEMENT MODELS
4.1 Flow Model
The fluid model without the participation of solid structure (tee wall) was
created firstly. The fluid geometry (Fig 3.) was then defined in the program so that its
diameter was equal to the inner diameter of pipe tee. After that, the fluid density and
viscosity were introduced to the model. In order to define the inlet and outlet, thin
shell elements must be created at that positions as shown in Fig 4. In addition, the
element was also generated on the tee surface for containing surface properties and
roughness of the tee. The element was planar triangle with the length of 0.08 m and
zero thickness.
Figure 4. Thin shell elements at inlet and outlet of the pipe tees.
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After creating the thin shell elements, tetrahedral solid elements were then
generated on the fluid volume. The elements were linear tetrahedral with the length of
0.08 m as shown in Fig 5. Finally, the operating conditions and surface roughness of
pipe tees were introduce to the program.
Figure 5. Tetrahedral solid elements on the fluid volume within the pipe tees.
4.2 Solid Model
In this research, solid model means the F tee and the impact tee The
pressure of fluid contacting the tee wall from the fluid flow simulation performed as a
load set to the solid model. This pressure was converted to the force acting on the tee
wall which induced the stress and deformation of the tee structure. The stress results
were then compared to the yield strength of the pipe tee material to investigate the
material yielded.
Since the program limits the data transferring only on the same geometry.
Therefore, the shape and size of the solid model must be identity to the fluid model.
Hence the model geometry in Fig 3 was adopted and defined with the new finite
element conditions including material properties, boundary conditions and load set.
Properties of pipe tee material, including Poisson’s Ratio, density and Modulus of
elasticity, were entered into the program. The isotropic material, which had the same
mechanical properties in all directions, was assumed.
For this study, the rectangular thin shell element was suitable because of the
excellent results compared to thin wall theory. However, the rectangular elements had
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the limitation of meshing at the junction area of the pipe tees. Some elements had the
abnormal shape called distorted and stretched elements; as shown in Fig 6, which may
affect the simulation results. Therefore, the junction area was meshed with triangular
thin-shell elements with element size of 0.04 m and thickness of 0.0127 m while the
other areas were meshed with 0.08 m rectangular elements as shown in Fig 7.
Figure 6. Distorted and stretched elements at the junction of the pipe tees.
Figure 7. Rectangular and triangular thin-shell elements on the pipe tees.
The pipe tees were restrained at three ends by six degree of freedom (3
translations and 3 rotations) whereas the area around three ends of pipe tees cannot
move indepently to any directions.
After applying boundary conditions, the pressure result from fluid model
was then transferred into the solid geometry. The graphical representation of the
pressure result; called “Data Surface”, shows how data variations occur over a surface
or a given domain. The program deforms the data surface at any location by an
amount proportional to the data value at that point, as shown in Fig 8.
In addition, we have to define the direction of pressure acting on the tee
wall by entering –1 into the pressure dialog box. By this way, the values of pressure
from the data surface were multiplied by 1 while the minus sign indicates that the
pressure was acting from internal of the pipe tee.
Figure 8.
a. The result of internal pressure from the flow model.
b. Graphical representation of data surface on the solid model.
4.3 Sensitivity Analysis
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The final step of this study is to determine the effect of flow properties on
the stress and deformation of F tee and impact tee. The fluid flowrate and gas-liquid
ratio were varied for observing their effects on the stress and deformation of pipe tee.
Since the GLR in the real operation was about 3.5, therefore, the GLR in the first case
was kept constant at 3.597. The second case was to vary the GLR at 33.57 kg/s. of gas
flow rate. The input data for the first case and the second case is shown in Tables 3
and 4, respectively [1].
Table 3.
Input data and flow property in the case of varying fluid flowrate.
Table 4.
Input data and flow property in the case of varying GLR.
5. RESULTS AND DISCUSSIONS
5.1 Flow Model
I-DEAS program reported and displayed velocity profile and totalpressure distribution of pipe tee system. The velocity profiles of fluid within F tee and
impact tee at element size of 0.08 m are shown in Figures 9 and 10, respectively. It
was noticed that the highest velocity appeared around the inlet area and rapidly
decreased after passed the tee junction. The inlet velocities of the F tee and the impact
tee were 4.5463 m/s and 4.5576 m/s, respectively. The outlet velocities were nearly
the same for the impact tee (2.2508 and 2.2591 m/s) and quite different for the F tee
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(0.8775 and 3.5813 m/s). This means that the impact tee can split the flow into two
equal streams which agrees with the previous work [1].
Figure 9. Velocity profile of 1-phase fluid flow within the F tee.
Figure 10. Velocity profile of 1-phase fluid flow within the impact tee.
The pressure is displayed as the gauge pressure with the unit of Pa.
Figures 11 and 12 present the total pressure of F tee and impact tee, respectively.
From these figures, the program gave the inlet pressure of the F tee and the impact tee
equal to 3.4184 MPa. In addition to the inlet section of the pipe tees, the elbow of the
F tee and the tee wall of the impact tee were also subjected to high internal pressure.
The high pressure at these areas occurred from the impacting of fluid. However, the
magnitude of pressure throughout the pipe tees was quite constant and was close to
the outlet pressure specified by the company. Therefore, the pressure of the fluid flow
or the dynamic pressure was very low compared to the internal operating pressure of
the company.
Figure 11. Distribution of the internal pressure (Pa) within the F tee.
Figure 12. Distribution of internal pressure (Pa) within the impact tee.
5.2 Solid Model
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5.2.1 Stress Distribution
There are 2 important stresses related to this study, namely, maximum
shear stress and von Mises stress. The highest values of maximum shear stress and
von Mises stress of the pipe tees, as shown in Figures 13 and 14, respectively,
occurred at the intersecting area. This is due to the fact that abrupt changes in
geometry of a component give rise to stress concentration. In contrast, the stress
values at other areas, such as inlet and outlet, were very small compared with the
maximum stress at the intersecting area. From the yield criteria, the maximum shear
stress must be compared with the half value of yield strength. It states that yielding
will occur when the maximum shear stress exceeds the half value of yield strength or
the von Mises stress reaches the yield strength of the material. The results of
maximum shear stress and von Mises stress at various locations of pipe tees are
shown in Table 5.
Figure 13. Maximum Shear Stress (Pa) of the pipe tees.
Figure 14. von Mises Stress (Pa) of the pipe tees.
Table 5. Simulation results of maximum shear stress and von Mises stress at various
locations.
From Table 5, the stresses at elbow of the F tee and tee wall of the impact
tee were very low compared with the intersecting area at the junction of pipe tees.
Moreover, the value of these stresses was much lower than the yield strength of the
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pipe tee material. This can conclude that the acting force from fluid flow did not cause
any serious problem to the pipe tee.
However, the maximum shear stress of both tees exceeded the half value
of yield strength of the material (120 MPa). In addition, the von Mises stresses also
exceeded the yield strength of the material (240 MPa). Therefore, it is concluded that
although the pipe tees might not collapse since the von Mises stress was lower than
the ultimate strength (415 MPa), but they were deemed to had yielded.
5.2.2 Deformation of the Pipe Tees
The displacement result as shown in Fig. 15 indicates the magnitude of
deformation of the pipe tees. The maximum displacement was 0.59 mm for the F tee
and 0.68 mm for the impact tee, which was located at the junction of the pipe tees. For
the area of interest, the displacement values for the elbow of F tee as well as the tee
wall of impact tee were only about 0.15 mm and 0.17 mm, respectively. There was no
displacement in any other area such as inlet and outlet area of the pipe tees.
Figure 15. Displacement results (m) of the F tee and the impact tee.
5.3 Simulation Results for Sensitivity Analysis
There are 2 cases of sensitivity analysis, varying fluid flowrate and
varying gas-liquid ratio (GLR). The results are shown in Tables 6 and 7, respectively.
Since the von Mises stresses of elbow and tee wall are quite constant in all cases, the
von Mises stresses only at the tee junction are plotted as shown in Figures 16 and 17.
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Table 6. von Mises stress (MPa) at various fluid flowrate with constant GLR .
Table 7. von Mises stress (MPa) at various GLR with constant gas flowrate .
The von Mises stress of F tee and impact in Figure 16 was increased after
increasing the fluid flowrate. When the flowrate increases the velocity and pressure of
fluid will also increase which result in increasing of stresses in the pipe tees. In
contrast, after increasing GLR in the second case, the stress in the pipe tees was
slightly decreased. This is due to the fact that when the GLR increases, the liquid
flowrate is reduced, which result in decreasing of fluid density, pressure, and stresses
in the pipe tees. However, for both cases of varying flowrate and GLR, the von Mises
stress was slightly changed. Therefore, we may conclude that the flow properties,
such as fluid flowrate and GLR, did not significantly affect the stresses of the pipe
tees.
Figure 16. von Mises stress at various fluid flowrate with constant GLR.
Figure 17. von Mises stress at various GLR with constant gas flowrate.
6. CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
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The study was divided into 3 parts; fluid flow simulation, solid structure
simulation, and sensitivity analysis. For all of them, the I-DEAS software is employed
and produced the following conclusions.
6.1.1
The flow models were meshed with triangular thin-shell element
and tetrahedral solid element with element size of 0.08 m. The F tee model contained
7661 elements whereas the impact tee model contained 7660 elements. The model
gave acceptable results compared to the results from branch flow calculation. The
maximum error was about 13% for the F tee and 1% for the impact tee.
6.1.2
The pressure result from the flow model simulation was
transferred as a load set into the solid model. The junction of pipe tees was meshed
with 0.04 m triangular thin shell element while the other areas were meshed with 0.08
m rectangular thin shell element. There were 4687 nodes and 1972 elements for the F
tee as well as 4790 nodes and 1980 elements for the impact tee. The simulation
showed a very good agreement with the thin-wall theory. Comparison between
simulation and calculated results gave maximum error of 3.1% for the F tee and 5.7%
for the impact tee.
6.1.3
The highest stress occurred at the intersecting area around the
junction of the pipe tees. The von Mises stress at this area was as high as 287.78 MPa
and 287.41 MPa for F tee and impact tee, respectively. This is due to the fact that the
maximum stress always occurs at the area of geometric changes such as hole and
intersection. However, the stress at the elbow and tee wall was still very low
compared with the maximum stress and was about 20 – 30% of the yield strength.
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6.1.4
Although the pipe tees might not collapse, they were deemed to
have yielded since the von Mises stress exceeded the yield strength of the material.
The safety factor for F tee and impact tee was 0.83 and 0.84 based on von Mises
criterion.
6.1.5
The maximum displacement occurred at the junction of the pipe
tees which was 0.59 mm for F tee and 0.68 mm for impact tee. The displacement at
elbow of the F tee and tee wall of the impact tee was 0.15 and 0.17 mm, respectively.
6.1.6
From the sensitivity analysis, the flow properties, such as GLR
and fluid flowrate, did not significantly affect the stresses of the pipe tees. This may
be the effect of internal operating pressure which was very high and dominated the
dynamic pressure generated by fluid flow.
6.2 Recommendations
6.2.1
From the simulation results, the flow properties did not
significantly affect the stresses of the pipe tees. Furthermore, the stress distributions
of the F tee and the impact tee were nearly the same. Therefore, the company can use
impact tee instead of F tee to eliminate the flow splitting problem.
6.2.2
The way to reduce the stress concentration at the tee junction is
to apply fillet to the intersecting area. Assume that the company uses standard pipe tee
with the radius of 11 cm as shown in Figure 18, the von Mises stress will be reduced
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to only 178.46 MPa. This stress value is lower than the yield strength of the material
and results in a safety factor of 1.35.
Figure 18. von Mises stress (Pa) for the impact tee with fillet radius of 0.11cm.
6.2.3
Since the I-DEAS software can handle only 1-phase fluid flow,
therefore, the model may be improved by using other programs which are more
powerful in CFD aspect. This way the model will include the effect of 2-phase fluid
flow and provide more accurate results.
6.2.4
Experiments should be conducted in order to evaluate the
simulation results. The experiment may be conducted by installing a strain gauge
around the tee junction. This can also help the company to steadily inspect the
condition of pipe tees.
7. ACKNOWLEDGEMENT
Special thanks go to UNOCAL Thailand, Ltd. and Khun Mala Sirilumpen,
an associate production engineer, for experimental data and opportunity to do this
work.
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REFERENCES
1.
Sritham, S., 1999, Simulation of Pressure Distribution of ERAWAN Pipeline
Circuit, Master of Engineering Thesis, Department of Chemical Engineering,
King Mongkut’s University of Technology Thonburi, 94 p.
2.
Thampanitchawong, P., 1999, Study of Corrosion Phenomena in Pipeline System
with Multiphase Flow Simulation Model, Center of Process Control and
Operation, Chemical Engineering Department, Kasetsart University.
3.
Mochizuki, M., Hayachi, M. and Hattori, T., 2000, “Residual Stress Distribution
Depending on Welding Sequence in Multi-Pass Welded Joint with X-Shaped
Groove”, Journal of Pressure Vessel Technology, Vol. 122, February 2000, pp.
27 – 32.
4.
I-DEAS User’s Guide, Simulation: Electronic System Cooling.
20
NOMENCLATURE
C
=
Model constant [dimensionless]
H
=
Static enthalpy
k
=
Turbulent kinetic energy
Lt
=
Turbulent eddy length scale [m]
P
=
Pressure
Pr
=
Molecular Prandtl number
Prt
=
Turbulence model constant
SU and SH
=
Source terms for momentum and energy
Ui
=
the Cartesian components of the mean velocity
Vm
=
Mean flow velocity scale [m/s]
i, j
=
1, 2, 3 is the Einstein summation convention
H
=
Energy term
m
=
Mean flow scale
t
=
Turbulent
Subscript
21
u
=
Momentum term

=
Dissipation of turbulent kinetic energy
t
=
Turbulence viscosity [kg/m-s]
Greek Letters
22
LIST OF FIGURES
Figure 1.
Two-phase flow splitting using F tee
Figure 2.
Two-phase flow splitting using impact tee
Figure 3.
Dimensions of F tee and impact tee
Figure 4.
Thin shell elements at inlet and outlet of the pipe tees
Figure 5.
Tetrahedral solid elements on the fluid volume within the pipe tees
Figure 6.
Distorted and stretched elements at the junction of the pipe tees
Figure 7.
Rectangular and triangular thin-shell elements on the pipe tees
Figure 8.
a. The result of internal pressure from the flow model
b. Graphical representation of data surface on the solid model
Figure 9.
Velocity profile of 1-phase fluid flow within the F tee
Figure 10.
Velocity profile of 1-phase fluid flow within the impact tee
Figure 11.
Distribution of the internal pressure (Pa) within the F tee
Figure 12.
Distribution of internal pressure (Pa) within the impact tee
Figure 13.
Maximum Shear Stress (Pa) of the pipe tees
Figure 14.
von Mises Stress (Pa) of the pipe tees
Figure 15.
Displacement results (m) of the F tee and the impact tee
Figure 16.
von Mises stress at various fluid flowrate with constant GLR
Figure 17.
von Mises stress at various GLR with constant gas flowrate
Figure 18.
von Mises stress (Pa) for the impact tee with fillet radius of 0.11cm
23
LIST OF TABLES
Table 1. Physical properties and operating conditions of fluid within the pipe tees.
Table 2. Dimensions and material properties of F tee and impact tee
Table 3.
Input data and flow property in the case of varying fluid flowrate
Table 4.
Input data and flow property in the case of varying GLR
Table 5. Simulation results of maximum shear stress and von Mises stress at
various locations
Table 6. von Mises stress (MPa) at various fluid flowrate with constant GLR
Table 7. von Mises stress (MPa) at various GLR with constant gas flowrate
24
Gas
Gas
Liquid
Liquid
Separator A
Separator B
Figure 1. Two-phase flow splitting using F tee
Separator A
Separator B
Figure 2. Two-phase flow splitting using impact tee
25
1.5 m
R = 0.6858 m
1.2985 m
2.2 m
4m
Figure 3. Dimensions of F tee and impact tee
26
Figure 4. Thin shell elements at inlet and outlet of the pipe tees
Figure 5. Tetrahedral solid elements on the fluid volume within the pipe tees
27
Figure 6. Distorted and stretched elements at the junction of the pipe tees
Figure 7. Rectangular and triangular thin-shell elements on the pipe tees
28
a.
Figure 8.
b.
a. The result of internal pressure from the flow model
b. Graphical representation of data surface on the solid model
Figure 9. Velocity profile of 1-phase fluid flow within the F tee
29
Figure 10. Velocity profile of 1-phase fluid flow within the impact tee
Figure 11. Distribution of the internal pressure (Pa) within the F tee
30
Figure 12. Distribution of internal pressure (Pa) within the impact tee
Figure 13. Maximum Shear Stress (Pa) of the pipe tees
31
Figure 14. von Mises Stress (Pa) of the pipe tees
Figure 15. Displacement results (m) of the F tee and the impact tee
von Mises Stress (MPa)aa
32
287.9
287.8
287.7
287.6
287.5
287.4
287.3
21.45
42.91
51.49
Fluid Mass Flow (kg/s)
F Tee
Impact Tee
von Mises Stress (MPa) a
Figure 16. von Mises stress at various fluid flowrate with constant GLR
287.9
287.8
287.7
287.6
287.5
287.4
287.3
1.439
3.597
7.194
Gas-Liquid Ratio
F Tee
Impact Tee
Figure 17. von Mises stress at various GLR with constant gas flowrate
33
Figure 18. von Mises stress (Pa) for the impact tee with fillet radius of 0.11cm
34
Table 1. Physical properties and operating conditions of fluid within the pipe tees.
Property and operating condition
Outlet pressure of the pipe tees (Pa)
Value
3417666
25
Temperature (C)
Fluid density (kg/m3)
53.8171
Fluid viscosity (kg/m-s)
0.000298
Fluid velocity (m/s)
Table 2.
Table 3.
4.547
Dimensions and material properties of F tee and impact tee
Dimension & Property
Value
Inner Diameter
0.4 m
Pipe Thickness
0.0127 m
Surface Roughness
0.0000127 m
Tensile Strength
415 - 585 MPa
Yield Strength
240 MPa
Poisson's Ratio
0.27 - 0.3
Modulus of Elasticity
208109 Pa
Density
7850 kg/m3
Input data and flow property in the case of varying fluid flowrate
Mass Flow (kg/s)
Fluid Property
GLR
Density
Viscosity
Velocity
(kg/m3)
(kg/m-s)
(m/s)
3.597
55.6565
0.000182
3.067
9.33
3.597
52.2629
0.000255
6.529
11.20
3.597
48.5751
0.000279
8.438
Gas
Liquid
16.79
4.67
33.57
40.29
35
Table 4.
Input data and flow property in the case of varying GLR
Mass Flow (kg/s)
Gas
Fluid Property
Liquid
GLR
Density
Viscosity
Velocity
(kg/m3)
(kg/m-s)
(m/s)
33.57
23.34
1.439
60.1415
0.000653
7.528
33.57
9.33
3.597
52.2629
0.000255
6.529
33.57
4.67
7.194
48.4016
0.000130
6.285
Table 5. Simulation results of maximum shear stress and von Mises stress at various
locations
Stress Value (MPa)
Location
F tee
Impact tee
Max. Shear
von Mises
Intersecting Area
148.23
287.78
Elbow
24.78
42.91
Intersecting Area
145.77
287.41
Tee wall
37.37
67.25
Table 6. von Mises stress (MPa) at various fluid flowrate with constant GLR
Mass Flow (kg/s)
Gas
Liquid
16.79
4.67
33.57
40.29
GLR
F Tee
Impact Tee
Junction
Elbow
Junction
Tee Wall
3.597
287.78
26.016
287.39
74.291
9.33
3.597
287.80
26.015
287.45
74.306
11.20
3.597
287.81
26.016
287.50
74.317
Table 7. von Mises stress (MPa) at various GLR with constant gas flowrate
Mass Flow (kg/s)
Gas
Liquid
33.57
23.34
33.57
33.57
GLR
F Tee
Impact Tee
Junction
Elbow
Junction
Tee Wall
1.439
287.82
26.016
287.50
74.316
9.33
3.597
287.80
26.015
287.45
74.306
4.67
7.194
287.79
26.015
287.44
74.304
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