structural and statistical analysis of horizontal spherical end pressure … · 2018-05-06 ·...
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STRUCTURAL AND STATISTICAL ANALYSIS OF
HORIZONTAL SPHERICAL END PRESSURE VESSEL
Dr.T.Mothilal1, A.K.Manikandan
2, B.Aravind
3, J.Jayakumar
4, S.Arokyaraj
5S.Kaliappan
6M.D.Rajkamal
7
1 Professor, Velammal Institute of Technology, Chennai, India, [email protected]
2345 UG Students,Department of Mechanical Engineering, Velammal Institute of Technology, Chennai, India,
6Associate Professor, Department of Mechanical Engineering, Velammal Institute of Technology , Chennai-601204, India. 7Assistant Professor, Department of Mechanical Engineering, Velammal Institute of Technology, Chennai-601204, India.
Abstract— Pressure vessels are closed containers used
for handling and storing the fluids, chemicals and
gaseous things at high pressure are used in fertilizer
industries, petroleum and petro-chemical industries for
performing various operations. To improve the
withstanding capacity of the pressure vessels, in this
paper the material of the pressure vessel is changed to
Duplex2205 stainless steel. It will reduce the weight of
the pressure vessel and increase the withstanding
capacity of the pressure vessels. The significance of the
project comes to front with designing structure of the
pressure vessel for static loading and its assessment by
ANSYS. The increment in the thickness beyond a
certain value not only possesses fabrication difficulties
but also demands stronger material for the vessel
construction. To find the effect of residual stress and its
bursting pressure. The material selection was based on
the American Society of Mechanical Engineering
(ASME) codes. The theoretical result and simulation
result are compared.
Keywords—ASME codes, ANSYS, Bursting pressure.
I. INTRODUCTION
The term pressure vessel referred to those reservoirs
or containers, which are subjected to internal or
external pressures. The pressure vessels are used to
store fluids under pressure. The fluid being stored may
undergo a change of state inside the pressure vessels
as in case of steam boilers or it may combine with
other reagents as in chemical plants. Pressure vessels
find wide applications in thermal nuclear power
plants, chemical industries [1]. The inside pressure is
usually higher than the outside pressure, except for
some isolated situations. The fluid inside the vessel
may undergo a change in state as in the case of steam
boilers, or may combine with other reagents as in the
case of a chemical reactor. Pressure vessels often have
a combination of high pressures together with high
temperatures, in some cases flammable fluids or
highly radioactive materials, because of such hazards
it is imperative that the design be such that no leakage
can occur. In addition these vessels have to be
designed carefully to cope with the operating
temperature and pressure. It should be borne in mind
that the rupture of a pressure vessel has a potential to
cause extensive physical injury and property damage.
Plant safety and integrity are of fundamental concern
in pressure vessel design and these of course depend
on the adequacy of design codes. When discussing
pressure vessels we must also consider tanks. Pressure
vessels and tanks are significantly different in both
design and construction: tanks, unlike pressure
vessels, are limited to atmospheric pressure. The use
of a bi-material cylindrical body of large dimensions
ending by two half-spheres as nuclear reactor pressure
vessel (NRPV) is very common. The two structural
materials forming the NRPV wall are: (i) stainless
steel, for the inner layer of the wall acting as cladding
or reinforcement material, and (ii) low carbon steel,
for the outer layer of the wall acting as base material
[7]. Cylindrical pressure vessels are used in various
fields such as chemical and nuclear industries, rocket
motor case manufacturing and production of many
weapon systems. Evaluation of failure pressure that a
cylindrical pressure vessel can withstand is an
important consideration in the design of pressure
vessels. While prediction of failure pressure of
pressure vessels, it is also necessary to consider the
residual stresses already present in the pressure vessels
[2]. It is important, but difficult to validate the
theoretical stress formulations for complex structures,
and only few works have been reported for FGM
(Functionally graded materials) structures in open
literatures. Various efforts would have done to find the
theoretical solutions for FGM structures using FE
theory [3]. Manufacturing of High Strength Low
Alloy Steel is Capable for manufacturing pressure
vessel because of its ease of fabrication and welding
and also the properties of the materials [4, 5]. Storage
cylinders for compressed natural gas (CNG) used in
vehicles are pressure vessels that have been
traditionally produced using isotropic materials, such
as steel and Aluminium. Nevertheless, polymer
composites have recently been introduced for that
purpose [7], usually relying on the composite
manufacturing technique of filament winding (FW)
[6]. The size and geometric form of pressure vessels
vary greatly from the large cylindrical vessels used for
high-pressure gas storage to the small size used as
hydraulic units for aircraft.
A. HIGH PRESSURE VESSELS:
High Pressure vessels are used as reactors,
separators and heat exchangers. They are vessel with
an integral bottom and a removable top head, they are
generally provided with an inlet, heating and cooling
International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 13493-13501ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
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system and also an agitator system. High Pressure
vessels are used for a pressure range of 15 N/mm2 to a
maximum of 300 N/mm2. These pressure ranges are
essentially thick walled cylindrical vessels, ranging in
size from small tubes to several meters diameter.
B. CONSTRUCTION OF HIGH-PRESSURE
VESSELS:
1. A solid wall vessel is produced by forging,
boring a solid rod of metal.
2. A cylinder vessel is formed by bending a
sheet of metal and welded in the
longitudinal edges of the sheet metal.
3. Shrink fit construction in which, the vessel
is built up of two or more concentric
shells, each shell progressively shrunk
from the inside wall to outward. From
economic and fabrication considerations,
the number of shells should be limited to
two.
4. A vessel built up by wire winding around a
central cylinder. The wire is wound under
tension around a cylinder of about 6 to 10
mm thick.
5. A vessel built up by wrapping a series of
sheets of relatively thin metal tightly round
one another over a core tube, and holding
each sheet with a longitudinal weld. Rings
are inserted in the ends to hold the inner
shell round while subsequent layers are
added. The liner cylinder generally up to12
mm thick, while the subsequent layers are
up to 6 mm thick.
6. Making proper insulations on inner wall of
pressured vessel.
Fig.1 High pressure vessel
C. DESIGN OBJECTIVES:
1. Multilayer pressure vessels are suitable for
high operating pressures than solid wall
pressure vessels.
2. Significant saving in weight of material may
be made by use of a multilayer vessel in place
of a solid wall vessel.
3. Suitability of using different materials for
Liner shell and remaining layers for reducing
the cost of the construction of the vessel.
4. Theoretical stress distribution caused by
internal pressure at outside surface of the shell
and to ascertain that the stresses do not reach
yield point value during testing.
II. PROBLEM IDENTIFICATION
Normally pressure vessel faces different problems.
Some of them are noticed below: Cracking due to an
external load,this occurs as a result of abnormally high
nozzle loads that exceeded the designed nozzle load.
The root cause for the high external load is poor
design or poor functioning support system, this occurs
when the load transferred from the support system to
the nozzle. Cracking due to lack of penetration is the
lack of adequate weld filler metal deposit at the root of
the joint. The root of the nozzle joint is interface
between the nozzle wall and head of the pressure
vessel. Cracking due to chemical attacks occurs in the
inner wall of pressure vessel, due to the lack of
insulating material deposited on the inner walls of the
cylinder.
Some of the principle causes for the failure of
pressure vessel are:
Poor design
Poor maintenance of equipment
An unsafe system of work
Operator errors (improper training or
supervisions)
Poor installations
Inadequate repairs or modifications
III. DESIGN PAREMETERS
The design of solid pressure vessel includes
1. Vessel thickness
2. Hydrostatic Test Pressure
3. Bursting Pressure
A. MATERIAL
The material chosen for manufacturing the pressure
vessel is Duplex 2205 Stainless Steel. The main
reason for choosing this materialisbased on the
following properties:
High strength and toughness
Good corrosion resistance and weldability
Light weightand High magnetic strength
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Table No 1: Chemical Composition:
Table No 2: Physical properties:
Table No 3: Mechanical Properties:
IV. THEORITICAL ANALYSIS
The design of solid pressure vessel includes,
(a) Design of Vessel thickness
(b) To find Thin or Thick cylinder
(c) Calculation of Radial and Tangential stress
(d) Calculation of shear stress
(e) Calculating bursting pressure
Input Data:
Inner Diameter Di = 381mm,
Inner Radius Ri= 190.5mm
Internal Pressure P = 300N/mm2
Design of Vessel thickness:
Thickness = PDi
2SE−0.2P
= 300x381
2x1303−0.2x300
= 56.45 mm
To find Thin (or) Thick cylinder: di
t =
381
56.45 = 6.749 < 20
Therefore, it is Thick cylinder.
Outer diameter do = di + 2t
= 381+2x56.45
= 493.9 mm
Usually the internal high pressure fluid develops two
kinds of stresses namely,
Tangential stress
Radial stress.
1. Longitudinal stress calculation
ro= od
2 =
493.9
2 =246.95
r1 = 190.5
σl = -PoClo, = ro
r1 =
246.95
190.5 = 1.296
Where,
Clo= (2+1)/(
2-1)
Clo=(1.2962+1)/(1.296
2-1)= 3.942 mm
2
σl = PoCl
= 29x3.942
= 114.318 N/mm2 (compressive)
2. Radial and Tangential stress:
Inner radius (r = ri)
Clo = 1/(2-1)
= 1/(1.2962-1)
= 1.4714 mm2
σt= -PoClo
= -300x1.4714
σt = -441.42 N/mm2 (compressive)
σr (r = ri) = 0 Natural Boundary condition for
Pi= o
Outer radius (r = ro)
Ct = (2+1)/(
2-1)
= (1.2962+1)/(1.296
2-1)
= 3.9429 mm2
σt (r = ro) = -PoCti= -300x3.9429
= -1182.87 N/mm2 (compressive)
σrr = ri) = -Po (Natural Boundary condition)
= -300 N/mm2
3. Define Principal stress:
Inner Radius
σ1= σr= 0
σ2=σl=-1182.85N/mm2
σ3=σt=-441.42 N/mm2
Material Limit C Mn Si P S Cr Mo Ni N
Duplex 2205 Min - - - - - 21.0 2.5 4.5 0.08
Max 0.030 2.00 1.00 0.030 0.020 23.0 3.5 6.5 0.20
Material Density Elastic
modulus
Mean Coefficient of Thermal Expansion Thermal Conductivity Specific Heat Electrical
Resistivity 0-100°c 0-315°c 0-538°c at 100°c at 500°c
Unit Kg/m³ GPa µm/m/°c µm/m/°c µm/m/°c W/m.K W/m.K J/Kg.K nΩ.m
Duplex
2205
7800 200 13.7 14.7 - 19.0 - 450 850
Material
Tensile Strength
Yield Strength
Elongation
Hardness
Rockwell C Brinell
Unit MPa MPa % in 50 mm HR C HB
Duplex 2205 620 450 25 31 293
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13495
Outer Radius
σ1 = σr = -300N/mm2
σ2=σl=-1182.85 N/mm2
σ3=σt=-1182.87 N/mm2
4. Maximum shear stress:
Inner Radius = σ1−σ3
2
= 0+441.42
2
= 220.7 N/mm2
Outer Radius=σ1−σ3
2
=−300+1182 .87
2
=441.435 N/mm2
5. Bursting pressure:
Pb= UTS * (K2-1/K
2+1)
= 620* (1.2962-1/1.296
2+1)
=157.32 N/mm2
Table No 4: Theoretical result
SL.N
O.
PARAMET
ER
DESCRIPTI
ON
INFEREN
CE
1. Material DUPLEX
2205
STAINLES
S STEEL
2. Vessel
Thickness
56.45 mm Fabrication
is difficult.
Cost is very
high.
3. Maximum
Tangential
stress(N/mm2
)
-441.42
N/mm2
(compressive)
At the inner
radius of
vessel
4. Minimum
Tangential
stress(N/mm2
)
-1182.87
N/mm2
(compressive)
At the outer
radius of
vessel
5. Bursting
Pressure
157.32 N/mm2
Develops a
stress of
inside vessel
V. SOFTWARE ANALYSIS
INTRODUCTION TO CREO PARAMETRIC 3.0:
PTC Creo Parametric offers powerful, reliable, yet easy-
to use modelling tools that accelerate the design process.
This software helps to design parts, assemblies, create
manufacturing drawings, pre-form analysis, create
renderings and animations and optimize the productivity
across a full range of other mechanical design tasks. PTC
Creo Parametric will help to design with higher quality-
products in a faster manner and communicate more
efficiently with the manufacturing industry and your
suppliers.
FEATURES:
Creating the 3D models of any parts or
assembly in a short period of time.
Design aesthetics are improved with
comprehensive surface capabilities.
Large number of tools are present in Creo
parametric 3.0 for making the part or assemblies
in an easier manner.
Solid models which are created through other
than Creo parametric 3.0 is easy to import.
INTRODUCTION TO ANSYS WORKBENCH 15.0:
ANSYS Workbench environment is a finite element
analysis tool that is used in conjunction with CAD
systems and/or Design Modeller. ANSYS Workbench is
a software environment for performing structural,
thermal, and electromagnetic analyses. The class focuses
on geometry creation and optimization, attaching
existing geometry, setting up the finite element model,
solving, and reviewing results. The class will describe
how to use the code as well as basic finite element
simulation concepts and results interpretation.
MODEL OF PRESSURE VESSEL:
Fig.2 Isometric view of Pressure Vessel
International Journal of Pure and Applied Mathematics Special Issue
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Fig.3 Finite Mesh of Pressure Vessel
ANALYSIS RESULTS:
For Duplex 2205 Stainless steel:
The result of total deformation, shear stress and strain
for the applied load (50 MPa) is obtained through Ansys
15.0
Fig.4 Total Deformation under Load
Fig.5 Equivalent Stress under load
Fig.6 Equivalent Strain under load
For Carbon Steel:
The result of total deformation, shear stress and strain for
the applied load (50 MPa) is obtained through Ansys
15.0
International Journal of Pure and Applied Mathematics Special Issue
13497
Fig.7 Total Deformation under Load
Fig.8 Equivalent Stress under load
Fig.9 Equivalent Strain under load
Table No 5. Analysis Result:
Graph No 1: Stress-Strain Curve
The above graph represents the stress- strain
relationship of pressure vessel for the given load of 50
MPa. The above graph increase linearly. It shows that
there is no breaking point occurs on the pressure vessel.
So the design of the pressure vessel is safe for the given
load.
0.00E+00
5.00E+07
1.00E+08
1.50E+08
2.00E+08
2.50E+08
0.00E+00 5.00E-04 1.00E-03 1.50E-03
Stre
ss (
Pa)
Strain
Result Total Deformation Shear Stress Shear Strain
Unit M Pa m/m
Material Min Max Min Max Min Max
Duplex 2205 0.0001017 0.00022423 1.2728e5 2.354e8 6.414e-7 0.0011774
Carbon Steel 0.00010894 0.00023392 1.2787e5 2.354e8 6.6971e-7 0.0012197
International Journal of Pure and Applied Mathematics Special Issue
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VI. CONCLUSIONS
This paper reports about the evaluation of certain
horizontal spherical end pressure vessel. It is observed
that all the pressure vessel components are selected on
basis of available ASME standards. The manufactures
also follow the ASME standards while manufacturing
the components. Based on ASME standards the pressure
vessel dimensions are chosen and the designed with the
help of PTC Creo Parametric 3.0. With the help of the
dimensional values theoretical calculations were made
and then the bursting pressure of the pressure vessel is
calculated. The designed pressure vessel is analyzed
through ANSYS 15.0, and the analysis results are taken
to verify the safeness of the pressure vessel. The material
here we are chosen is compared with the existing
pressure vessel material carbon steel. The values
obtained for duplex 2205 from ansys is less than the
values obtained for carbon steel. Stress-strain curve is
drawn through the analyzed data’s. Here the curve
increases linearly, because for the given load there is no
breakage for the pressure vessel. So the curve shows that
the pressure vessel design is safe for the given load. The
bursting pressure of the pressure vessel is less than the
maximum shear stress noted from the analysis result. It is
clear that our pressure vessel design is safe forthe given
load.
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