Mgdyn shows ~20% of expected flux through a surface

Numerical methods and mathematical models of Elmer
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mkloter
Posts: 1
Joined: 15 May 2018, 18:06
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Mgdyn shows ~20% of expected flux through a surface

Post by mkloter » 16 May 2018, 21:45

I am attempting to use the mgdyn solver to determine the inductance (dc) of an arbitrary structure in 3d via Image

I have created two basic hand solvable test geometry's, a wire loop and parallel wire to test my understanding of the solver. With each geometry I only see approximately 42% of the expected inductance which stems from an incorrect total flux. The simulated current density (and by extension total current used in the above formula) always matches hand calculations. I have tried stimulating through boundary and body force cases. I am post processing through paraview and calculating flux with the surface flow filter (Integrate filter gives same answer) through an extracted surface. I have also visually inspected the flux field orientation of the entire simulation and extracted surface areas to make sure they are as expected.

Am I defining my Dirichlet conditions incorrectly?
Am I deriving the total flux density incorrectly in paraview?
Am I over/under constraining something?

The attached images show:
-Parallel wire geometry
-Parallel wire extracted plane an integration area for flux
-Parallel wire flux field
-Loop geometry

Sif for parallel wire boundary stimulation

Code: Select all

Check Keywords "Warn"

Header
  Mesh DB "."
End

Simulation
  Max Output Level = 5
  Coordinate System = "Cartesian"
  Simulation Type = Steady
  Steady State Max Iterations = 1
  Output Intervals(1) = 1

  !Coordinate Scaling = 1.0e-3
End

Constants
  Gravity(4)             = 0 0 -1 9.81 ! N            | m s^-2
  Stefan Boltzmann       = 5.67e-08    ! W m^-2 °K^-4 | kg s^-3 °K^-4
  Permittivity of Vacuum = 8.8542e-12  ! F m^-1       | A^2 s^4 kg^-1 m^-3
  Permeability of Vacuum = 1.2566e-6   ! H m^-1       | kg m s^-2 A^-2
  Boltzmann Constant     = 1.3807e-23  ! J °K^-1      | m^2 kg s^-2 °K^-1
  Unit Charge            = 1.602e-19   ! C            | A s
End

Body 1
  Name = "Wire1"
  Equation = 1
  Material = 1
End

Body 2
  Name = "Air"
  Equation = 1
  Material = 2
End

Body 3
  Name = "Wire2"
  Equation = 1
  Material = 1
End

Material 1
  Name = "Cu"
  Relative Permittivity = 1
  Relative Permeability = 1
  Electric Conductivity = 58e6
End

Material 2
  Name = "Air"
  Relative Permittivity = 1.0
  Relative Permeability = 1.0
  Electric Conductivity = 0.0
End 

Equation 1
  Active Solvers(2) = 1 2 
End


Solver 1
  Equation = "MGDynamics"
  Variable = "AV"
  Procedure = "MagnetoDynamics" "WhitneyAVSolver"
  
  Element = n:1 e:1  
  
  Fix Input Current density = Logical  True
  
  Automated Source Projection BCs = Logical False

  Linear System Symmetric = True
  Linear System Solver = "Iterative"
  Linear System Preconditioning = none
  Linear System Residual Output = 50
  Linear System Max Iterations = 1000
  Linear System Iterative Method = GCR
  Linear System Convergence Tolerance = 1.0e-5
  BicgStabl Polynomial Degree = 4
  Linear System Abort Not Converged = False
End


Solver 2
  Equation = "MGDynamicsCalc"

  Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
  Linear System Symmetric = True

  Potential Variable = String "AV"

  Calculate Current Density = Logical True
  Calculate Electric Field = Logical True
  Calculate Magnetic Field Strength = Logical True
  Calculate Joule Heating = True

  Steady State Convergence Tolerance = 0
  Linear System Solver = "Iterative"
  Linear System Preconditioning = None
  Linear System Residual Output = 0
  Linear System Max Iterations = 2000
  Linear System Iterative Method = CG
  Linear System Convergence Tolerance = 1.0e-8

  Calculate Nodal Fields = Logical False
  Impose Body Force Potential = Logical True
  Impose Body Force Current = Logical True

  Discontinuous Bodies = True
End


Solver 3
  Exec Solver = after all
  Equation = "ResultOutput"
  Procedure = "ResultOutputSolve" "ResultOutputSolver"
  Output File Name = inductor
  Vtu format = Logical True
  Discontinuous Bodies = Logical True
End

Boundary Condition 1
  Name = "WireStart"
  Target Boundaries(1) = 1 

  !Coil Start = Logical True

  !AV {e} 1 = Real 0.0
  !AV {e} 2 = Real 0.0
  !AV {e} 3 = Real 0.0
  !AV = Real 10e-3
  
  Electric Current Density = Real 3.18e3
  
End


Boundary Condition 2
  Name = "WireEnd"
  Target Boundaries(3) = 2 6 7

  !Coil End = Logical True

  AV {e} = Real 0.0

  !Electric Current Density = Real 125e3
  
  AV = Real 0
End

Boundary Condition 3
  Name = "Torus_surface"
  Target Boundaries(1) = 4 !Surface 3&5 are wire boundaries

  AV {e} = Real 0.0

End


Sif for parallel wire body force stimulation

Code: Select all

Check Keywords "Warn"

Header
  Mesh DB "."
End

Simulation
  Max Output Level = 5
  Coordinate System = "Cartesian"
  Simulation Type = Steady
  Steady State Max Iterations = 1
  Output Intervals(1) = 1

  !Coordinate Scaling = 1.0e-3
End

Constants
  Gravity(4)             = 0 0 -1 9.81 ! N            | m s^-2
  Stefan Boltzmann       = 5.67e-08    ! W m^-2 °K^-4 | kg s^-3 °K^-4
  Permittivity of Vacuum = 8.8542e-12  ! F m^-1       | A^2 s^4 kg^-1 m^-3
  Permeability of Vacuum = 1.2566e-6   ! H m^-1       | kg m s^-2 A^-2
  Boltzmann Constant     = 1.3807e-23  ! J °K^-1      | m^2 kg s^-2 °K^-1
  Unit Charge            = 1.602e-19   ! C            | A s
End

Body 1
  Name = "Wire1"
  Equation = 1
  Material = 1
  Body Force = 1
End

Body 2
  Name = "Air"
  Equation = 1
  Material = 2
End

Body 3
  Name = "Wire2"
  Equation = 1
  Material = 1
End

Material 1
  Name = "Cu"
  Relative Permittivity = 1
  Relative Permeability = 1
  Electric Conductivity = 58e6
End

Material 2
  Name = "Air"
  Relative Permittivity = 1.0
  Relative Permeability = 1.0
  Electric Conductivity = 0.0
End 

Equation 1
  Active Solvers(2) = 1 2 
End


Solver 1
  Equation = "MGDynamics"
  Variable = "AV"
  Procedure = "MagnetoDynamics" "WhitneyAVSolver"
  
  Element = n:1 e:1  
  
  Fix Input Current density = Logical  True
  
  Automated Source Projection BCs = Logical False

  Linear System Symmetric = True
  Linear System Solver = "Iterative"
  Linear System Preconditioning = none
  Linear System Residual Output = 50
  Linear System Max Iterations = 1000
  Linear System Iterative Method = GCR
  Linear System Convergence Tolerance = 1.0e-5
  BicgStabl Polynomial Degree = 4
  Linear System Abort Not Converged = False
End


Solver 2
  Equation = "MGDynamicsCalc"

  Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
  Linear System Symmetric = True

  Potential Variable = String "AV"

  Calculate Current Density = Logical True
  Calculate Electric Field = Logical True
  Calculate Magnetic Field Strength = Logical True
  Calculate Joule Heating = True

  Steady State Convergence Tolerance = 0
  Linear System Solver = "Iterative"
  Linear System Preconditioning = None
  Linear System Residual Output = 0
  Linear System Max Iterations = 2000
  Linear System Iterative Method = CG
  Linear System Convergence Tolerance = 1.0e-8

  Calculate Nodal Fields = Logical False
  Impose Body Force Potential = Logical True
  Impose Body Force Current = Logical True

  Discontinuous Bodies = True
End


Solver 3
  Exec Solver = after all
  Equation = "ResultOutput"
  Procedure = "ResultOutputSolve" "ResultOutputSolver"
  Output File Name = inductor
  Vtu format = Logical True
  Discontinuous Bodies = Logical True
End

Body Force 1
    Name = "Current"
    Current Density 3 = real 150e3
End

Boundary Condition 1
  Name = "Farfield"
  Target Boundaries(1) = 3 4 5 !Surface 3&5 are wire boundaries
  AV {e} = Real 0.0

End


Thanks everyone,
Mike
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Takala
Posts: 182
Joined: 23 Aug 2009, 23:59

Re: Mgdyn shows ~20% of expected flux through a surface

Post by Takala » 18 May 2018, 07:53

Hi Mike,

you could try to compute the average flux through some surface by defining a keyword in a boundary section:

Code: Select all

Boundary 1
  Name = "Boundary where flux is computed"
  Target Boundaries(1) = $ flux_boundary
  Magnetic Flux Average = Logical True
End
Another way to compute inductance is via energy. In fact, if I remember correctly,
Elmer does report the total magnetic field energy. I would advice to do all the computations
always in Elmer and only the visualization in Paraview.

You should also remember the fact that the A-formulation naturally gives too low inductance
and too low magnetic energy. You get closer to the correct result by increasing the number of elements.

BR,

Eelis

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