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DESIGN AND ANALYSIS OF VERTICAL PRESSURE VESSEL
D. Balaji1, G.S. Vivek2
1PG Scholar, Department of Mechanical Engineering, Chadalawada Ramanamma
Engineering College, Tirupati-517502, Andhra Pradesh, India
Email: [email protected]
2 Assistant Professor, Department of Mechanical Engineering, Chadalawada
Ramanamma Engineering College, Tirupati-517502, Andhra Pradesh, India
Abstract. This technical paper presents the design and structural analysis of Vertical
pressure vessel (Volume tank) to understand the structural behaviour of pressure
vessels under various loading conditions. In a pressure vessel high pressures are
developed during its operations and it has to with stand severe forces. In the design of
pressure vessel safety is the primary consideration, due the potential impact of possible
accidents at working environment. There have a few main factors to design the safe
pressure vessel. Efforts are made in this paper to design a Solid model as per ASME
Code & Standard guide lines and analysis has been carried out at various pressure
conditions by using ANSYS to analyse the safety parameter of allowable working
pressure and Max. Allowable stress. The bursting of the vessel are probability occur at
maximum pressure which is the element that only can sustain that pressure.
Keywords: Pressure Vessel; Volume tank; ASME BPVC; Solid works; ANSYS.
1. INTRODUCTION
Tanks, vessel and pipelines that carry, store or receive flu-ids are called pressure vessel. A
pressure vessel is defined as a container with a pressure differential between inside and outside.
The inside pressure is usually higher than the outside. As high operating pressures are a danger,
utmost care should be taken while designing the pressure vessels. Any mechanical structure
fails if there are stresses induced in them. The pressure vessel life under cyclic load is related
to the number of cycles it is exposed to and to the intensity of the stress [9]. The pressure vessel
is assumed to be a thin cylinder, and therefore the analysis follows the thin cylinder formulae.
The fluid inside the vessel may undergo a change in state as in the case of steam boiler or may
combine with other reagent as in the case of chemical reactor. Pressure vessel often has a
combination of high pressure together with high temperature and in some cases flammable
fluids or highly radioactive material. Because of such hazards it is imperative that the design
be such that no leakage can occur. In addition vessel has to be design carefully to cope with
the operating temperature and pressure.
Pressure vessels are usually spherical or cylindrical with dome end. The cylindrical vessels are
generally preferred because of the present simple manufacturing problem and make better use
of the available space. Boiler, heat exchanger, chemical reactor and so on, are generally
cylindrical.
The modelling was done on a modelling software Solid works, and a finite element analysis
was carried out to highlight the various points of stress concentration. As anticipated the highest
stress value occurs at the junction of the nozzle attachment, to analyze the aspects of stress
concentration which may develop when the end closure of a high-pressure vessel is attached to
a conically shaped nozzle. The main reason for this occurrence is that the conical nozzle must
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Volume 10 Issue 3 - 2020
ISSN: 1548-7741
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be connected separately. This process would result in geometrical discontinuities between the
pressure vessel and the nozzle at the point of attachment. The solution for the value of stress at
the connection of a cylindrical nozzle to an ellipsoidal shape pressure vessel. The stress
calculations were carried out using finite element method, and a parametric model was
developed.
The accuracy of a finite element model depends on how the mesh is. If the mesh is coarse, the
efficiency of the results decreases. At one point, we reach the point of diminishing returns
where no matter how good the mesh is, it won‘t have a significant effect on the accuracy of the
results. The mesh is said to be converged at this point. For all the models analyzed below,
convergence will be observed as the mesh get refined.
From the result, the convergence seen is a monotonous one rather than an oscillating one. As
the number of nodes and elements increases, the accuracy of the result also increases. From the
analysis, the maximum stress occurs at the junction of the nozzle and pressure vessel. High-
stress concentration is developed due to the abrupt change of the geometry and change in the
stress. Symmetry is a significant factor than some nozzles as it is observed that peak stress for
a symmetrical nozzle is very low and the stress increment factor also lowers.
The finite element analysis based workbench is used for analyzing pressure vessel components.
It discusses modelling methods for various parameters in a cracked pressure vessel. It also
gives few rules for performing analysis using fem like starting with a simple design and using,
closed-form solutions for analysis.
2. MODELLING:
SolidWorks is a 3D solid modelling Computer Aided Design (CAD) and Computer Aided
Engineering (CAE) program that runs on Microsoft Window, published by Dassault systems.
It is feature based, parametric solid modelling design tool that makes advantage in learning
windows graphical user interface easily. SolidWorks helps in creating fully associative 3D
solid models by enabling with or without constraint sketch features while utilizing automatic
or user-defined relations to capture design intent.
2.1 MODELLING OF VERTICAL PRESSURE VESSEL IN SOLIDWORKS:
Creation of 3D model of pressure vessel using SolidWorks software as per the required
dimensions. This contains individual part creation like Elliptical dish ends, Shell, leg supports
which requires the sectional views of the volume tank components drawn in the sketcher and
cylindrical cross section is obtained by using Revolve Boss feature. Selection of materials can
be done with the help of Material option in Feature manager tree area. The created parts are
assembled as per the requirement of the project.
2.2 DIMENSIONS OF THE SOLID MODEL:
In view of the conditions laid down in the objectives solid model has been created with the
given dimensions.
Journal of Information and Computational Science
Volume 10 Issue 3 - 2020
ISSN: 1548-7741
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Table 2.1: DESIGN DATA
DESCRIPTION VALUE UNIT
CONSTRUCTION CODE ASME VIII DIC.1 EDITION
2017
Design Pressure P 0.8 MPa
Operating Temperature T 50 to 65 oC
Design Temperature Td 132 oC
Min. Design Metal Temperature Tm
0 oC
Max. Allowable Stress at design temperature. (ASME
SEC II D) S 138 MPa
Joint Efficiency E 1.0 -
Corrosion Allowance CA 1.0 mm
Medium Air -
Vessel Size
ID Di 600 mm
Nominal Thickness t 10 mm
T/L - T/L L 1000 mm
Support Detail - Leg Support
PRESSURE VESSEL SHELL DESIGN THICKNESS CALCULATION:
Thickness of Shell under Internal Pressure as per ASME SEC VIII DIV 1 UG-27:
For Circumferential Stress tr =
=
P x R
S x E – 0.6P
= 3.3 mm
For Longitudinal Stress tr =
=
P * R
2S x E + 0.4P
= 2.9 mm
2.3 SOLIDWORKS PART MODELLING AND ASSEMBLY:
Elliptical Dish end Cylindrical Shell Pressure Vessel Assembly
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3. ANALYSYS:
We used ‘Finite Element Method (FEM) for the analysis of vertical pressure vessel. FEM is
widely used to solve problems of engineering mechanics. FEM is the numerical technique used
to perform analysis of many physical phenomenon. Structural & Fluid behaviour, thermal
transportation, wave propagation etc. processes are described using partial differential
equation. For a computer to solve PDE, one numerical technique have been developed, which
is called ‘Finite Element Method’. The geometry divided into thousands of small parts and
calculation is done on each part thousands of time, which is called as ‘iteration’. It uses some
mathematical approximation method to converge the solution. This method restricts some
‘Degrees of Freedom’ of the component when we select different boundary conditions like
fixed support or hinged supports etc.
FEM is a general method used for static, dynamic, fluid flow and heat flow analysis. We use
‘Static Structural Analysis’ for the vertical pressure vessel which means when the body is in a
Rigid condition fixed at some point and the given load is quasi(Very Slow), inertial forces can
be neglected. To restrict the motion of the component leg supports are fixed at some points and
applied particular amount of force to calculate Stress, Strain and Deformation. The procedure
for static analysis consists of these main steps.
1. Building the model
2. Obtaining the Solution
3. Validation of the results.
3.1 Material Properties 3.2 Mesh Data for Analysis
Fig 3.1: Mesh View Fig 3.2: Fixed Support Fig 3.3: Load Criteria
4. ANALYSIS OF PRESSURE VESSEL:
Static analysis is carried out at various locations such as Change in area of cross section, weld
zones of upper and lower elliptical dish, upper and lower nozzle connections to determine the
stress concentration, developed forces, Strain and displacements by keeping the thickness of
the vessel as constant (i.e. t = 10mm).
At Operating Pressure 8 Bar: (Change in area of cross section):
Material SA516 Gr 70
Density 7.8 g/cc
Young's Modulus 200 GPa
Poisson's Ratio 0.29
Min Yield Strength (ASME SEC IID) 260 MPa
Max. Allowable Stress at 65o C (ASME SEC IID) 138 MPa
Mesh Data for Analysis
Number of Nodes 2002375
Number of elements 1152760
Size Function Adaptive
Relevance Centre Medium
Element size 3 mm
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Volume 10 Issue 3 - 2020
ISSN: 1548-7741
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Equivalent Stress Equivalent Elastic Strain
At Operating Pressure 8 Bar: (Bottom nozzle Weld Zone)
Equivalent Stress Equivalent Elastic Strain
At Operating Pressure 8 Bar: (Bottom Elliptical Dish End)
Equivalent Stress Equivalent Elastic Strain
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Volume 10 Issue 3 - 2020
ISSN: 1548-7741
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At Operating Pressure 8 Bar: (Upper nozzle Weld Zone)
Equivalent Stress Equivalent Elastic Strain
At Operating Pressure 8 Bar: (Upper Elliptical Dish End Weld Zone)
Equivalent Stress Equivalent Elastic Strain
At Operating Pressure 8 Bar: (Complete Vessel)
Total Von-Mises Stress Total Equivalent Strain Total Deformation
Similarly the analysis is carried out at various pressure conditions and the results are obtained
as shown below.
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Volume 10 Issue 3 - 2020
ISSN: 1548-7741
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5. ANALYSIS RESULT
ANALYSIS RESULTS
S.No Point of Analysis Parameter Obtained results
At 8 bar At 10 bar 15 bar
1 Bottom Nozzle Weld
Zone
Equivalent Stress
Concentration in N/mm2 5.86 17.1 19.92
Equivalent Elastic Strain 3.7977x10-5 8.013x10-5 7.0161x10-5
2 Change in area of cross
section
Equivalent Stress
Concentration in N/mm2 18.94 23.25 34.92
Total Strain 9.475x10-5 1.1847x10-4 1.7372x10-4
3 Upper Elliptical head
weld zone
Equivalent Stress
Concentration in N/mm2 23.72 32.9 38.8
Total Strain 1.114x10-4 1.641x10-4 2.3273x10-4
4 Lower Elliptical weld
zone
Equivalent Stress
Concentration in N/mm2 23.7 30.87 42.1
Total Strain 1.156x10-4 1.25x10-4 2.3008x10-4
5 Upper Nozzle weld
zone
Equivalent Stress
Concentration in N/mm2 60.9 76.12 114.2
Total Strain 3.08x10-4 3.8545x10-4 5.7814x10-4
6 Complete Vessel
Total Von-Mises stress
(3D) 60.9 76.12 114.2
Total Equivalent Strain 3.08x10-4 3.854x10-4 5.7814x10-4
Total deformation 1.577x10-4 1.9818x10-4 2.9922x10-4
CONCLUSION:
In this way a case study has been performed by conducting a linear static analysis on a vertical
pressure vessel for stress analysis which carried out as per the ASME codes and from this
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Volume 10 Issue 3 - 2020
ISSN: 1548-7741
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analysis it is concluded that the FEA Analysis results shows that equivalent stress concentration
in pressure vessel at various pressure conditions are less than maximum allowable stress of the
SA 516 Gr 70 (i.e. 138 MPa at 65 Dec). This helps in understanding the max. Design pressure
that can be used to operate the pressure vessel. From the above results it is clear that the pressure
vessel can be operated till 15 bar above which the equivalent stresses will go higher than the
max. Allowable pressure which in turn lead to failure of pressure vessel. From this analysis,
the mechanical design of a pressure vessel can be easily verified by a third party organization
to ensure the quality of a pressure vessel system that it can easily fulfils the requirements as
per ASME codes and standards .
References
[1] Yun-Jae Kim, Kuk-Hee Lee and Chi-Yong Park, “Limit loads for thin-walled piping branch
junctions under internal pressure and in-plane bending ‟‟, International Journal of Pressure
Vessels and Piping 83 (2006) 645–653 [2] Z. F. Sang, et.al, “Limit & burst pressure for a cylindrical shell interaction with intermediate
diameter ratio”, International Journal of Pressure Vessel and Piping (Aug 2002), Vol. 79 pp.
341-349.
[3] ASME Boiler & Pressure Vessel Code, Section VIII Devision-1, “Rule for Construction of
Pressure vessel.” 2017 Edition,
[4] ASME Boiler & Pressure Vessel Code, Section VIII Devision-2, “Rule for Construction of
Pressure vessel.” 2017 Edition.
[5] ASME Boiler & Pressure Vessel Code, Section II Part- A, “Ferrous Material Specifications
(Beginning to SA-450)” 2017 Edition.
[6] ASME Boiler & Pressure Vessel Code, Section II Part- D, “Ferrous Material Specifications
(Beginning to SA-450)” 2017 Edition.
[7] ASME B16.25-2017 Buttwelding Ends.
[8] John F. Harvey, “Theory and Design of Modern Pressure Vessels”, Second Edit ion.
Journal of Information and Computational Science
Volume 10 Issue 3 - 2020
ISSN: 1548-7741
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