Int. J. Adv. Res. Sci. Technol. Volume 2, Issue2, 2013, pp 67-73.
www.ijarst.com S. Sanyasinaidu. et. al. Page | 67
International Journal of Advanced Research in
Science and Technology
journal homepage: www.ijarst.com
ISSN 2319 – 1783 (Print)
ISSN 2320 – 1126 (Online)
Design and Thermo Mechanical Analysis of High Pressure Vessels with Dish End
S. Sanyasinaidu and K. Chandanarao*
Department of Mechanical Engineering, M. V. G. R. College of Engineering, Vizianagaram, India
*Corresponding Author’s Email: [email protected]
A R T I C L E I N F O
A B S T R A C T
Article history: Received
Accepted
Available online
07 Aug. 2013
19 Aug. 2013
26 Aug. 2013
In the present work design and finite element analysis of solid cylinder and
multilayer cylinder with dish end are performed, due to which thermal
stress have found using ANSYS software. Solid, multi cylinder and
hemisphere dish end are designed according to ASME and results are
compared with simulation software ANSYS and thermal analysis are
performed according to design temperate and results are imported in to
structural analysis to find out thermal stresses.
© 2013 International Journal of Advanced Research in Science and Technology (IJARST).
All rights reserved.
Keywords: Design, fem, solid, multi layer,
cylinder, hemisphere dish end,
couple field analysis, ANSYS
Introduction:
In thick walled cylinders subjected to internal
pressure only, it can be seen from the equation of the
hoop stress that the maximum stresses occur at the inside
radius and this can be given. It can be shown that for
large internal pressures in thick walled cylinders the wall
thickness is required to be very large. This is shown
schematically in figure.
Fig: 1. internal pressures V/s thickness
This means that the material near the outer edge of
the cylinder is not effectively used since the stresses near
the outer edge gradually reduce. In order to make thick-
walled cylinders that resist elastically large internal
pressure and make effective use of material at the outer
portion of the cylinder the following methods of
prestressing are used:
• Shrinking a hollow cylinder over the main cylinder.
(Compound cylinders)
• Multilayered or laminated cylinders.
An outer cylinder (jacket) with the internal diameter
slightly smaller than the outer diameter of the main
cylinder is heated and fitted onto the main cylinder.
When the assembly cools down to room temperature, a
compound cylinder is obtained. In this process the main
cylinder is subjected to an external pressure leading to
radial compressive stresses at the interface as shown in
figure
Fig: 2. internal cylinder
Int. J. Adv. Res. Sci. Technol. Volume 2, Issue2, 2013, pp 67-73.
www.ijarst.com S. Sanyasinaidu. et. al. Page | 68
Fig: 3. External cylinder
The outer cylinder is subjected to an internal
pressure leading to tensile circumferential Stresses at the
interface as shown in figure. Under these conditions as
the internal pressure increases, the compression in the
internal cylinder is first released and then only the
cylinder begins to act in tension.
Laminated cylinders:
The laminated cylinders are made by stretching
the shells in tension and then welding along a
longitudinal seam. This is shown in figure
Fig: 4. Laminated cylinder
In that laminated cylinder tangential stresses,
shrinkage stresses and warping stresses are developed
due to which we can find stresses distribution along each
layer of cylindrical shell.
Design of Thick Shell with Dish End:
A solid wall vessel consists of a single cylindrical
shell, with closed ends. Due to high internal pressure and
large thickness the shell is considered as a ‘thick’
cylinder design pressure has taken as 25 M.Pa, internal
radius 1000mm , thickness has found 227 mm to carry
specified pressure
Fig: 5. Solid pressure vessel
Material of Construction:
Vessel SA 515 GR 70
Dished Ends SA 515 GR 70
Allowable Stress value:
Vessel & Dished Ends - 125 N/mm2
The thickness of the Vessel is calculated from the
equation
= 227.74 mm
Design of Hemispherical Dished End:
The thickness of the dished end is given by
= 105.04mm
(Adopted Thickness of the dished end is, td = 227 mm)
C.A 1]- P)-(SJ
P)J (S[ R t i +
+=
3.0 1]- 25) - 1 x (125
25)1 x (125[ 1000 t +
+=
C.A P 0.2J S 2
R P t
i
d +−
=
0.3 25 x 0.2 1.0 x 125 x 2
1000 x 25 t d +
−=
Int. J. Adv. Res. Sci. Technol. Volume 2, Issue2, 2013, pp 67-73.
www.ijarst.com S. Sanyasinaidu. et. al. Page | 69
1
MN
MX
X
Y
Z
97.204
101.79106.377
110.964115.55
120.137124.723
129.31133.897
138.483
JUL 12 2013
23:40:24
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =.681708
SMN =97.204
SMX =138.483
Fig: 6. Total stresses developed in cylindrical shell
Fig: 7. Graph represents stresses developed along wall
thickness from inside.
1
MN
MXX
Y
Z
-24.466
-7.639.206
26.04242.877
59.71376.549
93.385110.221
127.056
JUL 12 2013
23:43:33
NODAL SOLUTION
SUB =1
TIME=1
/EXPANDED
SX (AVG)
RSYS=0
DMX =.681708
SMN =-24.466
SMX =127.056
Fig: 8. x-directional stresses in cylindrical shell
1
MN
MX
X
Y
Z
43.914
48.11552.315
56.51660.716
64.91769.117
73.31877.519
81.719
JUL 12 2013
23:55:44
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =5.328
SMN =43.914
SMX =81.719
Fig: 9. Total Stresses developed in hemisphere end
1
MN
MX
X
YZ
35.631
46.03956.447
66.85577.263
87.67198.079
108.487118.895
129.303
JUL 13 2013
00:07:47
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =.589994
SMN =35.631
SMX =129.303
Fig: 10. Stresses developed in cylinder and Hemisphere
ends (inside view)
1
MN
MX
X
YZ
35.631
46.03956.447
66.85577.263
87.67198.079
108.487118.895
129.303
JUL 13 2013
00:09:13
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =.589994
SMN =35.631
SMX =129.303
Fig: 11. Stresses developed in cylinder and Hemisphere
ends (Outside view)
1
99.934
103.557
107.18
110.803
114.426
118.049
121.672
125.295
128.918
132.541
136.166
0
605.128
1210.256
1815.384
2420.512
3025.64
3630.768
4235.896
4841.024
5446.152
6051.281
DIST
JUL 12 2013
23:42:25
POST1
STEP=1
SUB =1
TIME=1
PATH PLOT
NOD1=2
NOD2=1
SEQV
Int. J. Adv. Res. Sci. Technol. Volume 2, Issue2, 2013, pp 67-73.
www.ijarst.com S. Sanyasinaidu. et. al. Page | 70
Table: 1.
Theoretical
M.Pa
Ansys
M. Pa
Cylinder 125 127
Dish End 125 81 (For Adapted Thickness)
Cylinder +
Dish End 129
Fig: 12. Multi layer Pressure Vessel
The thickness of the shell is calculated from the
ASME modified membrane theory equation as
= 169.66 mm
Provided thickness, t = 162 mm (12 mm Liner) + 27
layers of 6 mm thick)
The Thickness of Liner (core Tube) = 12 mm
The Thickness of Each Layer = 6 mm
Number of Layers = 27
The thickness of the dished end is given by
= 105 mm
The adopted thickness of the dished end = 162 mm.
Tangential Stresses Due To Internal Pressure:
The tangential stress induced due to internal
pressure in the multi layer shell at different layers is
expressed by Seely,F.B., and Smith, A.O., as Tangential
stress developed in nth
layer due to internal pressure
Wrapping Stresses Due to Wrapping Pressure:
The wrapping stress in the layer “27thi" due to
wrapping pressure is given by the equation
= 0.429 N/mm2
Wrapping Stress on 27th
layer:
S = (0.429 * 1162) / 6 = 83.08 N/mm2
Shrinkage Stresses - Weld Shrinkage of Layers.
Stress in any layer due to welding other layers around it
is given by the equation
Where X = (Rn-1 + Rn-2)/2
Shrinkage Stress on 27th
layer.
Shrinkage Stress on 20th
layer due to welding of 21th
layer.
C.A P 0.6J S
R P t
i+
−=
3.0 25 x 0.61 x 165
1000 x 25 +
−=
C.A P 0.2J S 2
R P t
i
d +−
=
0.3 25 x 0.2 1.0 x 125 x 2
1000 x 25 t d +
−=
( ) 1X
R
RR
R P
2
2
o
2
i
2
o
2
ii
+
−=S
.16.1611006
1168
10001168
10005 Pa M 1
2
2
22
2 x2
LINER =
+
−=
)RR (R 4
)RR( )RR ( E K wn
2
1
2
2i
3
1i
2
1i
2
2i
2
1
2
1i1i −
−−=
++
++++ πP
t
PS
1i1ii
R ++=
R - R
R P
X
R1 S
n
i2
1
2
1i
2
1i 1i
2
2
1x ∑∑∑∑
++++
++++++++
++++−−−−====
2
x N/mm . S 000====
)10001168 ( 1162 4
)1162(1168 )10001162 ( 2.1e5 x 100.1x x 3
223
2222
−
−−=
πP
/ 42.24 37.2010001120
1120 x 0.456*
1117
10001 2
22
2
2
2
x mmNS −=
+
−
+−=
Int. J. Adv. Res. Sci. Technol. Volume 2, Issue2, 2013, pp 67-73.
www.ijarst.com S. Sanyasinaidu. et. al. Page | 71
1
JUL 13 2013
10:09:04
VOLUMES
TYPE NUM
Fig: 13. Multi layer planning in ANSYS geometric
model
1
MN
MX
X
Y
Z
-24.386
-3.96516.456
36.87757.297
77.71898.139
118.56138.98
159.401
JUL 13 2013
09:53:08
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SX (AVG)
RSYS=0
DMX =.923806
SMN =-24.386
SMX =159.401
Fig: 14. x-directional stresses developed in multi layer
cylinder
1
MN
MX
X
Y
Z
132.6
137.956143.313
148.669154.026
159.382164.738
170.095175.451
180.808
JUL 13 2013
09:54:02
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =.923806
SMN =132.6
SMX =180.808
Fig: 15. Total stresses developed in multi layered for
pressure cylinder
1
MN
MX
X
Y
Z
60.719
64.97669.234
73.49277.75
82.00786.265
90.52394.781
99.039
JUL 19 2013
21:47:36
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =.512157
SMN =60.719
SMX =99.039
Fig: 16. Total stresses developed in hemisphere end
multilayer vessel
1
MN
MX
X
YZ
56.497
68.89681.295
93.695106.094
118.493130.892
143.291155.69
168.089
JUL 13 2013
11:03:09
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =2.95
SMN =56.497
SMX =168.089
Fig: 17. Total stresses developed in multi layer cylinder
and hemisphere ends (inside view)
1
MN
MX
XY
Z
56.497
68.89681.295
93.695106.094
118.493130.892
143.291155.69
168.089
JUL 13 2013
11:04:09
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =2.95
SMN =56.497
SMX =168.089
Fig: 18. Total stresses developed in multi layer cylinder
and hemisphere ends (outside)
Int. J. Adv. Res. Sci. Technol. Volume 2, Issue2, 2013, pp 67-73.
www.ijarst.com S. Sanyasinaidu. et. al. Page | 72
Table: 2.
Theoretical
M.Pa
Ansys
M.Pa
Cylinder 165 168.401
Dish End 125
99 (For Adapted
Thickness)
Cylinder+
Dish End 168
1
MN
MX
X YZ
couple field analysis of solid shell
2757.333
87.667118
148.333178.667
209239.333
269.667300
JUL 13 2013
13:27:36
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP (AVG)
RSYS=0
SMN =27
SMX =300
Fig: 19. Temperature distribution along solid cylinder
and dish end
1
MN
MX
X
YZ
couple field analysis of solid shell
-27.231-7.717
11.79831.312
50.82770.341
89.856109.37
128.885148.399
JUL 13 2013
13:30:07
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SX (AVG)
RSYS=0
DMX =2.424
SMN =-27.231
SMX =148.399
Fig: 20. x- directional Thermal stresses in solid cylinder
hemisphere ends 1
MN
MX
X
YZ
couple field analysis for multilayer shell
45.29958.932
72.56486.197
99.83113.462
127.095140.728
154.36167.993
JUL 13 2013
13:14:48
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =7.183
SMN =45.299
SMX =167.993
Fig: 21. Stresses in multi layer cylinder and hemisphere
ends
1
MNMX
X
YZ
couple field analysis of solid shell
23.21935.562
47.90560.247
72.5984.932
97.275109.618
121.96134.303
JUL 13 2013
13:30:28
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SEQV (AVG)
DMX =2.424
SMN =23.219
SMX =134.303
Fig: 22. Thermal stresses in solid cylinder and
hemisphere ends
1
MN
MX
X
YZ
couple field analysis for multilayer shell
-29.192-5.004
19.18443.372
67.5691.748
115.936140.124
164.312188.5
JUL 13 2013
13:14:32
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
/EXPANDED
SX (AVG)
RSYS=0
DMX =7.183
SMN =-29.192
SMX =188.5
Fig: 23. X-directinal thermal stress in multilayer cylinder
hemisphere ends
Conclusions:
1. Replacing of multi cylinder instead of solid
cylinder to getting uniform stress distribution
over inside to outside wall.
2. According to design 25.55% of thickness is
reduced due to multi layer cylinder and dish end.
3. According to fabrication multi layer technique is
an easy process compared with solid cylinder.
4. Analysis software is used to perform all analysis
and compared with design results.
5. Deviation between analysis and design results is
in minimum.
6. All stress are in allowable limit of used material.
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Int. J. Adv. Res. Sci. Technol. Volume 2, Issue2, 2013, pp 67-73.
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