Contents
Contents
List of
Tables
List of
Figures
List of
Symbols
1. Domestic
LPG cylinder
1.1 Introduction.
1.2 Background.
1.2.1 Size and pressure.
1.2.2 Material
1.2.3 The axial and tangential stresses in the
walls of the domestic LPG cylinder.
1.3 Methodology.
1.4 Modeling and analysis of pressurized part of
cylinder.
1.4.1 Analysis using Plane 42 and Plane 82
1.4.2 Similarities and differences
1.5 Design improvements and optimization
1.5.1 Analysis of flat end cylinders
1.5.2 Analysis of spherical end cylinders
1.5.3 Spherical pressure vessel.
1.6 Dynamic loading of cylinders.
1.7 Conclusion.
References
List of Tables
Table No.
|
Title of the table
|
Pg.No.
|
Table
2.1
|
Structural properties of Low carbon steel
|
6
|
Table
2.2
|
Analysis report with various meshes.
|
8
|
List of Figures
Figure
No.
|
Title of the figure
|
Pg.No.
|
Figure 2.1
|
Dimensions of domestic gas cylinder
|
4
|
Figure 2.2
|
Technical drawing of Cylinder from
Hindustan petroleum corporation Ltd.
|
5
|
Figure 2.3
|
Stress acting on wall of cylinder
|
6
|
Figure 2.4
|
Loads and boundary conditions applied in
Ansys
|
7
|
Figure 2.5
|
Size control for mapped meshing
|
8
|
Figure 2.6
|
Stress in y and z axis using Plane 42
(Set 7)
|
9
|
Figure 2.7
|
Stress in y and z axis using Plane 82
(Set 6)
|
10
|
Figure 2.8
|
Axial and
hoops stress in vertical wall using Plane 42
|
11
|
Figure 2.9
|
Axial and
hoops stress in vertical wall using Plane 82
|
11
|
Figure 2.10
|
Stress in y axis using Plane 82
|
12
|
Figure 2.11
|
Stress in z axis using Plane 82
|
13
|
Figure 2.12
|
Stress in y axis using Plane 82
|
13
|
Figure 2.13
|
Stress in z axis using Plane 82
|
14
|
Figure 2.14
|
Stress in x, y & z axis using Plane
82
|
15
|
List of Symbols
Symbol
|
Description
|
Units
|
K
|
Temperature
|
kelvin
|
MPa
|
Mega pascal
|
MPa
|
1.
Domestic LPG
cylinder
1.1 Introduction.
Pressure vessels are used to hold compressed gas. As per gas
cylinder rules 2004 published by the gazette of India, “Compressed gas” means
any permanent gas, liquefiable gas or gas dissolved in liquid under pressure or
gas mixture which in a closed gas cylinder exercises a pressure either
exceeding 2.5MPa at +15°C or a pressure exceeding 3MPa at +50°C or both. Pressure
vessels are found in many mechanical systems such as chemical plants, airplanes,
ships, submersible vehicles and manufacturing systems. The most
common forms of pressure vessels to hold liquids or gases under internal
pressure are spheres and closed end cylinders. The commonly used pressure
vessel is the domestic gas cylinder.
1.2 Background.
1.2.1 Size and
pressure.
Figure
1.1 Dimensions of domestic gas cylinder. [1 &2]
Figure 2.1 shows a domestic
LPG cylinder. The density of the LPG is approximately half that of water and
ranges from 525 to 580 kg /m3 @ 15°C. If we consider a domestic gas
cylinder, it will be filled with 14.2kg. The pressure inside a LPG storage
vessel / cylinder will be equal to the vapour pressure corresponding to the
temperature of LPG in the storage vessel. The vapour pressure is dependent on
temperature as well as on the ratio of mixture of hydrocarbons. Domestic LPG is
a mixture of 70% Propane and 30% Butane. The
maximum pressure exerted by LPG at 65°C is 1.66 MPa. The details of the
pressure, water capacity of cylinder and dimensions are as per Hindustan petroleum
corporation Ltd.
Figure
1.2 Technical drawing of Cylinder from Hindustan petroleum corporation Ltd. [3]
Let consider the following
as base values for analysis.
Internal pressure P= 2.5MPa
Internal diameter d= 314.4 mm
Thickness, t = 2.5 mm
1.2.2 Material
Material used for LPG cylinder is Low Carbon Steel
Table One Structural properties of Low carbon steel [4]
Young's Modulus
|
2.e+005 MPa
|
Poisson's Ratio
|
0.3
|
Density
|
7.85e-006 kg/mm³
|
Thermal Expansion
|
0. 1/°C
|
Tensile Yield Strength
|
240. MPa
|
Compressive Yield Strength
|
240. MPa
|
Tensile Ultimate Strength
|
420. MPa
|
1.2.3 The axial and tangential stresses in the walls of the
domestic LPG cylinder.
Figure
1.3 Stress acting on wall of cylinder.
Consider a thin cylinder of
internal radius r, length L and wall thickness t. The cylinder is under internal pressure p as
shown in Figure 2.3.
The major stresses acting
on cylinder wall is axial and tangential stresses.
Tangential stress
σy = Pr/t = Pd/2t
Equation 1
Axial stress
σx = Pr/2t = Pd/4t
Equation 2
The axial stress and
tangential stress of LPG cylinder are calculated below.
Tangential stress, σy =
Pd/2t = (2.5 x 314.4) / (2 x 2.5) = 157.2MPa
Axial stress, σx =Pd/4t = (2
x 314.4) / (4 x 2.5) = 78.6MPa
1.3 Methodology.
After proper background
study the theoretical values are calculated. The Analysis is done for existing
cylinder shape. The model is idealized and only the pressurized part is
considered for analysis. Optimization in existing shape are considered for
analysis by changing end shapes and overall shape of the cylinder.
1.4 Modeling and analysis of
pressurized part of cylinder.
1.4.1 Analysis using Plane 42 and Plane 82
Plane 42 and Plane 82 are elements
having elemental behavior of axisymmetric. So using this element, the problem
is solved in axisymmetric approach. For that only cross sectional area is
required. In this approach, y axis is the axis of symmetry. Axial stress is the
stress along y axis and tangential stress is the stress along z axis. The major
difference is that plane 42 is linear and plane 82 is quad elements.
For modeling, proe is the
software used. The dimensions such as inner diameter, external height and
thickness are considered from Figure 1.2. An acceptable approximation of a 2: 1
Ellipsoidal head is one with a knuckle radius of 0.17D and a spherical radius
of 0.90D. As part of idealization only pressurized part of cylinder is made.
The welding of lower and upper half of cylinder is not considered of analysis.
For both the elements, as
it is approached using axisymmetric concept, modeling and boundary conditions
remains the same. A surface is made with required dimension using proe using
fill option and is imported as iges. Then area is splited to 5 no. of pieces: 2
caped ends, 2 fillets and one vertical wall. Then for manual meshing, the size
is controlled. After mapped messing, boundary conditions are applied. Figure 2.4
shows the loads and boundary conditions applied.
Figure
2.4 Loads and boundary conditions applied in Ansys
Figure 2.5 shows the edges that are controlled for mapped meshing.
Figure
2.5 Size control for mapped meshing.
Table Two Analysis report with various meshes.
SET No.
|
NO. OF DIVISIONS
|
PLANE 42
|
PLANE 82
|
|||||
1
|
A
|
B
|
C
|
D
|
σy
|
σz
|
σy
|
σz
|
2
|
1
|
50
|
20
|
100
|
149.147
|
171.628
|
151.619
|
171.718
|
3
|
1
|
100
|
40
|
200
|
150.894
|
171.718
|
151.604
|
171.756
|
4
|
1
|
150
|
50
|
300
|
151.083
|
171.691
|
151.559
|
171.732
|
5
|
2
|
150
|
50
|
300
|
151.191
|
171.706
|
151.51
|
171.701
|
6
|
2
|
200
|
60
|
400
|
151.251
|
171.712
|
151.454
|
171.704
|
7
|
3
|
200
|
60
|
400
|
151.326
|
171.704
|
151.481
|
171.699
|
Table 2.2 shows the no of divisions applied in various lines
for size control. Nodal solutions, the axial stress (σy) and tangential stress (σz) for various elements are also tabulated.
In both element, y component
of stress shows the axial and z component of stress shows the tangential
stress. Our calculated value of axial stress is in range of the analysis
result. But the tangential stress (z component) obtained by the analytical
method is not matching with the theoretical value.
While using plane 42, we
need more no of elements for the convergence of result as the element is
linear. If we use plane 82 the convergence is much aquarate with less no of
elements. The convergence to 151 on stress in y and 171 on stress in z is
reached in set 1 for plane 82 element but to reach that accurate convergence
with plane 42 we have to go much heigher no of elements. While analysing 6th
and 7th sets, we can identify that both stress values reached to a
convergence. But the accuracy of 6th set of plane 82 is same to 7th
set of plane 42. The no of elements used in plane 82 is 2/3 of plane 42.
An approximate calculation of
no. of elements is shown below.
No. of elements used in 7th
set of plane 42= 3 x [(2 x 200)+(2 x 60)+400]=2760
No. of elements used in 6th
set of plane 82= 2 x [(2 x 200)+(2 x 60)+400]=1840
Figure
2.6 Stress in y and z axis using Plane 42 (Set 7)
Figure 2.5 shows the Stress
in y and z axis using Plane 42 element. The axial stress acting is 151.33 and
tangential stress is 171.704. The axial stress and tangential stress doesn't match
the theoretical value.
Figure
2.7 Stress in y and z axis using Plane 82 (Set 6)
Figure 2.7 shows the Stress
in y and z axis using Plane 82 element. The axial stress acting is 151.45 and
tangential stress is 171.704. The axial stress and tangential stress doesn’t
match the theoretical value. The results plotted in figure 2.6 and 2.7 are
nodal solutions.
The actual theoretical
value is the stress exerted on vertical wall of cylinder. To plot the exact
theoretical value we have to go with path operation. First we have to define a
path through the nodes on same line in the vertical wall area. Then map stress
on to define path: stress in y as axial and stress in z as hoops (tangential).
If we plot graph of axial
and hoops stress along the path, we will get the result matching to the
theoretical value. There will not be much variation in no of elements used in
Plane 42 and Plane 82.
Figure 2.8 shows the graph
of axial and tangential stress exerted on vertical walls of cylinder using
Plane 42.
Figure 2.9 shows the axial
and tangential stress exerted on vertical walls of cylinder using Plane 82.
1.4.2 Similarities and differences
The tangential stress value
is converging to 171.704 in both the cases. But the axial stress value is not
converged. The major difference is the no of elements used. Path plot gives result
that matches with theoretical value. But it is difficult to identify what will
be happening at each area especially at capped ends. For easier comparison,
nodal solutions of stress in y and z axis are considered throughout the
procedures.
1.5 Design improvements and
optimization
The pressure vessel can be optimized by rethinking the shape of the
cylinder. Flat ends and spherical ends are considered for new shapes. Spherical
Vessels are considered
1.5.1 Analysis of flat end cylinders
In case of flat end
cylinder, the stress concentration is high in corner fillets.
Figure 2.8 shows the axial
stress in flat end cylinders. In that, the overall stress is in range is in
range of 280. But in the areas of fillet the stress rises tremendously. The overall
displacement (deformation) is also high.
Figure 2.9 shows the
tangential stress in flat end cylinders. In that, the overall stress is in
range is in range of 760. But in the areas of fillet, the stress rises
tremendously. The overall displacement (deformation) is also high. The capped end
is exerted with higher amount of stress. The values may be wrong but the
concentration of stress will be accurate. The hoops stress in flat end is much
higher compared to other shapes.
Figure
2.10 Stress in y axis using Plane 82
Figure
2.11 Stress in z axis using Plane 82
1.5.2 Analysis of spherical end cylinders
Figure
2.13 Stress in z axis using Plane 82
In case of spherical end
cylinder, the values of axial and tangential stress are reduced. If we consider
the analysis report of curved end type cylinders, the stress concentration is
less than that.
Figure 2.10 shows the axial
stress in spherical end cylinders. In that, the maximum stress is in range is
in range of 101.It is much lower than curved end cylinder. The displacement
(deformation) is also low.
Figure 2.11 shows the
tangential stress in spherical end cylinders. In that, the maximum stress is in
range is in range of 101.It is much lower than curved end cylinder. The displacement
(deformation) is also low. The spherical area can withstand much stress. So we
can reduce wall thickness only on capped area. The manufacturing of this type
is much difficult.
1.5.3 Spherical pressure vessel.
The water capacity of 14.2
kg cylinder is 33 L
Volume =4Πr3 /3= 0.33 m3
Inner radius r = 199. 02 mm
Consider a sphere with
radius r and wall thickness t filled with gas or fluid with pressure p.
Stresses in all directions
are same. Stress exerted on walls σ = p r / 2t
The maximum stress exerted
in the case of curved end cylinders are 171 MPa.
Wall thickness t= p r / 2 σ
= (2.5x 199.02) / (2 x 171) = 1.46 mm
For analysis, consider
Wall thickness = 1.5 mm
Internal radius = 200 mm
Figure
2.14 Stress in x, y & z axis using Plane 82
The stress value is 166.67
and the wall thickness considered is 1.5 mm
So a spherical cylindrical
vessel with 200 mm internal radius and wall thickness 1.5 mm can hold a
pressure of 2.5 MPa.
The advantage of using
spherical pressure vessel is that, the wall thickness is lower compared to
other shaped pressure vessel. That reduces the weight of pressure vessel and
hence used is ships etc.
The main disadvantage is
that it consumes larger floor area compared to other types. It makes
transportation difficult. The manufacturing of spherical vessel is much
difficult compared to other shapes.
1.6 Dynamic loading of cylinders.
Cylinders ate transported
through trucks. The uneven road and during loading and unloading, these
experiences various vibrations. Vibrations are nothing else but disturbances
which can be ideally considered as certain frequency. These frequencies can be
calculated by Modal analysis in ansys.
If the forced frequency
matches the natural frequency, the component undergoes failure. Since mass and
loads acting will change the frequencies, it is better to calculate the natural
frequency of filled cylinder than empty cylinder.
As part of idealization,
only pressure vessel area is taken for analysis. Welding, handle and base are
avoided.
If we consider empty cylinder,
there will not be much disaster.
Figure
2.15 Frequencies of empty cylinder.
Figure 2.13 shows the first
20 frequencies. The first six values will be their 6 degrees of freedom and 7th
value 20.010 can be considered as the natural frequency of empty cylinder. That
will be the first frequency that causes catastrophic failure of empty cylinder.
The main concern is in the
case of filled cylinders that cause major destruction. So first we perform a
static analysis with 2.5MPa pressure and the pre-stress effects are included
for modal analysis. For modal analysis we consider 20 mode shapes. We will get
many no. of frequencies as we analyze for large no. of mode shapes.
Figure
2.16 Frequencies of Filled cylinder.
Figure 2.14 shows the first
20 frequencies of a pressurized cylinder at 2.5MPa. The first six values will
be their 6 degrees of freedom and 7th value 26.154 can be considered
as the natural frequency of filled cylinder. That will be the first frequency
that causes catastrophic failure of filled cylinder.
1.7 Conclusion.
From all these analysis
done, the shape that can be used is spherical vessels as the wall thickness and
weight can be reduced. Due to its difficulty in transportation, spherical end
vessels can be used as the cost of cylinder will increase. The frequency of
disturbance during loading unloading and transportation will not match with
natural frequencies of empty (20.010) as well as filled (26.154) cylinder as
these frequencies cause the failure of gas cylinder.
Keywords: Gas Cylinder, Pressure Vessel, LPG
References
___________________________________________________________________________
1.
Miss Cheah (December 21, 2011) Vital
Knowledge about LPG Gas Cylinder. www.blogspot.in http://shuangxingfu.blogspot.in/2011/12/vital-knowledge-about-lpg-gas-cylinders.html (16-12-2012)
2.
Laxmikant D. Rangari, P. M. Zode &
P.G. Mehar (2012) International Journal of Applied Research in Mechanical
Engineering (IJARME) ISSN: 2231 –5950, Volume-2, Issue-1, 2012
3.
Technical drawing of LPG Cylinder from Hindustan petroleum
corporation Ltd. http://tenders.hpcl.co.in/tenders/tender_prog/TenderFiles/649/Tender/p1.drawing%2014.2%20kg%20cylinder.pdf
4.
International Journal of Applied
Research in Mechanical Engineering (IJARME)ISSN: 2231 –5950, Volume-2, Issue-1,
2012
