pressure vessel design for hpgtpc•pressure vessel thickness calculations by a. design rule ......
TRANSCRIPT
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