1 by terence james haydock pressure vessel a simulated response in ansys
TRANSCRIPT
1
By Terence James Haydock
Pressure VesselA simulated response in ANSYS
2
Overview• Introduction
• Required Knowledge
• Key Equations
• Tutorial / Methodology
Engineering Data
Geometry
Model
Setup
Solution
Results
• Summary
3
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.
4
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.
5
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.
6
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.
7
ANSYS Methodology
Engineering Data
Geometry/Sketch
8
• 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
9
• 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
10
Mesh and Refine your Part
Mesh with the default values i.e. Advanced
size function OFF
Change to FIXED
Change to On: Proximity
11
Provide a frictionless support to three
surfaces
Provide a pressure to the inside surfaces
with a magnitude of 100MPa
Apply Boundary Conditions
12
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)
13
Hoop Stress (x-direction)
Axial Stress (y-direction)
Radial Stress (z-direction)
Generate your Results
14
Compare Results
Theory ANSYS % error
Hoop (x) MPa
Axial (y) MPa
Radial (z) MPa
15
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
16
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