Skin effect in an electric conductor

Numerical methods and mathematical models of Elmer
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Franz
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Joined: 31 May 2016, 08:24
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Skin effect in an electric conductor

Post by Franz »

Hello,

i have a problem with the WhitneyAVHarmonicSolver. For verification issues i tried to simulate the ohmic losses in a single wire for different frequencies.
For that i applied a positive and a negative potential on the wire surfaces and fix the magnetic flux density so that a didn't have a z-component.
The resulting fields look's like that of an infinite wire, which was my requirement. In principle i can also see that the current density is higher at the wire skin with increasing frequencies, but the value of the total resistance do not match with the analytic and the FEMM solution. I calculate the ohmic losses with R=U^2/P, where P is the eddy current power.

For frequencies below 100Hz (there is no skin effect) the resistance is ok. Mesh refinements have no effect on the result.
What could be the problem?

Thanks Franz
singleWire10kHz.png
Joule Field at a frequency of 10kHz
(36.77 KiB) Not downloaded yet

Code: Select all

Header
  CHECK KEYWORDS Warn
  Mesh DB "." "singleWire"
  Include Path ""
  Results Directory ""
End

    $ f = 1.e4
    $ omega = 2*pi*f

Simulation
  Max Output Level = 7
  Coordinate System = "Cartesian"
  Simulation Type = Steady State
  Steady State Max Iterations = 1
!  Output Intervals(1) = 0
  Solver Input File = singleWire.sif
  Post File = singleWire.ep
  Coordinate Scaling = Real 0.001
End

Constants
  Permittivity of Vacuum = real 8.8542e-12
  Permeability of Vacuum = real 1.2566e-6
End

Body 1
  Target Bodies(1) = 1
  Name = "Body Property 1"
  Equation = 1
  Material = 2
End


Body 2
  Target Bodies(1) = 2
  Name = "Body Property 2"
  Equation = 1
  Material = 1
End


Equation 1
  Name = "Equation 1"
  Active Solvers(5) = 1 2 3 4 5
End

Solver 1
  Equation = Static Current Conduction
  Variable = -dofs 1 Potential
  Procedure = "StatCurrentSolve" "StatCurrentSolver"  
  Exec Solver = Always
  Calculate Volume Current = True
  Calculate Loads = True
  Constant Weights = True
  Calculate Joule Heating = True
  Stabilize = True
  Bubbles = False
  Lumped Mass Matrix = False
  Optimize Bandwidth = True
  Steady State Convergence Tolerance = 1.0e-5
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStab
  Linear System Max Iterations = 1500
  Linear System Convergence Tolerance = 1.0e-12
  Linear System Preconditioning = ILU0
  Linear System ILUT Tolerance = 1.0e-3
  Linear System Abort Not Converged = False
  Linear System Residual Output = 10
  Linear System Precondition Recompute = 1
End

Solver 2
  Equation = "MGDynamics"
  Variable = P[P re:1 P im:1]
  Procedure = "MagnetoDynamics" "WhitneyAVHarmonicSolver"
  Exec Solver = Always
  Fix Input Current Density = Logical False
  Angular Frequency = $ omega
  Steady State Convergence Tolerance = 1.0e-4
  Linear System Symmetric = True
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStabL
  BiCGStabL Polynomial Degree = 4
  Linear System Max Iterations = 5000
  Linear System Convergence Tolerance = 1.0e-8
  Linear System Preconditioning = None
  Linear System ILUT Tolerance = 1.0e-5
  Linear System Abort Not Converged = False
  Linear System Residual Output = 10
  Linear System Precondition Recompute = 1
End

Solver 3
    Equation = "MGDynamicsCalc"
    Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
    Exec Solver = After all
    Linear System Symmetric = True
    Potential Variable = String "P"
    Angular Frequency = $ omega
    Show Angular Frequency = Logical True
    Calculate Magnetic Field Strength = Logical True
    Calculate Current Density = Logical True
    Calculate Joule Heating = Logical True
    Calculate Nodal Fields = Logical True
    Calculate Magnetic Field Strength = Logical True
    Calculate Electric Field = Logical True
    Calculate Magnetic Field = Logical True
    Steady State Convergence Tolerance = 0
	Linear System Symmetric = True
    Linear System Solver = "Iterative"
    Linear System Preconditioning = None
    Linear System Residual Output = 0
    Linear System Max Iterations = 500
    Linear System Iterative Method = CG
    Steady State Convergence Tolerance = 1e-6
    Linear System Convergence Tolerance = 1.0e-8
End

Solver 4
  Exec Solver = after all
  Equation = "ResultOutput"
  Procedure = "ResultOutputSolve" "ResultOutputSolver"
  Output File Name = singleWire
  Vtu format = Logical True
End

Solver 5
  Exec Solver = After all
  Equation = SaveScalars
  Procedure = "SaveData" "SaveScalars"
  Filename = "singleWire.dat"
  operator 1 = boundary sum
  variable 1 = Potential Loads
  operator 2 = Volume !convective flux
  variable 2 = Joule Heating !Current Density
End

Material 1
  Name = "Air"
  Relative Permittivity = Real 1
  Relative Permeability = Real 1
  Electric Conductivity = Real 0
End

Material 2
  Name = "Cu"
  Relative Permittivity = Real 1
  Relative Permeability = Real 1
  Electric Conductivity = Real 58e6
End


Boundary Condition 1
  Target Boundaries(1) = 1
  Name = "PositiveOne"
! Define zero magnetic flux in z-direction
  P re {e} 1 = real 0.
  P im {e} 1 = real 0.
  P re {e} 2 = real 0.
  P im {e} 2 = real 0.
! End define zero magnetic flux in z-direction
  P re = real 0.001
  P im = real 0.
  Potential = 0.001
  Save Scalars = Logical True
End

Boundary Condition 2
  Target Boundaries(1) = 2
  Name = "NegativeOne"
! Define zero magnetic flux in z-direction
  P re {e} 1 = real 0.
  P im {e} 1 = real 0.
  P re {e} 2 = real 0.
  P im {e} 2 = real 0.
! End define zero magnetic flux in z-direction
  P re = real -0.001
  P im = real 0.
  Potential = -0.001
  Save Scalars = Logical True
End

Boundary Condition 3
  Target Boundaries(2) = 3 4
  Name = "BoundingBoxWire"
! Define zero magnetic flux in z-direction
  P re {e} 1 = real 0.
  P im {e} 1 = real 0.
  P re {e} 2 = real 0.
  P im {e} 2 = real 0.
End

Boundary Condition 4
  Target Boundaries(1) = 5
  Name = "BoundingBox"
  P re {e} = real 0.
  P im {e} = real 0.
End
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