 Open Access
 Total Downloads : 1132
 Authors : Mayank Nirbhay, Prashant Tripathi, Vivek Kumar Gupta
 Paper ID : IJERTV3IS10911
 Volume & Issue : Volume 03, Issue 01 (January 2014)
 Published (First Online): 27012014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Implementation of ASME Codes to Design A Pressure Vessel and Toexplore the Influence of Various Design Parameters
Mayank Nirbhay1, Prashant Tripathi2, Vivek Kumar Gupta3
1,2,3 M.Tech(Design) Student, Mechanical Engineering, School of Engineering, Gautam Buddha University, Gr. Noida
Abstract
In this research, the design of a pressure vessel is carried out using ASME Codes. Various components of the pressure vessel are designed by calculating the appropriate design factors like thickness of the shell, head, stress analysis etc. To validate the design result the pressure vessel is modelled and analysed in ABAQUS. The preferred method to conduct the analysis is finite element method. Further the study in the variation of effective parameters in design of pressure vessel is done. Different graphs are plotted to study the variation of internal pressure and diameter of shell. The applicability of various types of heads is also evaluated.
Keywords: ASME, FEA, Pressure vessel design, Saddle support, Torispherical, Zicks analysis.

Introduction
Pressure Vessels are the reservoir of fluids at pressure more or less than ambient, internal or external. The pressure source can be pump, compressor, fluid head etc. Pressure vessels are used for wide variety of industrial applications such as in thermal and nuclear power plants, petrochemical refineries, process and chemical industry. The shapes of pressure vessels are usually spherical or cylindrical with dished ends.
Designingis to calculate the dimensions of a component so that it can endure the applied loads and perform the desired function. It also involves the process of estimating the stresses and deformations for the specified loads and boundary conditions at different critical points of a component [1]. While designing the pressure vessel safety is the primary concern because the rupture of pressure vessel or explosion may cause loss of lives and property.
Further the analysis (finite element) whichis a subpart of the design process includes the estimation of deformations, stresses and failure modes in the pressure vessel and its components.
Many researchers have contributed in the design and analysis of the pressure vessel like, M. Pradeep [2] has discussed the importance of circular crosssection over rectangular crosssection vessel. Similarly, Shaik Abdul [3] has discussed about the optimum thickness required for the safe design conditions. Draan Kozak
[4] has worked on the numerical analyses of cylindrical pressure vessel with variable head geometry.This research paper highlights the importance of ASME Code in designing the pressure vessel by validating the design using FEA. Further, the influence of variation in different design parameters is also studied.

Classification of pressure vessels
The two important factors for the classification of pressure vessel are [2]:
According to thickness

Thin cylinder when t/d < 0.1

Thick cylinder when t/d > 0.1 According to end construction

Closed ended

Open ended



Structure of paper
The paper comprises of five sections. Section 2 deals with the design philosophy and design implementation. Sections 3 validates the design by FEA. Section 4 discuses about the effect of different design parameters. Lastly, section 5 concludes the research work.


Theoretical basis

Design philosophy
Pressure vessels are generally designed according to the ASME Code, Section VIII DivisonI and DivisionII. The appropriate analytical procedures are followed for determining thickness and stress of basic components of pressure vessel. Here the basic component of pressure vessel refers to shell, head, and nozzles, stiffening rings, supports and other external attachments.
There are various factors [5] which must be considered while selection and designing of the pressure vessel such as

Dimensions and geometry diameter, length, thickness and their limitations.

Operating conditions pressure and temperature

Functions and location

Nature of fluid, corrosive nature

Availability of materials, its physical properties and cost.

Theories and type of failure

Construction or fabrication techniques

Economic consideration


Design theory and procedure

Generally a pressure vessel consists of a shell with closed ends. Plates or sheets are used to manufacture the pressure vessel components. Parts or components are attached either by welds or riveted joints. Thus a joint efficiency factor is incorporated into account.
Design procedure as in ASME Code Section VIII DivI
[6] is followed to design a long horizontal pressure vessel with torispherical heads and saddle support.The steps and sequence involved in designing the vessel are illustrated in the flowchart shown in Figure 1.
Figure 1. Design procedure flowchart

Selection of material of elements
The material of pressure vessel selected according to ASME section II part A [7] is SA516 GRADE 70 Carbon steel.
Properties of material (SA516 Grade 70) for the shell and heads are shown in Table1[3]:
Table 1. Properties of material for shell and head
Maximum
allowable stress value (S)
1406 kgf/cm2 (137.88 N/mm2)
Density
7850 kg/m3

Input design data
Code of design and construction
ASME SecVIII DivI
Internal design pressure (P)
10.64 Kg/cm2
External design pressure
Nil
Design temperature (C)
120
Nominal inside diameter (Di)
1750 mm
Corrosion allowance (C.A.)
3 mm
Weld joint efficiency (E)
0.85
Shell length (L)
5894 mm
Type of head
Torispherical
Density Of Fluid
961.3 kg/m3
Material of construction
Carbon Steel
Table 2. Design specifications

Calculation of the shell thickness under internal pressure for horizontal vessel As per UG27
When a thin circular cylinder is under the action of radial forces uniformly distributed along its circumference, hoop stress will be produced. These hoop stress will act throughout its thickness in tangential direction as given by Harvey [11].
= 1 3 +
4
Now, M = 1/4 * (3 + (1400/262.3)) = 1.327
For head joint efficiency, E= 1.0
t= (10.64*1400*1.327) / (2*1406*10.2*10.64) + 3 = 7.03+3=10.03mm
Taking a standard 12 mm thick plate for fabrication of
=
=
head. Thus the thickness of tori spherical head, t = 12
Where
2
mm.
P = Internal Pressure, r = Radius of shell, t = Thickness, hoop = Hoop stress, long= longitudinal stress
Compiling the fabrication and inspection quality factor into account, ASME has modified the formula for calculating shell thickness as:
Required shell thickness considering the hoop/circumferential stress
=
0.6
where, Ri= R + C.A. = 875+3 = 878mm or 87.8cm tr= 10.64*87.8/(1406*0.850.6*10.64)= 7.85 mm
Total shell thickness = tr + C.A. = 7.85+3= 10.85mm
Required shell thickness considering the longitudinal stresses:
=
(2 + 0.4)
tr=10.64*87.8/(2*1406*0.85+0.4*10.64)=3. 9
Total shell thickness = tr + C.A. = 3. 9+3= 6.9mm
Since tcircumferential> tlongitudinal , therefore t=10.85mm
Generally the next standard fabrication plate available is 12 mm thick, so the shell thickness under internal pressure is 12mm.

Design of headas per UG 31
Type of head used: tori spherical head

Calculation of Nozzle thickness as per UG 45
Nozzles attached to shell have different thickness other than which are attached at the heads. Generally nozzles at head have higher thickness than the nozzle at the shell.
The nozzle at the head has outside diameter, Do = 60.33mm.
The nozzle at the shell has outside diameter, Do =
168.28 mm.

Vessel saddle support analysis
The designing of supports for horizontal vessels is based on the method given by L. P. Zicks Analysis presented in 1951. Further the Zicks work was published as standard by ASME [8]. As suggested by the ASME Code the minimum contact angle should be 120Â°.
The pressure vessel platform should suitably be strong enough to bear all dead load and wind loads during construction stage, test and operation while at the same time preventing high restraining forces on the shell [9].
For the vessels supported by saddles are mainly subject to three types of stresses:

Longitudinal bending stress

Tangential shear stress

Circumferential stress
=
2 0.2
Here, L = inside crown radius
+ . .
M = factor depending on the head proportion L/R
Table 3. Parameters for Zicks Analysis
Since total induced tension stress is less than allowable stress(12553.86 < psi 16600psi). Hence design is safe.
Tangential Shear:
If A>R/2. The appropriate formula is
R
Radius of shell
875mm
34.44in
A
Dist. from tangent line of head to the center of
saddle
1568mm
61.73in
H
Depth of tori spherical head
449.5mm
17.71in
L
Length of vessel tantan
5599.93mm
220.47in
P
Internal design pressure
10.64
kg/cm2
151.33psi
Q
Load on one saddle
5735.84 kg
12641.8 lbs
ts
Thickness of the shell
12mm
0.472in
S
Material allowable
stress
1406.14
kg/cm2
16600psi
Contact angle
120
K1
For =120
0.335
K2
For =120
1.171
= 2 2
2
+ 4
3
S2=2127.55 psi
Since S2 shall not exceed 0.8 times the allowable stress
value of vessel material.
Thus according to the given condition, S2< ( 0.8 *
Longitudinal Stress:
S1 Stress at saddles (Tension):
1 + 2 2
4
1 2
1+
1
= Â± 3
12
For 12mm shell S1= 7388.37 psi
S1 Stress at midpan:
16600) = 2127.55 < 13280
Since total induced tangential shear stress is less than allowable stress. Hence design is safe.
Circumferential stress:
Similarly the induced stress at the horn of saddle and at the bottom of shell is less than 1.5 and 0.5 times the allowable stress respectively.
1+2 2 2
4
For the given design consideration all induced stress in
2
4 1+4
vessel is below the allowable stress, so the design is
1
= Â± 3
2
For 12mm shell S1= 355.49 psi
Sip Stress due to internal pressure
Sip= PR/2ts = 151.33*34.44/2*0472 = 5520.98 psi
Sum of total stresses for 12mm, 7388.37 355.49+5520.98= 12553.86 psi
safe.


Preparation of cad drawings
AutoCAD software is used to prepare the cad drawing of pressure vessel as shown in Figure2. The vessel drawing is prepared with the results obtained in the design procedure.
Figure 2.Cad drawing of long horizontal pressure vessel with saddle supports.

Finite element analysis of pressure vesssel
Objective of the analysis is to conduct FEA of a long horizontal pressure vessel and determine the maximum stress induced in it. For a safe design, the maximum induced stress in the pressure vessel should be less than the maximum allowable stress of the vessel material.
Modelling and analysis software:The detailed 3D modelling and analysis of pressure vessel was done using Abaqus. It is a general purpose finite element modelling and analysis package for numerically solving a variety of mechanical engineering problem.
Modelling:Since the main aim of the investigation is to determine the maximum induced stress. During modelling many small features of the vessel were not modelled because they will have only a local effect and will not play much significant role in the overall stability of the system.
Shell and head of the vessel were formed as shell by revolve tool in the Abaqus part module as shown in Figure3. The part modelling is done on the basis of the dimensions which are calculated in designing procedure.
Figure 3. Modelling the pressure vessel in ABAQUS Part module.
Boundary and loading conditions: The inside pressure in the pressure vessel is set to 10.64 kg/cm2 and the outer periphery of the shell is fixed.
Meshing: Themeshing of the pressure vessel is done at element sizing of 150 mm and with Tri element. Instead of using a coarse mesh, fine mesh is used to produce more accurate results, as shown in Figure4.
Figure 4. Fine meshing of the pressure vessel with Tri element size of 150mm.
Analysis results: As shown in Figure5 & 6, the maximum stress induced in the vessel is 128.2 N/mm2 (or 1307.27 kg/cm2) which is less than the maximum allowable stress i.e. 137.88 N/mm2 (or 1406 kg/cm2), as shown in Table1. Thus, the analysis results achieved concludes that the design is appropriate and safe.
Figure5 Stress distribution in the pressure vessel.
Figure6. Stress distribution in the torispherical head of the pressure vessel.

Analysis of effective parameters in design of pressure vessel.
In ASME Code Section VIII DivI, the overall designing criteria of pressure vessel is based upon the basic design parameters which are to be decided to initiate the design like diameter of shell, internal design pressure, length of vessel etc.
In the present section, effect of change in the value of parameters like shell diameter, internal pressure is demonstrated. The necessity of analysing the pressure parameter is because the vessel material is subjected to pressure loading due to which stresses are formed in all direction [10]. Thus certain modifications would be needed either in the material or in the design of the pressure vessel so that it would be able to resist those stresses.
Mathcad software is used for programming the numerical steps involved in designing. The use of Mathcad simplifies the calculation and generates accurate results involved in design of shell and head.

Efect of varying the pressure
The shell thickness is the major design parameter and is usually controlled by internal pressure. The thickness should be sufficient to resist the longitudinal and hoop stress. Figure7 shows that the thickness of the shell increases on increasing the internal pressure parameter because the optimum thickness is required to resist the shell to deform readily without incurring large stress.
Table 4. Variation on the thickness considering hoop stress and longitudinal stress when pressure value is increasing.
Hoop Thickness Long. Thickness
20
Thickness (mm)
15
10
5
0
10 12 14 16 18 20 22
Pressure (kg/cm2)
Figure 7. Variation on the thickness considering hoop stress and longitudinal stress when pressure value is increasing.
From Figure7 the thickness corresponding to the hoop stress denoted as hoop thickness is more than the thickness corresponding to the longitudinal stress denoted as longitudinal thickness and hence the maximum thickness value from the two cases should be considered as the optimum shell thickness.

Effect of varying the shell diameter
The shell thickness varies as we change the diameter of the shell. Figure8 shows that the thickness of the pressure vessel increases on increasing the diameter of the shell, because according to the formula of thin pressure vessel the thickness is directly proportional to the diameter for constant internal pressure and allowable stress.
i.e. t= (p*d)/(2*allowable stress)
S.No.
Diameter
Hoop Thickness
Long. Thickness
1
175.6
10.384
6.667
2
200
11.951
7.44
3
240
13.741
8.332
4
310
16.784
9.888
5
360
19.112
10.998
Table5. Variation on the thickness considering hoop stress and longitudinal stress when diameter of the shell is increasing & keeping other factor constant
S.No.
Pressure (kg/cm2)
Hoop Thickness
Long. Thickness
1
10
10.384
6.667
2
10.64
10.859
6.901
3
12
11.869
7.399
4
15
14.1
8.496
5
17
15.597
9.227
6
21
18.592
10.687
Hoop Thickness Long. Thickness
20
Thickness (mm)
18
16
14
12
10
8
6
160 210 260 310 360 410
Diameter (cm)
Ellipsoidal H.T.
19 Torispherical H.T.
Thickness (mm)
Hemispherical H.T.
14
9
4
9 12 15 18 21 24
Pressure (kg/cm2)
Figure 8. Variation on the thickness considering hoop stress and longitudinal stress when diameter of the shell is increasing & keeping other factor constant.
From Figure8 we can see some uneven variations both in hoop thickness as well as longitudinal thickness with increase in diameter. From figure8 the thickness corresponding to the hoop stress is more than the thickness corresponding to the longitudinal stress and hence the maximum value from the two cases should be considered as the optimum shell thickness.

Effect of varying the pressure in different head configuration
The heads can be generally classified as hemispherical, torispherical and ellipsoidal. From Figure9 it is clear that as the pressure increases the thickness of all types of heads increases linearly.
Table 6. Variation on the thickness of various types of heads used when pressure value is increasing. (H.T.=head thickness in mm)
S.N
o.
Pressu re
Ellipsoi dal H.T.
Torispheri cal H.T.
Hemispheri cal H.T.
1
10.64
6.24
10.04
8.3
2
12
6.65
10.94
8.98
3
15
7.57
12.92
10.48
4
17
8.18
14.25
11.47
5
21
9.4
16.9
13.47
Figure9. Variation on the thickness of various types of heads used when pressure value is increasing.
Torispherical heads are the most common type of head used for the manufacture of pressure vessels. Although the thickness of the torispherical head is largest on same pressure but they are most economical to manufacture, hence most extensively used.
Hemispherical heads are analysed as spheres. They can bear more pressure than any other head. However, the hemispherical head is the most expensive to form, as they are deepest of all heads. At same pressure the thickness of this head is in between the torispherical and ellipsoidal heads. Hemispherical heads are widely used in very high pressure applications and also in architectural applications.
Ellipsoidal heads are able to resist greater pressures than torispherical heads as they are deeper and therefore stronger. At same pressure the thickness of ellipsoidal head is least of all heads but they are more economical to form than hemispherical heads hence they are used according to their applicability.


Conclusion
Pressure vessel is designed in accordance with the ASME Code Sec. VIII DivI and different design parameters are calculated. The modelling and finite element analysis of pressure vessel is conducted using ABAQUS software and design results are validated. The result obtained is that the induced stress (128.2 N/mm2 )is less than the materials maximum allowable stress (137.88 N/mm2). The analysis result proved that the design procedure adopted is appropriate and design is safe.
The finite element analysis also helps to study the actual stress distributions in pressure vessel
components and the actual performance of pressure vessel.
Further, the importance of variation of different design parameter is examined. The results obtained are that on increasing the internal pressure the thickness of shell and head should also be increased in order to resist the stresses. Similarly on increasing the diameter of the shell the thickness need to be increased. In the present case as the working pressure is low, the outcome is that torispherical head is best suited for the present horizontal pressure vessel.
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