Prashant Kumar, Vikas Teotia, Sanjay Malhotra
Bhabha Atomic Research Centre Trombay, India
Pressure Vessel Design for HPgTPC
Topics discussed in previous meeting on 31.5.19
• Alloys of Al 5083
• Pressure Vessel Thickness calculations by a. Design rule
and b. design by analysis
• Deflection and Stress calculation of Pressure Vessel with
Hemispherical closure were presented
Outline of presentation
• Pressure Vessel Shell thickness calculation
• Design and Analysis for Torispherical Head
• Design and Analysis for Elliptical Head
• Comparison of Elliptical Heads based on ratio of Major to Minor axis
• Analysis of Support for Pressure Vessel
• Summary
• Future Work
Pressure Vessel with Torispherical Closure
40
Torispherical Head Design
Stresses at Junction of Crown and Knuckle
Stresses at Junction of Crown
As > is Compressive
Therefore, there will be localised
stress and Buckling
To minimise local stresses at junction:
ASME Specifies
1. Knuckle radius > = 6 % of Rc
2. Crown radius < 0.8 to 0.9 of ID
Reference: UG-32 of ASME Section VIII Div 1
Torispherical Head Design
Deflection = 6.086 mm
Stress = 143.482 MPa
Crown Radius = 5152.5 mm
Knuckle Radius = 343.5 mm
Thickness of Head = 45 mm
Yield Strength = 205 MPa
Material = Equivalent to Al 5083
Design Factor = 1.4
Small Knuckle > Higher Localized stresses
Deflection = 5.074 mm
Stress = 121.243 Mpa
Yield Strength = 205 Mpa
Thickness of Head = 45 mm
Design Factor = 1.7
Material = Equivalent to Al 5083
Reduction of localized stresses at Knuckle / Cont.…
R350
Stress Conc. at Junction of Flange & Knuckle end
Deflection = 4.998 mm
Stress = 85.955 Mpa
Yield Strength = 205 Mpa
Inner Rc = 5152.5 mm
Inner Rk = 350 mm
Design Factor = 2.4
At Crown
At Equator
Ellipsoidal Head Design
Courtesy: Theory and Design of Pressure Vessels by John F. Harvey
Ellipsoidal Head Design
a = 2862.5
b = 2000
a / b = 1.43
Deflection = 3.43 mm
Von-Mises Stress = 52.375 Mpa
Yield Strength = 205 Mpa
Material = Equivalent to Al 5083
Design Factor = 3.9
Thickness of Head = 40 mm
Deflection = 3.9 mm
Stress = 59.66 Mpa
Yield Strength = 205 Mpa
Material = Equivalent to Al 5083
Design Factor = 3.4
a = 2862.5
b = 2000
a / b = 1.43
Ellipsoidal Head Design / Cont...
Thickness of Head = 35 mm
For 0.7 – 1.5 Mpa Design Pressure
Most Preferred
Deflection = 23.87 mm
Stress = 259 Mpa
Yield Strength = 205 Mpa
Thickness of Head = 35 mm
Material = Equivalent to Al
5083
a = 2862.5 mm
b = 1431.25 mm
a / b = 2
a = 2862.5 mm
b = 2000 mm
a / b = 1.43
Deflection = 3.9 mm
Stress = 59.66 Mpa
Yield Strength = 205 Mpa
Thickness of Head = 35 mm
Material = Equivalent to Al
5083
a = 2862.5 mm
b = 954 mm
a / b = 3
Deflection = 9.5 mm
Stress = 107.287 Mpa
Yield Strength = 205 Mpa
Thickness of Head = 35 mm
Material = Equivalent to Al
5083
Comparison of Ellipsoidal Heads
Vessel Assembly with Ellipsoidal Head
Maximum Von
Mises Stress =
62.226 Mpa
Yield Strength
= 205 MPa
Maximum
Deflection =
4.234 mm
Ellipsoidal Head with Nozzle
Without Nozzle Stress = 52.375 Mpa
With Nozzle Stress = 95.792 Mpa
Yield Strength = 205 Mpa
Thickness of Head = 35 mm
Material = Equivalent to Al 5083
Design Factor = 2.1
Deflection = 3.556 mm
Remarks: Not Satisfying ASME Section VIII Div I Criteria
Therefore, Reinforcement near the Nozzle Section required
Stress Conc. around circular hole in Cylindrical Shell
2.5 σ
1.006 σ
r = 3a
r = a
How Far to reinforce ?
Nozzle Reinforcement Analysis
Maximum Von Mises Stress = 55.386 Mpa
Yield Strength = 205 Mpa
Design Factor = 3.7
• Shell is weakened around nozzles, and must
also support eccentric loads from pipes
• Principle of Area Compensation
• Usually weld reinforcing pads to thicken the
shell near the nozzle. Area of reinforcement
= or > area of nozzle
600 mm
600 mm
Deflection = 2.9 mm
Up to 2r from the
center
0.25r along the
nozzle
Deflection = 0.508 mm
Maximum Von-Mises Stress = 20.709 Mpa
Yield Strength = 205 MPa
Material = Equivalent to Al 5083
Design Factor = 9.9
Saddle Support Analysis
Conclusion: Over-conservative
Saddle Contact Angle = 120 Degree
Approximate Weight of Vessel
including Heads = 22 Ton
Total Weight of Support = 675 Kg
Deflection = 8.8 mm
Maximum Von-Mises Stress = 38.479 Mpa
Yield Strength = 205 MPa
Thickness of Head = 35 mm
Material = Equivalent to Al 5083
Design Factor = 5.3
Saddle Support Optimization Analysis
Saddle Contact Angle = 120 Degree
Approximate Weight of Vessel
including Heads = 22 Ton
Total Weight of Support = 470 Kg
Saddle Support Optimization Analysis
Deflection = 1.69 mm
Maximum Von-Mises Stress = 17.033 Mpa
Yield Strength = 205 MPa
Thickness of Head = 35 mm
Material = Equivalent to Al 5083
Design Factor = 12
Saddle Contact Angle = 120 Degree
Approximate Weight of Vessel
including Heads = 22 Ton
Total Weight of Support = 488 Kg
187 Kg Materials is saved compared to previous Design
Deflection = 5.894 mm
Maximum Von-Mises Stress = 59.587 Mpa
Yield Strength = 206.8 MPa
Material = AISI 304
Design Factor = 3.4
Saddle Contact Angle = 120 Degree
Approximate Weight of Vessel
including Heads = 22 Ton
Total Weight of Support = 436 Kg
Further 52 Kg Materials is saved compared to previous Design
Support Optimization / Cont.…
Summary and Conclusion
• Shell Thickness calculation done for Al 5083
• Initial Torispherical Head Design were carried out
• Initial Ellipsoidal Head Design were carried out
• Analysis for Nozzle reinforcement done partially
• Pressure Vessel Support System have been optimized
Note: In all calculation Joint efficiency were considered 1
Future Work
• Shell thickness calculation to be tried with other competing materials
• Rigorous analysis for both Torispherical Head & Ellipsoidal Design
to be carried out (Design by Rules & Design by Analysis)
• Nozzle reinforcement to be detailed (Design by Rule in particular)
• More configuration for Pressure Vessel Support System can be tried
• Joint Efficiency to be considered as per ASME BPV Code in further
calculation
Thank You
For
Your Kind Attention
