chapter 5 PRESSURE VESSELDesign and .pptx

chapter 5 pressure vessel

1. CHAPTER 5 PRESSURE VESSEL

2. Pressure Vessels Pressure vessels are containers, used to store fluids at higher pressure than the ambient. They are used in a variety of industries like Petroleum refining Chemical Power Food & beverage Pharmaceutical 2

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4. TYPES OF PRESSURE VESSELS Pressure vessels can be cylindrical or spherical by construction. Pressure vessels can be thin-walled or thick-walled . If the wall thickness ( t) is less than 1/10 of the internal diameter (d i ) and/or the internal pressure (p i ) is less than 1/6 of the allowable stress of the vessel material, it is called thin-walled otherwise it is called thick-walled . 4

5. 5 There are three main types of pressure vessels based on their orientation: Horizontal Pressure Vessels Vertical Pressure Vessels Spherical Pressure vessels However there are some special types of Vessels like Regeneration Tower , Reactors, Boilers but these names are given according to their use only.

6. Horizontal pressure vessel 6

7. Vertical pressure vessel The max. Shell length to diameter ratio for a small vertical drum is about 5 : 1 7

8. Spherical Pressurized Storage Vessel 8

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 attached equipment (piping, decks, ladders, etc ) Stresses at geometric discontinuities Bending moments due to Wind & snow loads Thermal expansion, Seismic loads Cyclic loads due to pressure or temperature changes Residual stresses from manufacture . 9

10. Potential Failure Modes ` Depending upon the application, the pressure level, the temperature level, the environment, and the composition of the pressurizing fluid , pressure vessels are vulnerable to potential failure by many possible modes. PV failure might occur by yielding, ductile rupture, brittle fracture , fatigue (including low-cycle, thermal, or corrosion fatigue), stress corrosion-cracking , creep , or combined creep and fatigue . 10

11. Design pressure Normal operating pressure: The expected pressure at which the process usually be operated. Maximum operating pressure: The highest pressure expected including upset conditions such as startup, shutdown, emergency shutdown. Design pressure: Maximum operating pressure plus a safety margin. Margin is typically 10% of maximum operating pressure. Usually specify pressure at top of vessel, where relief valve is located. 11

12. Design Temperatures Maximum: Highest mean metal temperature expected in operation, including transient conditions, plus a margin Margin is typically plus 50  F/10 degree centigrade. Minimum: Lowest mean metal temperature expected in operation, including transient conditions, upsets, auto-refrigeration, climatic conditions, anything else that could cause cooling, minus a margin Margin is typically -25 F MDMT: minimum design metal temperature is important as metals can become brittle at low temperatures . 12

13. Design of Thin-Walled Pressure Vessel In a thin cylinder subjected to an internal pressure, three principal stresses are induced in circumferential, axial and radial directions namely: circumferential or tangential or hoop stress (  h ) , longitudinal or axial stress (  l ) , radial stress ( r ) The magnitude of radial stress is equal to the internal pressure at the inner surface and zero at the outer surface of the cylinder. 13

14. 14 In thin cylinder, the internal pressure is small, the radial stress is also small and hence can be neglected . Hence, the thin cylinder is considered to be subjected to  h and  l . It is assumed that theses stresses are constant through out the thickness of the cylinder.

15. A thin-walled pressure vessel is mainly subjected to fluid (gas) force in the longitudinal (axial) ‘x’ direction due to longitudinal stress (  l ) And in the transverse ‘y’ direction due to hoop stress (  h ). 15

16. Stresses in Thin Cylindrical Shell due to an Internal Pressure The analysis of stresses induced in a thin cylindrical shell are made on the following assumptions: The effect of curvature of the cylinder wall is neglected. The tensile stresses are uniformly distributed over the section of the walls. The effect of the restraining action of the heads at the end of the pressure vessel is neglected. 16

17. When a thin cylindrical shell is subjected to an internal pressure, it is likely to fail in the following two ways: along the longitudinal section (i.e. circumferentially) splitting the cylinder into two troughs, across the transverse section (i.e. longitudinally) splitting the cylinder into two cylindrical shells. 17

18. Circumferential or hoop stress, When a thin cylindrical shell subjected to an internal pressure, a tensile stress acting in a direction tangential to the circumference is called circumferential or hoop stress. 18

19. Total force acting on a longitudinal section (i.e. along the diameter X-X) of the shell, = Intensity of pressure × Projected area = P × A = p× d× l ……….....( i ) Where, p = Intensity of internal pressure, d = Internal diameter of the cylindrical shell, l = Length of the cylindrical shell, t = Thickness of the cylindrical shell, and Total resisting force acting on the cylinder walls; = σ h × 2t× l (b/c of two sections) ……..(ii ) where, σ h = hoop stress for the material of the cylindr shell . 19

20. From equations ( i ) and (ii), we have; σ h × 2t× l = p× d× l or …….( iii)   20 (b) Longitudinal Stress Consider a closed thin cylindrical shell subjected to an internal pressure as shown below. A tensile stress acting in the direction of the axis is called longitudinal stress.

21. Let σt2 = Longitudinal stress. In this case, the total force acting on the transverse section (i.e. along Y-Y) = Intensity of pressure × Cross-sectional area ………………………..( i ) And total resisting force = σ t2 × π d.t …….(ii) From equations ( i )and (ii), we have σ l × π d.t ……………………….(iii) or   21

22. Thick Cylindrical Shells Subjected to an Internal Pressure When a cylindrical shell of a pressure vessel, hydraulic cylinder, gun barrel and a pipe is subjected to a very high internal fluid pressure, then the walls of the cylinder must be made extremely thick. In thick wall cylinders, the stress over the section of the walls cannot be assumed to be uniformly distributed.

23. We see that the tangential stress is maximum at the inner surface and minimum at the outer surface of the shell. The radial stress is maximum at the inner surface and zero at the outer surface of the shell.

24. In the design of thick cylindrical shells, the following equations are mostly used: Lame’s equation; Birnie’s equation; Clavarino’s equation; and Barlow’s equation. The use of these equations depends upon the type of material used and the end construction .

25. Lame’s equation . Assuming that the longitudinal fibers of the cylindrical shell are equally strained, the tangential stress at any radius x is : And radial stress at any radius x:  

26. Since we are concerned with the internal pressure (pi = p) only, therefore substituting the value of external pressure, po = 0. ∴ Tangential stress at any radius x, And radial stress at any radius x,

27. We know that the tangential stress is; maximum at the inner surface of the shell (when x= ri ) and minimum at the outer surface of the shell ( when x = ro ).

28. In designing a thick cylindrical shell of brittle material (e.g. cast iron, hard steel and cast aluminum) with closed or open ends and in accordance with the maximum normal stress theory failure, the tangential stress induced in the cylinder wall, Since ro = ri + t, therefore substituting this value of ro in the above expression, we get;

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