1. Prepared By Batch B of ME-1
Pressure Vessels
Prepared By
Batch B of ME-1

2. Cylinder
Cylinder is a mechanical device used for storing ,receiving processing the fluid.
Cylinder may be:
Pressure vessel
Storage vessel
Pipe
Engine cylinder
Thin Cylinder :- If The ratio of Di / t > 20
Thick cylinder :- if the ratio Di / t> 20

3. Stress in Thin Cylinder
Inside diameter, D
Forces due to internal pressure are balanced by shear stresses in wall
Horizontal section:
Vertical section:
Similar equations can be derived for other geometries such as heads (see Ch 13)
Wall thickness, t
Height, h L H
Longitudinal stress, L
Hoop stress, H

4. Stress in Thin Cylinder 1
Stress in Thin Cylinder 1.The tangential or hoop stress is given by: tl = Liner thickness (m) sc= Permissible cicumferential stress (kN/m2) Pmax= Maximum combustion Pressure (kPa) D = Inner liner Diameter (m)

5. 2. Longitudinal stress Stress in Thin Spherical Shell:- =PiDi / 4t

6. Stress in Thick cylinder
A Cylinder subjected to internal pressure:
In case of where Po =0
Cylinder subjected only internal pressure
Where ,b= outer radius
a= inner radius
= tangential stress

7. 2. Cylinder subjected to external pressure:
When internal pressure is zero and Cylinder subjected to only external pressure Po,

8. Failure of Materials
Failure of materials under combined tensile and shear stresses is not simple to predict. Several theories have been proposed:
Maximum Principal Stress Theory
Component fails when one of the principal stresses exceeds the value that causes failure in simple tension
Maximum Shear Stress Theory
Component fails when maximum shear stress exceeds the shear stress that causes failure in simple tension
Maximum Strain Energy Theory
Component fails when strain energy per unit volume exceeds the value that causes failure in simple tension

9. Loads Causing Stresses on Pressure Vessel Walls
Internal or external pressure
Dead weight of vessel
Weight of contents under normal or upset conditions
Weight of contents during hydraulic testing
Weight of internals
Weight of attached equipment (piping, decks, ladders, etc)
Stresses at geometric discontinuities
Bending moments due to supports
Thermal expansion, differential thermal expansion
Cyclic loads due to pressure or temperature changes
Wind & snow loads
Seismic loads
Residual stresses from manufacture
Loads due to friction (solids flow)
All these must be combined to determine principal stresses

10. Lame Equation

13. Autofrettage
The second method for inducing residual stresses in a cylinder is autofrettarage.
If a monobloc, thick-walled cylinder is subjected to an internal pressure exceeding its "idle pressure, plastic deformation will initiate at the bore and, as the pressure is increased, will proceed through the cylinder wall until the plastic-elastic interface reaches the outside surface.
At this point, the cylinder material is in a completely plastic state which is defined as complete overstrain, and the associated pressure referred to as the complete overstrain or collapse pressure.
The effect of exceeding this pressure and the problem of rupture will be discussed later under "Effect of Material Behavior".

14. Due to elastic recovery, when the internal pressure is
released after either partial or complete overstrain, the material near the outside surface, which has been deformed the least amount, will attempt to return. to its original diameter and the material near the bore, which has been deformed the must, will attempt to remain deformed.
This results in a residual compressive stress at the bore and a residual tensile stress at the outside surface with a gradual transition through the wall thickness. The process of producing this residual stress distribution by means of plastic deformation of the cylinder by internal pressure known as autofrettage.

15. COMPOUND CYLINDERS
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 by:

16. This means that as pi increases t may exceed yield stress even when pi< yield. Furthermore, it can be shown that for large internal pressures in thick walled cylinders the wall thickness is required to be very large.

17. 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 (Pc)

18. Compound cylinders

19. The tangential stress at any radius r for a cylinder open at both ends and subjected to internal pressure (Birnie’s equation)

20. The tangential stress at the inner surface of the inner cylinder
The tangential stress at the outer surface of the inner cylinder

21. The tangential stress at the inner surface of the outer cylinder,
The tangential stress at the outer surface of the outer cylinder,

22. Total shrinkage allowance when two cylinders are made of two different materials,

23. 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,

24. Gasketed Joints
Used when vessel must be opened frequently for cleaning, inspection, etc.
Also used for instrument connections
Not used at high temperatures or pressures (gaskets fail)
Higher fugitive emissions than welded joints

25. Full face gasket
Gasket within bolt circle
Spigot and socket
O-ring

26. Pressure Vessel
Pressure vessel are container or pipe line for storing , receiving or carrying the fluids under a pressure.
Unfired pressure vessel are: storage vessel ,reaction vessel , heat exchanger , evaporator
Other: Steam boiler, nuclear pressure vessel

27. Type of Welded Joints in pressure vessel
Some weld types are not permitted by ASME BPV Code
Many other possible variations, including use of backing strips and joint reinforcement
Sec. VIII Div. 1 Part UW has details of permissible joints, corners, etc.
Welds are usually ground smooth and inspected
Type of inspection depends on Code Division
Butt weld
Double welded
butt weld
Single fillet
lap weld
Double fillet
lap weld
Double fillet
corner joint

28. Materials Selection Criteria
Safety
Material must have sufficient strength at design conditions
Material must be able to withstand variation (or cycling) in process conditions
Material must have sufficient corrosion resistance to survive in service between inspection intervals
Ease of fabrication
Availability in standard sizes (plates, sections, tubes)
Cost
Includes initial cost and cost of periodic replacement

29. Commonly Used Materials
Steels
Carbon steel, Killed carbon steel – cheap, widely available
Low chrome alloys (<9% Cr) – better corrosion resistance than CS, KCS
Stainless steels:
304 – cheapest austenitic stainless steel
316 – better corrosion resistance than 304, more expensive
410
Nickel Alloys
Inconel, Incolloy – high temperature oxidizing environments
Monel, Hastelloy – expensive, but high corrosion resistance, used for strong acids
Other metals such as aluminum and titanium are used for special applications. Fiber reinforced plastics are used for some low temperature & pressure applications. See Ch 7 for more details

30. Some Maximum Allowable Stresses Under ASME BPV Code Sec. VIII D
Some Maximum Allowable Stresses Under ASME BPV Code Sec. VIII D.1, Taken From Sec. II Part D

31. Vessel Orientation Usually vertical
Easier to distribute fluids across a smaller cross section
Smaller plot space
Reasons for using horizontal vessels
To promote phase separation
Increased cross section = lower vertical velocity = less entrainment
Decanters, settling tanks, separators, flash vessels
To allow internals to be pulled for cleaning
Heat exchangers

32. Design for Internal Pressure
ASME BPV Code Sec. VIII D.1 specifies using the larger of the shell thicknesses calculated
For hoop stress
or for longitudinal stress
Where,
Values of S are tabulated in ASME BPV Code Sec.II for different materials as function of temperature
S is the maximum allowable stress
E is the welded joint efficiency

33. Head (Closure) Designs
Hemispherical
Good for high pressures
Higher internal volume
Most expensive to form & join to shell
Half the thickness of the shell
Ellipsoidal
Cheaper than hemispherical and less internal volume
Depth is half diameter
Same thickness as shell
Most common type > 15 bar
Torispherical
Part torus, part sphere
Similar to elliptical, but cheaper to fabricate
Cheapest for pressures less than 15 bar

34. Closures Subject to Internal Pressure
Hemispherical heads
Ellipsoidal heads
Torispherical heads
Rc is the crown radius

35. Vessel Supports Supports must allow for thermal expansion in operation
Smaller vessels are usually supported on beams – a support ring or brackets are welded to the vessel
Horizontal vessels often rest on saddles
Tall vertical vessels are often supported using a skirt rather than legs. Can you think why?

36. Vessel Supports
Note that if the vessel rests on a beam then the part of the vessel below the support ring is hanging and the wall is in tension from the weight of material in the vessel, the dead weight of the vessel itself and the internal pressure
The part of the vessel above the support ring is supported and the wall is in compression from the dead weight (but probably in tension from internal pressure)

37. Nozzles Vessel needs nozzles for More nozzles = more cost
Feeds, Products
Hot &/or cold utilities
Manways, bursting disks, relief valves
Instruments
Pressure, Level, Thermowells
Sample points
More nozzles = more cost
Nozzles are usually on side of vessel, away from weld lines, usually perpendicular to shell
Nozzles may or may not be flanged (as shown) depending on joint type
The number & location of nozzles are usually specified by the process engineer

38. Nozzle Reinforcement
Shell is weakened around nozzles, and must also support eccentric loads from pipes
Usually weld reinforcing pads to thicken the shell near the nozzle. Area of reinforcement = or > area of nozzle: see Code requirements

39. Swaged Vessels Vessel does not have to be constant diameter
It is sometimes cheaper to make a vessel with several sections of different diameter
Smaller diameters are usually at the top, for structural reasons
ASME BPV Code gives rules for tapered sections

40. Jacketed Vessels
Heating or cooling jackets are often used for smaller vessels such as stirred tank reactors
If the jacket can have higher pressure than the vessel then the vessel walls must be designed for compressive stresses
Internal stiffening rings are often used for vessels subject to external pressure
For small vessels the walls are just made thicker