Thermomechanical problem of a pressure vessel

[han2014]

Hi all,

I am a newbie in FEM and Elmer. I am interested in using it to solve thermomechanical problem of hydrogen storage tank. As an initial step, I have tested it on a pressure vessel problem described in this document (Problem 4, page 10) I found online:

http://www.openeering.com/sites/default ... Scilab.pdf

In a nutshell, it is a tank of 2 materials (steel in the inner side, and some insulation material in the outer side), modeled in 2D axi-symmetric coordinate. The tank contains a fluid, which exerts a constant pressure of 1 MPa to the inner wall of the tank. The fluid temperature changes with time.

I generated the geometry and mesh using Salome and exported the mesh as *.unv to Elmer, before converting it to Elmer readable format using ElmerGrid.

The *.sif is given below.

Code: Select all

Check Keywords Warn

Header
  Mesh DB "." "m1"
End

Simulation
  Coordinate System = Axi Symmetric 
  Coordinate Mapping(3) = 1 2 3
  Simulation Type = Transient
  Steady State Max Iterations = 20
  Timestepping Method = BDF
  BDF Order = 2
  Timestep Intervals = 150 
  Timestep Sizes = 1
  Output Intervals = 10
  Output File = "vessel-thermomech.result"
  Post File = "vessel-thermomech.vtu"
End

Body 1
  Name = "Steel"
  Equation = 1
  Material = 1
  Initial Condition = 1
End

Body 2 
  Name = "Insulation"
  Equation = 1
  Material = 2
  Initial Condition = 1 
End

Initial Condition 1
  Displacement 1 = 0
  Displacement 2 = 0
  Temperature = 273 
End

Material 1
   Density = 7850.0
   Heat Capacity = 434.0
   Heat Conductivity = 60.5
   Youngs modulus = 2.0e+11
   Poisson ratio = 0.3 
   Heat Expansion Coefficient = 1.2e-5 
End

Material 2 
   Density = 937.0
   Heat Capacity = 303.0
   Heat Conductivity = 0.5
   Youngs modulus = 1.1e+9
   Poisson ratio = 0.45 
   Heat Expansion Coefficient = 2e-4 
End

Solver 1 
  Equation = Heat Equation
  Stabilize = True
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStab
  Linear System Convergence Tolerance = 1.0e-12
  Linear System Max Iterations = 500
  Linear System Preconditioning = ILU
  Linear System Abort Not Converged = True 
  Nonlinear System Newton After Iterations = 1
  Nonlinear System Newton After Tolerance = 1.0e-4
  Nonlinear System Max Iterations = 50
  NonLinear System Convergence Tolerance = 1.0e-8
  Steady State Convergence Tolerance = 1.0e-8
  Nonlinear System Relaxation Factor = 0.7
End

Solver 2 
Equation = Linear Elasticity
Procedure = "StressSolve" "StressSolver"
Variable = -dofs 2 Displacement
Exported Variable 1 = -dofs 2 Displacement 1
Exported Variable 2 = -dofs 2 Displacement 2
Exec Solver = After All
Calculate Loads = True
Displace Mesh = False
Calculate Stresses = True
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Plane Stress = True
Steady State Convergence Tolerance = 1.0e-8
Nonlinear System Convergence Tolerance = 1.0e-8
Nonlinear System Max Iterations = 50
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-4
Nonlinear System Relaxation Factor = 0.7
Linear System Solver = Direct
Linear System Direct Method = Banded
Linear System Abort Not Converged = True 
End

Equation 1
  Active Solvers(2) = 1 2
  Calculate Stresses = True
End

Boundary Condition 1
   Name = "Symmetry"
   Target Boundaries = 1 
End

Boundary Condition 2
   Target Boundaries = 3 
   Heat Flux BC = True
   Heat Flux = 0.0
End

Boundary Condition 3 
   Target Boundaries = 2 
   Temperature = Variable Time
    Real
      0.0      273.0
      10.0     323.0
      100.0    323.0
      110.0    373.0
      190.0    373.0
      200.0    273.0
      500.0    273.0
    End

   Normal Force = -1.0e+6
End

The results, in comparison to the results from the paper, are given in the attached figures.

Temperature:

result-vm.png

von Mises

(505.77 KiB) Not downloaded yet

Displacements:

result-disp.png

Displacements

(243.16 KiB) Not downloaded yet

von Mises stress:

result-temp.png

Temperature

(471 KiB) Not downloaded yet

Whereas the temperature distribution agrees very well with that reported in the above pdf document, it is not the case for displacements and vonMises stress. In particular, the von Mises stress I obtained for the outer insulation is high but there is a thin region of small values in the vicinity of steel-insulation interface. I have been very much puzzled by this. I have tried to refine the mesh, but I still couldn't get the displacement & vonMises stress to match the paper.

I would really appreciate it if anyone could suggest what could've caused the difference & tell whether I did something wrong in Elmer.

Thanks a lot.

Han

[raback]

Hi Han

Overall your results agree quite well with the reference. The min/max stress values are highly mesh dependent. They could even be mathematically approaching infinity at some points so I would rather try to look that the isocurves of the stress fields agree. Now your mesh resolution could be better.

You could try to perform mesh multiplication i.e. in Simulation section set, for example

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Mesh Levels = 2

Or you could try with higher order elements i.e. in Solver section set, for example

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Element = p:2

-Peter

[han2014]

Hi Peter,

Thanks a lot for your reply.

I agree that the isocurves of the stress fields agree with the reference, but only in the top and inner part of the vessel. If you look at the outer part of the vessel (which is made of an insulation material), the results in the reference show that the vonMises stress is low, but Elmer results show that the stress is about as high as the stress in the inner material with a thin region of small value in the interface. This is what puzzles me. I've done the simulation on mesh level = 2, and still I got the same behavior.

result-vm-zoom.png

vonMises mesh1, mesh2, reference

(567.6 KiB) Not downloaded yet

I begin to wonder whether the material properties for the stress solver (either Young's modulus or Poisson ratio) described in the reference are not correct. I am going to vary them to see what changes in stress fields that would make.

Thanks again.

kind regards,

Han

[LeeA]

The difference may appear just because some BC are different (limits of deformation or etc).
You can also try CalculiX for this special problem http://calculix.de/
It supports thermo-mech problems and axi-symmetric elements

[han2014]

Hi LeeA,

Thanks. I will check on Calculix too.

regards,

Han