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ScienceDirect
Available online at www.sciencedirect.com
Procedia Manufacturing 35 (2019) 1330–1336
2351-9789 © 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
10.1016/j.promfg.2019.05.021
10.1016/j.promfg.2019.05.021 2351-9789
© 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
Available online at www.sciencedirect.com
ScienceDirect
Procedia Manufacturing 00 (2019) 000–000
www.elsevier.com/locate/procedia
2351-9789 © 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
*Corresponding Author
Email: smithsalifu@gmail.com
2nd International Conference on Sustainable Materials Processing and Manufacturing
(SMPM 2019)
Thermo-Mechanical Stress Simulation of Unconstrained Region of
Straight X20 Steam Pipe
Salifu S.Aa*, Desai D.Aa, Kok Sb, Ogunbiyi O.Fa
aDepartment of Mechanical Engineering, Mechatronics and Industrial Design, Tshwane University of Technology, Pretoria South Africa
bDepartment of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
Abstract
The thermo-mechanical stress, strain and temperature distribution across the thickness of X20 steam pipe at region less susceptible
to thermo-mechanical failure was simulated using finite element analysis software, Abaqus. The mesh convergence studies
conducted showed that 10 mm mesh size was suitable for the simulation. The temperature distribution profile across the thickness
of Pyrogel showed that pyrogel is an excellent insulation jacket for steam pipes. The maximum stress value obtained from the
simulation shows that the pipe is operating below the yield strength of X20 steel at the region under study. Hence, the pipe’s failure
at this region due to thermo-mechanical stress or strain only is practically impossible over a long period of time. A deviation of
0.5% was found to exist between the analytical and simulated stress value obtained. This indicates a strong correlation between the
simulated and analytical stress results.
© 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
Keywords: Abaqus, failure, pyrogel, simulation, thermo-mechanical stress
1. Introduction
Steam pipes are very important component of the power generation plant. They are used for transport steam from
the boiler to the turbines. Their role in the efficient performance of any power plant cannot be over emphasised. Like
every other heat transferring components, steam pipes are affected by thermal stresses and deformations that are
developed due to temperature distribution, heat accumulation or dissipation and other thermal related quantities while
in operation [1]. In spite of these, the increasing demand for energy has forced the power generation companies to
increase the operating parameters of their plants such as the temperature and pressure [2]. The operating cycle of the
steam pipe typically consist of a start-up phase followed by continuous high temperature operation under sustained
load in the form of pressure and eventually shutdown [3]. This sequence of operations lead to an increase in the
Available online at www.sciencedirect.com
ScienceDirect
Procedia Manufacturing 00 (2019) 000–000
www.elsevier.com/locate/procedia
2351-9789 © 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
*Corresponding Author
Email: smithsalifu@gmail.com
2nd International Conference on Sustainable Materials Processing and Manufacturing
(SMPM 2019)
Thermo-Mechanical Stress Simulation of Unconstrained Region of
Straight X20 Steam Pipe
Salifu S.Aa*, Desai D.Aa, Kok Sb, Ogunbiyi O.Fa
aDepartment of Mechanical Engineering, Mechatronics and Industrial Design, Tshwane University of Technology, Pretoria South Africa
bDepartment of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
Abstract
The thermo-mechanical stress, strain and temperature distribution across the thickness of X20 steam pipe at region less susceptible
to thermo-mechanical failure was simulated using finite element analysis software, Abaqus. The mesh convergence studies
conducted showed that 10 mm mesh size was suitable for the simulation. The temperature distribution profile across the thickness
of Pyrogel showed that pyrogel is an excellent insulation jacket for steam pipes. The maximum stress value obtained from the
simulation shows that the pipe is operating below the yield strength of X20 steel at the region under study. Hence, the pipe’s failure
at this region due to thermo-mechanical stress or strain only is practically impossible over a long period of time. A deviation of
0.5% was found to exist between the analytical and simulated stress value obtained. This indicates a strong correlation between the
simulated and analytical stress results.
© 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
Keywords: Abaqus, failure, pyrogel, simulation, thermo-mechanical stress
1. Introduction
Steam pipes are very important component of the power generation plant. They are used for transport steam from
the boiler to the turbines. Their role in the efficient performance of any power plant cannot be over emphasised. Like
every other heat transferring components, steam pipes are affected by thermal stresses and deformations that are
developed due to temperature distribution, heat accumulation or dissipation and other thermal related quantities while
in operation [1]. In spite of these, the increasing demand for energy has forced the power generation companies to
increase the operating parameters of their plants such as the temperature and pressure [2]. The operating cycle of the
steam pipe typically consist of a start-up phase followed by continuous high temperature operation under sustained
load in the form of pressure and eventually shutdown [3]. This sequence of operations lead to an increase in the
Available online at www.sciencedirect.com
ScienceDirect
Procedia Manufacturing 00 (2019) 000–000
www.elsevier.com/locate/procedia
2351-9789 © 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
*Corresponding Author
Email: smithsalifu@gmail.com
2nd International Conference on Sustainable Materials Processing and Manufacturing
(SMPM 2019)
Thermo-Mechanical Stress Simulation of Unconstrained Region of
Straight X20 Steam Pipe
Salifu S.Aa*, Desai D.Aa, Kok Sb, Ogunbiyi O.Fa
aDepartment of Mechanical Engineering, Mechatronics and Industrial Design, Tshwane University of Technology, Pretoria South Africa
bDepartment of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
Abstract
The thermo-mechanical stress, strain and temperature distribution across the thickness of X20 steam pipe at region less susceptible
to thermo-mechanical failure was simulated using finite element analysis software, Abaqus. The mesh convergence studies
conducted showed that 10 mm mesh size was suitable for the simulation. The temperature distribution profile across the thickness
of Pyrogel showed that pyrogel is an excellent insulation jacket for steam pipes. The maximum stress value obtained from the
simulation shows that the pipe is operating below the yield strength of X20 steel at the region under study. Hence, the pipe’s failure
at this region due to thermo-mechanical stress or strain only is practically impossible over a long period of time. A deviation of
0.5% was found to exist between the analytical and simulated stress value obtained. This indicates a strong correlation between the
simulated and analytical stress results.
© 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
Keywords: Abaqus, failure, pyrogel, simulation, thermo-mechanical stress
1. Introduction
Steam pipes are very important component of the power generation plant. They are used for transport steam from
the boiler to the turbines. Their role in the efficient performance of any power plant cannot be over emphasised. Like
every other heat transferring components, steam pipes are affected by thermal stresses and deformations that are
developed due to temperature distribution, heat accumulation or dissipation and other thermal related quantities while
in operation [1]. In spite of these, the increasing demand for energy has forced the power generation companies to
increase the operating parameters of their plants such as the temperature and pressure [2]. The operating cycle of the
steam pipe typically consist of a start-up phase followed by continuous high temperature operation under sustained
load in the form of pressure and eventually shutdown [3]. This sequence of operations lead to an increase in the
2 Author name / Procedia Manufacturing 00 (2016) 000–000
development of thermo-mechanical stresses and strains in the pipe. In order to withstand the harsh operating condition
of the steam resulting from its temperature and flowing pressure, martensitic stainless steel (X20 steel pipes) with
excellent creep resistant and thermal properties is used for transporting steam from the boiler to the turbine. Little or
no attention is paid to the steam pipes that are far away from the constrained region (boiler outlet and the turbine inlet).
Hence, the unannounced failure of the pipes at this region (unconstrained) with less attention becomes inevitable.
The aim of this paper is to numerically simulate the thermo-mechanical stress and strain developed in a straight
X20 steam pipe under operation at the unconstrained region. The material properties alongside operational condition
that depicts the real case scenario was implemented in the finite element analysis (FEA) software, Abaqus and the
steam pipe was also properly insulated with the aid of pyrogel insulation jacket.
2. Thermal Stress Distribution
The relation between the thermal stresses and strains follows the thermoelasticity formulae given below [4].
(1)
(2)
(3)
where, T represents the rise in temperature at radius r above the initial value.
(4)
Substituting Eqs (1) and (2) into Eq (4), the below equation is obtained
(5)
Solving the above equation with boundary condidtion = zero at the inside and outside surfaces,
, [5, 6] gives
(6)
(7)
(8)
The effective stress is the calculated using von-Mises theory
(9)
2.1. Mechanical Stress
In a thick walled pressured pipe, three principal stresses namely hoop stress, radial stress and longitudinal
stress are generated by internal pressure. Longitudinal stress occurs due to the thrust of pressure on the heads of
the cylinders or pipes. The value of the hoop stress and radial stress varies throughout the cylinder whereas, the
longitudinal stress is constant throughout [7].
S.A. Salifu et al. / Procedia Manufacturing 35 (2019) 1330–1336 1331
Available online at www.sciencedirect.com
ScienceDirect
Procedia Manufacturing 00 (2019) 000–000
www.elsevier.com/locate/procedia
2351-9789 © 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
*Corresponding Author
Email: smithsalifu@gmail.com
2nd International Conference on Sustainable Materials Processing and Manufacturing
(SMPM 2019)
Thermo-Mechanical Stress Simulation of Unconstrained Region of
Straight X20 Steam Pipe
Salifu S.Aa*, Desai D.Aa, Kok Sb, Ogunbiyi O.Fa
aDepartment of Mechanical Engineering, Mechatronics and Industrial Design, Tshwane University of Technology, Pretoria South Africa
bDepartment of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
Abstract
The thermo-mechanical stress, strain and temperature distribution across the thickness of X20 steam pipe at region less susceptible
to thermo-mechanical failure was simulated using finite element analysis software, Abaqus. The mesh convergence studies
conducted showed that 10 mm mesh size was suitable for the simulation. The temperature distribution profile across the thickness
of Pyrogel showed that pyrogel is an excellent insulation jacket for steam pipes. The maximum stress value obtained from the
simulation shows that the pipe is operating below the yield strength of X20 steel at the region under study. Hence, the pipe’s failure
at this region due to thermo-mechanical stress or strain only is practically impossible over a long period of time. A deviation of
0.5% was found to exist between the analytical and simulated stress value obtained. This indicates a strong correlation between the
simulated and analytical stress results.
© 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
Keywords: Abaqus, failure, pyrogel, simulation, thermo-mechanical stress
1. Introduction
Steam pipes are very important component of the power generation plant. They are used for transport steam from
the boiler to the turbines. Their role in the efficient performance of any power plant cannot be over emphasised. Like
every other heat transferring components, steam pipes are affected by thermal stresses and deformations that are
developed due to temperature distribution, heat accumulation or dissipation and other thermal related quantities while
in operation [1]. In spite of these, the increasing demand for energy has forced the power generation companies to
increase the operating parameters of their plants such as the temperature and pressure [2]. The operating cycle of the
steam pipe typically consist of a start-up phase followed by continuous high temperature operation under sustained
load in the form of pressure and eventually shutdown [3]. This sequence of operations lead to an increase in the
Available online at www.sciencedirect.com
ScienceDirect
Procedia Manufacturing 00 (2019) 000–000
www.elsevier.com/locate/procedia
2351-9789 © 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
*Corresponding Author
Email: smithsalifu@gmail.com
2nd International Conference on Sustainable Materials Processing and Manufacturing
(SMPM 2019)
Thermo-Mechanical Stress Simulation of Unconstrained Region of
Straight X20 Steam Pipe
Salifu S.Aa*, Desai D.Aa, Kok Sb, Ogunbiyi O.Fa
aDepartment of Mechanical Engineering, Mechatronics and Industrial Design, Tshwane University of Technology, Pretoria South Africa
bDepartment of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
Abstract
The thermo-mechanical stress, strain and temperature distribution across the thickness of X20 steam pipe at region less susceptible
to thermo-mechanical failure was simulated using finite element analysis software, Abaqus. The mesh convergence studies
conducted showed that 10 mm mesh size was suitable for the simulation. The temperature distribution profile across the thickness
of Pyrogel showed that pyrogel is an excellent insulation jacket for steam pipes. The maximum stress value obtained from the
simulation shows that the pipe is operating below the yield strength of X20 steel at the region under study. Hence, the pipe’s failure
at this region due to thermo-mechanical stress or strain only is practically impossible over a long period of time. A deviation of
0.5% was found to exist between the analytical and simulated stress value obtained. This indicates a strong correlation between the
simulated and analytical stress results.
© 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
Keywords: Abaqus, failure, pyrogel, simulation, thermo-mechanical stress
1. Introduction
Steam pipes are very important component of the power generation plant. They are used for transport steam from
the boiler to the turbines. Their role in the efficient performance of any power plant cannot be over emphasised. Like
every other heat transferring components, steam pipes are affected by thermal stresses and deformations that are
developed due to temperature distribution, heat accumulation or dissipation and other thermal related quantities while
in operation [1]. In spite of these, the increasing demand for energy has forced the power generation companies to
increase the operating parameters of their plants such as the temperature and pressure [2]. The operating cycle of the
steam pipe typically consist of a start-up phase followed by continuous high temperature operation under sustained
load in the form of pressure and eventually shutdown [3]. This sequence of operations lead to an increase in the
Available online at www.sciencedirect.com
ScienceDirect
Procedia Manufacturing 00 (2019) 000–000
www.elsevier.com/locate/procedia
2351-9789 © 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
*Corresponding Author
Email: smithsalifu@gmail.com
2nd International Conference on Sustainable Materials Processing and Manufacturing
(SMPM 2019)
Thermo-Mechanical Stress Simulation of Unconstrained Region of
Straight X20 Steam Pipe
Salifu S.Aa*, Desai D.Aa, Kok Sb, Ogunbiyi O.Fa
aDepartment of Mechanical Engineering, Mechatronics and Industrial Design, Tshwane University of Technology, Pretoria South Africa
bDepartment of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
Abstract
The thermo-mechanical stress, strain and temperature distribution across the thickness of X20 steam pipe at region less susceptible
to thermo-mechanical failure was simulated using finite element analysis software, Abaqus. The mesh convergence studies
conducted showed that 10 mm mesh size was suitable for the simulation. The temperature distribution profile across the thickness
of Pyrogel showed that pyrogel is an excellent insulation jacket for steam pipes. The maximum stress value obtained from the
simulation shows that the pipe is operating below the yield strength of X20 steel at the region under study. Hence, the pipe’s failure
at this region due to thermo-mechanical stress or strain only is practically impossible over a long period of time. A deviation of
0.5% was found to exist between the analytical and simulated stress value obtained. This indicates a strong correlation between the
simulated and analytical stress results.
© 2019 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of SMPM 2019.
Keywords: Abaqus, failure, pyrogel, simulation, thermo-mechanical stress
1. Introduction
Steam pipes are very important component of the power generation plant. They are used for transport steam from
the boiler to the turbines. Their role in the efficient performance of any power plant cannot be over emphasised. Like
every other heat transferring components, steam pipes are affected by thermal stresses and deformations that are
developed due to temperature distribution, heat accumulation or dissipation and other thermal related quantities while
in operation [1]. In spite of these, the increasing demand for energy has forced the power generation companies to
increase the operating parameters of their plants such as the temperature and pressure [2]. The operating cycle of the
steam pipe typically consist of a start-up phase followed by continuous high temperature operation under sustained
load in the form of pressure and eventually shutdown [3]. This sequence of operations lead to an increase in the
2 Author name / Procedia Manufacturing 00 (2016) 000–000
development of thermo-mechanical stresses and strains in the pipe. In order to withstand the harsh operating condition
of the steam resulting from its temperature and flowing pressure, martensitic stainless steel (X20 steel pipes) with
excellent creep resistant and thermal properties is used for transporting steam from the boiler to the turbine. Little or
no attention is paid to the steam pipes that are far away from the constrained region (boiler outlet and the turbine inlet).
Hence, the unannounced failure of the pipes at this region (unconstrained) with less attention becomes inevitable.
The aim of this paper is to numerically simulate the thermo-mechanical stress and strain developed in a straight
X20 steam pipe under operation at the unconstrained region. The material properties alongside operational condition
that depicts the real case scenario was implemented in the finite element analysis (FEA) software, Abaqus and the
steam pipe was also properly insulated with the aid of pyrogel insulation jacket.
2. Thermal Stress Distribution
The relation between the thermal stresses and strains follows the thermoelasticity formulae given below [4].
(1)
(2)
(3)
where, T represents the rise in temperature at radius r above the initial value.
(4)
Substituting Eqs (1) and (2) into Eq (4), the below equation is obtained
(5)
Solving the above equation with boundary condidtion = zero at the inside and outside surfaces,
, [5, 6] gives
(6)
(7)
(8)
The effective stress is the calculated using von-Mises theory
(9)
2.1. Mechanical Stress
In a thick walled pressured pipe, three principal stresses namely hoop stress, radial stress and longitudinal
stress are generated by internal pressure. Longitudinal stress occurs due to the thrust of pressure on the heads of
the cylinders or pipes. The value of the hoop stress and radial stress varies throughout the cylinder whereas, the
longitudinal stress is constant throughout [7].
1332 S.A. Salifu et al. / Procedia Manufacturing 35 (2019) 1330–1336
Author name / Procedia Manufacturing 00 (2016) 000–000 3
For a thick walled cylinder or pipe of internal and external radii
and
respectively; and internal and external
pressure
and
respectively, the radial and circumferential stresses in the cylinder were introduced by Lamé [8].
The radial and circumferential and axial stress components of a thick walled cylinder in the generalized forms are [8]:
(10)
(11)
(12)
When only the inner pressure is assumed on the thick-walled cylinder, i.e. = 0 then, the above equation can be
developed for an external pressure or pressure gradient over the entire cylinder.
Eqs (10 - 12) reduces to Eqs (13-15) for a purely internal pressure ( .
(13)
(14)
(15)
The effective mechanical stress is the calculated using von-Mises theory
(16)
3. Material Properties
Table 1: Material properties of X20 pipe and Insulation jacket [9-11]
Material Properties
X20 Steel Pipe
Pyrogel (Insulation)
Density (Kg/m3)
7800
171
Elasticity (GPa)
200
10× 10-3
Poisson Ratio
0.28
0.2
Expansion (K-1)
10 × 10-6
4.0 × 10-6
Thermal Conductivity (W/mK)
28
6.4 × 10-6
Specific Heat Capacity (J/KgK)
460
2300
3.1. Dimensions of Pipe and Insulation Jacket
Table 2: Dimension of pipe and Insulation jacket
Description
Pipe
Insulation Jacket
Internal Diameter (m)
0.26
0.32
External Diameter (m)
0.32
0.48
Thickness (m)
0.03
0.05
4 Author name / Procedia Manufacturing 00 (2016) 000–000
Internal Diameter (m)
0.26
0.26
4. Analysis Methodology
A sequentially coupled thermo-mechanical stress analysis of the steam pipe was carried out using the FEA software,
Abaqus. The procedure involves the development of a scaled down 2D model of X20 steel pipe and pyrogel insulation
jacket as shown in Fig. (1a) and (b). The material properties and dimension of the pipe and insulator are shown in
table (1) and (2) respectively. The various material properties for both the insulation jacket and the steel pipes are
input in the material property section of Abaqus cae. The pipe and insulation jacket are section and the section are
assigned to part after which dependent instance is created between before assembling the parts as shown in Fig. (1c).
Tie interaction was created between the pipe master and the insulation slave. Also, convection surface interaction
was created both on the pipe inner and insulation outer. The operating temperature of the steam (550 OC) is the sink
temperature in the pipe and the assumed film coefficient for steam (convective heat transfer coefficient) is 10000
W/(m2K) [12]. On the insulation outer, the sink temperature is 25 OC with an assumed film coefficient of 18 W/(m2K)
[12]. Steam operating pressure of 18 MPa is applied to the inner pipe.
A 4-node linear heat transfer quadrilateral (DC2D4) heat transfer element type was used for the thermal analysis while
a 4-node bilinear plane stress quadrilateral, reduced integration hourglass control (CPSAR) element type was used for
the thermo-mechanical stress analysis. A Quad element shape, free technique and medial axis algorithm with global
seed size of 10 mm was also used for the analysis. The open office database (odb) file obtained from the result output
of the thermal analysis was imported and used as the predefined temperature in step 1 of the thermo-mechanical stress
analysis.
Fig. 1: 2D model of (a) X20 steel pipe (b) Pyrogel Insulation jacket and (c) assembly mode of Pipe and insulation.
Fig. 2: Part mesh of (a) X20 steel pipe (b) Pyrogel insulation jacket and (c) assembly mesh of pipe and insulation.
(a)
(b)
(c)
(a)
(b)
(c)
S.A. Salifu et al. / Procedia Manufacturing 35 (2019) 1330–1336 1333
Author name / Procedia Manufacturing 00 (2016) 000–000 3
For a thick walled cylinder or pipe of internal and external radii and respectively; and internal and external
pressure and respectively, the radial and circumferential stresses in the cylinder were introduced by Lamé [8].
The radial and circumferential and axial stress components of a thick walled cylinder in the generalized forms are [8]:
(10)
(11)
(12)
When only the inner pressure is assumed on the thick-walled cylinder, i.e. = 0 then, the above equation can be
developed for an external pressure or pressure gradient over the entire cylinder.
Eqs (10 - 12) reduces to Eqs (13-15) for a purely internal pressure ( .
(13)
(14)
(15)
The effective mechanical stress is the calculated using von-Mises theory
(16)
3. Material Properties
Table 1: Material properties of X20 pipe and Insulation jacket [9-11]
Material Properties
X20 Steel Pipe
Pyrogel (Insulation)
Density (Kg/m3)
7800
171
Elasticity (GPa)
200
10× 10-3
Poisson Ratio
0.28
0.2
Expansion (K-1)
10 × 10-6
4.0 × 10-6
Thermal Conductivity (W/mK)
28
6.4 × 10-6
Specific Heat Capacity (J/KgK)
460
2300
3.1. Dimensions of Pipe and Insulation Jacket
Table 2: Dimension of pipe and Insulation jacket
Description
Pipe
Insulation Jacket
Internal Diameter (m)
0.26
0.32
External Diameter (m)
0.32
0.48
Thickness (m)
0.03
0.05
4 Author name / Procedia Manufacturing 00 (2016) 000–000
Internal Diameter (m)
0.26
0.26
4. Analysis Methodology
A sequentially coupled thermo-mechanical stress analysis of the steam pipe was carried out using the FEA software,
Abaqus. The procedure involves the development of a scaled down 2D model of X20 steel pipe and pyrogel insulation
jacket as shown in Fig. (1a) and (b). The material properties and dimension of the pipe and insulator are shown in
table (1) and (2) respectively. The various material properties for both the insulation jacket and the steel pipes are
input in the material property section of Abaqus cae. The pipe and insulation jacket are section and the section are
assigned to part after which dependent instance is created between before assembling the parts as shown in Fig. (1c).
Tie interaction was created between the pipe master and the insulation slave. Also, convection surface interaction
was created both on the pipe inner and insulation outer. The operating temperature of the steam (550 OC) is the sink
temperature in the pipe and the assumed film coefficient for steam (convective heat transfer coefficient) is 10000
W/(m2K) [12]. On the insulation outer, the sink temperature is 25 OC with an assumed film coefficient of 18 W/(m2K)
[12]. Steam operating pressure of 18 MPa is applied to the inner pipe.
A 4-node linear heat transfer quadrilateral (DC2D4) heat transfer element type was used for the thermal analysis while
a 4-node bilinear plane stress quadrilateral, reduced integration hourglass control (CPSAR) element type was used for
the thermo-mechanical stress analysis. A Quad element shape, free technique and medial axis algorithm with global
seed size of 10 mm was also used for the analysis. The open office database (odb) file obtained from the result output
of the thermal analysis was imported and used as the predefined temperature in step 1 of the thermo-mechanical stress
analysis.
Fig. 1: 2D model of (a) X20 steel pipe (b) Pyrogel Insulation jacket and (c) assembly mode of Pipe and insulation.
Fig. 2: Part mesh of (a) X20 steel pipe (b) Pyrogel insulation jacket and (c) assembly mesh of pipe and insulation.
(a)
(b)
(c)
(a)
(b)
(c)
1334 S.A. Salifu et al. / Procedia Manufacturing 35 (2019) 1330–1336
Author name / Procedia Manufacturing 00 (2016) 000–000 5
5. Results and Discussion
Fig. 3: Thermo-mechanical stress profile in (a) pipe and insulation and (b) pipe only.
Fig. 4: Thermo-mechanical strain in (a) pipe and insulation and (b) pipe only.
Fig. 5: Thermo-mechanical strain profile of (a) insulation jacket only and (b) temperature profile of both pipe and insulation jacket.
Fig. 6: Temperature profile of (a) pipe only and (b) insulation jacket only.
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
S.A. Salifu et al. / Procedia Manufacturing 35 (2019) 1330–1336 1335
Author name / Procedia Manufacturing 00 (2016) 000–000 5
5. Results and Discussion
Fig. 3: Thermo-mechanical stress profile in (a) pipe and insulation and (b) pipe only.
Fig. 4: Thermo-mechanical strain in (a) pipe and insulation and (b) pipe only.
Fig. 5: Thermo-mechanical strain profile of (a) insulation jacket only and (b) temperature profile of both pipe and insulation jacket.
Fig. 6: Temperature profile of (a) pipe only and (b) insulation jacket only.
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
6 Author name / Procedia Manufacturing 00 (2016) 000–000
Fig. 7: Graph of thermo-mechanical (a) stress, (b) strain and (c) temperature across the pipe and insulation jacket.
Fig. 8: Mesh convergence graph.
The mesh convergence study in Fig. 8 shows that a global seed size of 10 mm is suitable for this analysis. The
temperature field in Fig. 5(b) and Fig. (6a) show that the maximum temperature in the pipe is 549.4 oC. The
distribution of temperature across the insulation jacket is also shown in Fig. 6(b). The temperature of outer part of the
insulation jacket is 44.6 oC. This implies that pyrogel is a poor conductor of heat and thus a good insulation material
for power generation plant. Fig. 7(b) shows how the temperature drops across the pipe-insulation jacket thickness.
Fig. 3(a) shows the thermos-mechanical stress distribution profile in the pipe-insulation assembly while the stress
distribution across the pipe alone is shown in Fig. 3(b). The maximum stress developed in X20 pipe at the region
under study is 91.71 MPa. This value is far below the yield strength of X20. Hence, the pipe is expected to operate
over a long period of time under this condition prior to failure due to thermo-mechanical stress or strain. The stress
(b)
(a)
(c)
1336 S.A. Salifu et al. / Procedia Manufacturing 35 (2019) 1330–1336
Author name / Procedia Manufacturing 00 (2016) 000–000 7
profile across the pipe thickness alone is shown in Fig. 7(a) and the strain distribution profile across the pipe-insulation
assembly, insulation jacket and pipe alone is shown in Fig. (3a), (4a) and (4b) respectively. As expected, the maximum
strain is found in the pipe inner.
5.1. Analytical Validation
Using Lame’s equations and the equations of thermal stresses developed in an unconstrained pipe above, the
calculated value of maximum stress developed in the pipe is 92.12 MPa.
Table 3: Analytical validation of simulated stress result
Simulated Stress (MPa)
Analytical Stress (MPa)
Deviation (%)
91.71
92.12
0.5
6. Conclusion
The thermo-mechanical stress simulation of power generation steam pipe (X20) was achieved through a
sequentially coupled thermo-mechanical stress analysis procedure in Abaqus cae. The temperature distribution along
the pipe-insulation jacket assembly shows that pyrogel is an effect insulation material for steam pipes. The stress and
strain developed in the pipe at the region under examination indicates that failure of pipe due to thermal stress or
thermal fatigue will not happen anytime soon since the developed stress is far below the yield strength of X20 steel.
The stress obtained is validated analytically using Lame’s equations and the thermal stress equations stated above. A
deviation of 0.5 % was observed between the simulated and calculated stress. This signifies a strong correlation
between the simulated and analytical result.
7. Acknowledgments
This work has been supported by Eskom and Tshwane University of South Africa. I will also want to appreciate
the immense contributions of every member of my research group towards the success of this work.
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