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By Terence James Haydock

Pressure VesselA simulated response in ANSYS

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Overview• Introduction

• Required Knowledge

• Key Equations

• Tutorial / Methodology

Engineering Data

Geometry

Model

Setup

Solution

Results

• Summary

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Introduction

Aim: To design a steel pressure vessel and subject it to an internal

pressure of 100MPa. A finite element analysis is to be carried out

in ANSYS and will show the stress responses of the simulation.

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Required Knowledge

Strength of cylinders subjected to internal pressure: When designing a cylinder to withstand internal pressure there are three key questions that need to be answered so as to choose the right formula, these are –

1. The kind of material i.e. brittle or ductile? (Cast iron, steel etc. are brittle. Brass, bronze etc. are ductile)2. Open or closed cylinder ends/caps?3. Is the cylinder classed as a thin or thick walled cylinder? (ratio of wall thickness to inside dia. Is <=0.1 for thin walled, >0.1 for thick walled cylinder.

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Key Equation’s for Design

• Thin walled cylinders:

σa = stress in axial direction (MPa)pi = internal pressure in the cylinder (MPa)po = external pressure in the cylinder (MPa)di = internal diameter of cylinder (mm)

𝑡=𝐷𝑝2𝑆

• Thick walled cylinder (brittle) open or closed: Lame’s equation is applied.

do = external diameter of tube or cylinder (mm)t = wall thickness (mm)u = poisson’s ratio (typically 0.3)S = allowable stress (MPa)

• Thick walled cylinder (ductile) closed ends: Clavarino’s equation is applied.

• Thick walled cylinder (ductile) open ends: Birnie’s equation is applied.

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Tutorial

The vessel in question is subjected to an internal pressure of

100MPa. It has an outer diameter of 500mm, a total height of

700mm and a wall thickness of 25mm. The interior wall surface has

a 25mm fillet radius to provide a smooth transition to the end caps.

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ANSYS Methodology

Engineering Data

Geometry/Sketch

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• Sketch and revolve

• What do you notice?

• The vessel has planes of

symmetry above and

below its mid-point. As

such, you need only

analyze the top or

bottom of the vessel!

Generate 3D Model

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• We can take our simplification even further.

• Once you have split the vessel, the same method can

be applied again, only this time we can section into quarters.

• As shown, we scale down the dimensions, though this

time we revolve at 90⁰, instead of the previous 360⁰

Simplify were possible

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Mesh and Refine your Part

Mesh with the default values i.e. Advanced

size function OFF

Change to FIXED

Change to On: Proximity

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Provide a frictionless support to three

surfaces

Provide a pressure to the inside surfaces

with a magnitude of 100MPa

Apply Boundary Conditions

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σc = [(pi ri2 - po ro

2) / (ro2 - ri

2)] - [ri2 ro

2 (po - pi) / (r2 (ro2 - ri

2))]    

1) Stress in Circumferential Direction (Hoop Stress) (x-axis)

3) Stress in Radial Direction (z-axis)

σr = [(pi ri2 - po ro

2) / (ro2 - ri

2)] + [ri2 ro

2 (po - pi) / r2 (ro2 - ri

2)]  

σa = (pi ri2 - po ro

2 )/(ro2 - ri

2)

2) Stress in Axial Direction (y-axis)

σa = stress in axial direction (MPa)pi = internal pressure in the tube or cylinder (MPa)po = external pressure in the tube or cylinder (MPa)ri = internal radius of tube or cylinder (mm)ro = external radius of tube or cylinder (mm)

Check Your Results in Theory

1)

2)

3)

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Hoop Stress (x-direction)

Axial Stress (y-direction)

Radial Stress (z-direction)

Generate your Results

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Compare Results

Theory ANSYS % error

Hoop (x) MPa

Axial (y) MPa

Radial (z) MPa

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Summary

Through this tutorial a number of key issues have been addressed with regards to the design and analysis of pressure vessels. 1. Materials2. Construction3. Thick or Thin walled4. Various formula have been presented to help determine the

right course of action in designing for wall thickness5. Various formula have been presented to help determine the

stress generated in the x, y, and z direction6. Numerical (ANSYS) and analytical methods for results

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References

1. Oberg. E. et al. Machinery’s Handbook 28th Edition, 2008

Industrial Press INC, New York

2. Lawrence. K. ANSYS Workbench Tutorial, 2007

SDC Publications