Pressure Vessel Design for HPgTPC Prashant Kumar, Vikas Teotia, Sanjay Malhotra Bhabha Atomic Research Centre Trombay, India
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 To minimise local stresses at junction: ASME Specifies As > is Compressive 1. Knuckle radius > = 6 % of Rc 2. Crown radius < 0.8 to 0.9 of ID Therefore, there will be localised stress and Buckling 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
Reduction of localized stresses at Knuckle / Cont.… R350 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
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
Ellipsoidal Head Design At Equator At Crown Courtesy: Theory and Design of Pressure Vessels by John F. Harvey
Ellipsoidal Head Design Thickness of Head = 40 mm 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
Ellipsoidal Head Design / Cont... a = 2862.5 b = 2000 a / b = 1.43 Thickness of Head = 35 mm Deflection = 3.9 mm Stress = 59.66 Mpa Yield Strength = 205 Mpa Material = Equivalent to Al 5083 Design Factor = 3.4 For 0.7 – 1.5 Mpa Design Pressure Most Preferred
Comparison of Ellipsoidal Heads a = 2862.5 mm a = 2862.5 mm a = 2862.5 mm b = 1431.25 mm b = 2000 mm b = 954 mm a / b = 2 a / b = 1.43 a / b = 3 Deflection = 3.9 mm Deflection = 9.5 mm Deflection = 23.87 mm Stress = 59.66 Mpa Stress = 107.287 Mpa Stress = 259 Mpa Yield Strength = 205 Mpa Yield Strength = 205 Mpa Yield Strength = 205 Mpa Thickness of Head = 35 mm Thickness of Head = 35 mm Thickness of Head = 35 mm Material = Equivalent to Al Material = Equivalent to Al Material = Equivalent to Al 5083 5083 5083
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 Deflection = 3.556 mm 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 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 = a r = 3a How Far to reinforce ?
Nozzle Reinforcement Analysis • 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 Deflection = 2.9 mm Up to 2r from the 600 mm center Maximum Von Mises Stress = 55.386 Mpa 0.25r along the Yield Strength = 205 Mpa nozzle Design Factor = 3.7 600 mm
Saddle Support Analysis Deflection = 0.508 mm Saddle Contact Angle = 120 Degree Maximum Von-Mises Stress = 20.709 Mpa Approximate Weight of Vessel Yield Strength = 205 MPa including Heads = 22 Ton Material = Equivalent to Al 5083 Total Weight of Support = 675 Kg Design Factor = 9.9 Conclusion: Over-conservative
Saddle Support Optimization Analysis Deflection = 8.8 mm Saddle Contact Angle = 120 Degree Maximum Von-Mises Stress = 38.479 Mpa Approximate Weight of Vessel Yield Strength = 205 MPa including Heads = 22 Ton Thickness of Head = 35 mm Total Weight of Support = 470 Kg Material = Equivalent to Al 5083 Design Factor = 5.3
Saddle Support Optimization Analysis Deflection = 1.69 mm Saddle Contact Angle = 120 Degree Maximum Von-Mises Stress = 17.033 Mpa Approximate Weight of Vessel Yield Strength = 205 MPa including Heads = 22 Ton Thickness of Head = 35 mm Total Weight of Support = 488 Kg Material = Equivalent to Al 5083 Design Factor = 12 187 Kg Materials is saved compared to previous Design
Support Optimization / Cont.… Deflection = 5.894 mm Saddle Contact Angle = 120 Degree Maximum Von-Mises Stress = 59.587 Mpa Approximate Weight of Vessel Yield Strength = 206.8 MPa including Heads = 22 Ton Material = AISI 304 Total Weight of Support = 436 Kg Design Factor = 3.4 Further 52 Kg Materials is saved compared to previous Design
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
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