DESIGN OF THIN PRESSURE VESSELS FOR MECHANICAL ENGINEERS
DESIGN OF THIN PRESSURE
VESSELS FOR
MECHANICAL ENGINEERS
Thin vessels are common to process
industries. Examples of thin vessels are
LPG cylinder, boiler and distillation
column. Stresses are uniform in a thin
shell. Radial stress is neglected as
compared to hoop and longitudinal
stresses. Most common material of
construction is flange quality steel. These
vessel are riveted and welded. In high
temperature applications, like in a boiler,
riveted vessels are used. In majority of the
applications, welded vessels are in use.
These are designed on the basis of hoop stress.
DEFINITION OF A THIN PRESSURE VESSEL
Pressure vessel is a closed container having fluid under pressure.
Examples of pressure vessels
(a) Storage pressure vessels
LPG cylinder
Oxygen cylinder
Nitrogen cylinder
Hydrogen cylinder
Acetylene cylinder
LPG spherical shell
Automobile tires
Shaving cream cans
Tooth paste cans
(b) Process vessels
Autoclave—High pressure vessel with agitation and heating
Distillation tower
Absorption tower
Heat exchanger
Scrubbing tower
Mixing chamber
Boiler
Condenser
Evaporator
Drying chamber
(c) Power generating pressure vessels
Boilers
Furnace
Reactors
Practical Data on Pressure Vessels
Sr.No. |
Cylinder/Vessel |
Pressure |
Capacity |
Material |
1. |
Oxygen |
125 atm |
40.1 Lts |
Mild steel |
2. |
Nitrogen |
120 atm |
7 m3 |
m.s. |
3. |
C2H2 |
10 atm |
6 m3 |
m.s. |
4. |
LPG |
2.9 atm |
15 kg |
m.s. |
5. |
Cl2 |
14 to 17 atm |
60 kg |
m.s. |
6. |
Pressure cooker |
3.5 atm |
1,2,5,10—Lts |
Duralumin |
Table: Fuels, their minimum ignition temperature and theoretical flame temperatures
Sr. No. |
Type of gas |
Minimum ignition temperature, 0C |
Theoretical flame temperature, 0C |
1. |
H2 |
574 |
2142 |
2. |
Co |
609 |
2121 |
3. |
C2H2 |
429 |
— |
4. |
CH4 |
632 |
1918 |
5. |
C2H6 |
472 |
1949 |
6. |
C3H8 |
481 |
1967 |
7. |
C4H8 |
441 |
1973 |
8. |
H2S |
292 |
— |
SIZES OF PRESSURE VESSELS
(a) Minimum diameter = few mm
(b) Maximum diameter 50 m
LOCATION OF PRESSURE VESSELS
(a) Buried under ground
(b) Buried deep in oceans
(c) Positioned on ground
(d) Used in vehicles/aircrafts
(e) Used in houses
PRESSURE LIMITS FOR PRESSURE VESSELS
(a) Minimum 25 mm water gage
(b) Maximum=20000 atm
(c) Normal pressures =1 to 300 atm
(d) As per ASME code pressure > 1 atm and up to 200 atm
SHAPES OF PRESSURE VESSELS
(a) Cylindrical
(b) Spherical
(c) Conical
(d) Mixed shape
ORIENTATION OF PRESSURE VESSELS
(a) Horizontal
(b) Vertical
(c) Inclined
BASIS OF SELECTION OF PRESSURE VESSELS
(a) Safety
(b) Economics
Materials and Fabrication Methods
MATERIAL OF PRESSURE VESSELS
(a) Ferrous with Fe >50 %
(i) Carbon steels
(ii) Alloy steels
(iii) Stainless steels
(iv) Cast iron
(v) Wrought iron
(b) Non Ferrous Materials
(i) Aluminum
(ii) Copper
(iii) Nickel
(iv)Titanium
(v) Zirconium
(c) Non –Metallic Materials
(i) FRP-Fiber-reinforced plastic
(ii)Concrete vessels
FABRICATION METHODS
(i) Fusion welding: There are two processes in this.
(a) Gas welding for sheet of thickness gage 20, 21, 22 and of less thickness
(b) Arc welding most common because of less heat, reduction in oxidation, better control of deposited metal as compared to gas welding
(ii) Casting—(a) Cast iron small diameter and thin walled vessels
(b) cast steel-small diameter and thick walled vessels and also small pipe fittings
(iii) Forging—where thickness > 100 mm, for end closures, flanges and fittings
(iv) Machining—for matching parts, for flange faces, bushings and bearings
(v) Brazing and soldering—used with non-ferrous metals like copper, Monel metal and stainless steels
(vi) Sheet metal forming— used with non-ferrous metals like copper, Monel metal and stainless steels
(vii) Riveting—It is used with steel but now it is more common with non-ferrous materials like copper and aluminum
Definition of a sheet
SHEET when t < 6 mm (Normally thin walled pressure vessels)
PLATE when t > 6 mm ( Normally thick walled pressure vessels)
COMMONLY USED GAGE NUMBERS OF SHEETS
Gage No. Thickness of sheet
22 0.028” (0.7 mm)
20 0.035” (0.875 mm)
18 0.049” (1.225 mm)
16 0.065” (1.625 mm)
Definition of a plate
When thickness is > than 6 mm.
DESIGN OF THIN WALLED PRESSURE VESSELS
There are two types of thin walled pressure vessels.
(i) Welded pressure vessels
(ii) Riveted pressure vessels
Design of a pressure vessel consists of two parts.
-
Shell design
-
Design of Head(s) or End Closure(s)
Shell design includes selection of
(i) Material of construction
(ii) Method of manufacture
(iii) Diameter and length of shell
(iv) Number of cylindrical portions to make the full length pressure vessel
(v) Wall thickness
(vi) Type of longitudinal joint
(vii) Type of circumferential joint
Design of head includes
(i) Type of head
(ii) Decide whether Convex or concave side of head faces the pressure side
(iii) Head thickness
(iv) Crown radius
(v) Knuckle radius
(vi) Depth of dish
(vii) Straight flange length
Design of Thin Walled Welded Pressure Vessels
Shell Design
(a) Selection of the material of construction: Flange quality steel
(b) Selection of the method of fabrication: Rolling and welding
(c) Selection of length and inside diameter from volume
V= (π/4) Di2L,
assuming L/Di ratio, L and Di is calculated
(d) Number of shells (or courses)
Maximum length of one shell is 2m. Therefore, number of courses, n=L/2.
n will have a larger value if length of one course selected is less than 2 m. Normally length one shell is much less than 2 m because of lesser cost.
(e) Wall thickness (uses mean diameter)
t= [pi Dm/2σ] + C
T = [pi (Di +t)/2σ], Dm is the mean diameter
t = [piDi/ (2ση–pi)] + C
Where σ is allowable stress and is found from the relation
σ = σult Fs Fm Fr Fa
σult = Ultimate tensile stress =300 t0 500 MN/m2 for flange quality steel
Fs = % of ultimate stress allowed
Its value depends on maximum operating temperature. it is found from a table given in design books. Higher is the temperature, lower will be the value of Fs.
Fm = Material factor depending on the grade of the material,
Its value is Fm =0.92 for structural steel. Structural steel not used in pressure vessels
Fm =0.98 for flange quality steel
Further Fm = 1.0 for firebox quality of steel
Fr = Stress relieving factor, if internal stresses due to fabrication/heat treatment/welding are released by annealing. Its value is 1.06. For wall thickness > 31 mm, it is compulsory to carry out stress relieving. If no stress relieving carried out, its value is 1.0.
Fa = Radio-graphing factor
It is regarding testing of welded joints for defects with X-Rays. This includes subsequent treatment till joint becomes defect less. Its value is 1.12. Radio-grapy of the welded joint is highly desirable. It is compulsory for wall thickness > 31 mm. If no radio-grapy is carried out, then its value is 1.0.
(f) Selection of the Type of longitudinal joint
Longitudinal joint is normally butt joint. It has to be strong as it is subjected to hoop stress. Hoop stress is the highest in pressure vessels.
(g) Selection of the Type of Circumferential Joint (round joint)
Normally it is a lap joint because it is subjected to longitudinal stress which is a lower stress.
DESIGN OF HEAD
The end closure of the pressure vessel is called the HEAD.
Types of head
(a) Flat heads
(b) Flanged and shallow dished head L > Do, used up to 2 atm pressure
For example, Do= 1800 mm, L = 3000 mm and icr=2th,
(c) Flanged and standard dished when L < Do, used up to 2 atm pressure
For example for D = 1800 mm, L = 1650 and icr = 2th.
(d) Flanged and dished head (tori-spherical head), used up to 12 atm pressure
For example for D = 1800 mm, L = 1650 and icr = 3th.
(e) Elliptical flanged and dished head, used up to 12 atm pressure
(f) Hemispherical head, used up to 25 atm pressure
(g) Conical head, used in special applications
Design decides whether
(h) Convex side faces the pressure side
(i) Concave side faces the pressure side
PARAMETERS IN THE DESIGN OF HEAD
(j) head thickness
(k)crown radius
(l) knuckle radius
(m) depth of dish
(n) length of straight flange
WHEN CONCAVE SIDE OF HEAD FACES THE PRESSURE SIDE
th = (pi L W/2 σ η) + C
Where L is crown radius
W is the factor, it depends on the ratio of mean knuckle radius to mean crown radius. It is found from a standard table.
σ is allowable stress, already found in the design of shell
η is the efficiency of any joint in the head itself. It will be applicable only for big size of head when it cannot be made from a single sheet.
C is the corrosion allowance, normally 1.5 mm
WHEN CONVEX SIDE OF HEAD FACES THE PRESSURE SIDE
th = (pi L W/2 σ η) x (5/3) + C
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