Calculate magnetic energy

[ftrillaudp]

Good evening,

I would like to know if there is an example to show how the magnetic energy can be computed for a magnetostatic problem. I have simulated a solenoid in 2D axi-symmetry using the magnetostatic solver, I would like to compute the magnetic energy.

Best,

Frederic

[mzenker]

i,

you can enter mathematical expressions in the ElmerPost command line. For example to calculate the magnitude of an electric field, you can write

Code: Select all

  math efield = tovector(Electric.field.1,Electric.field.2,Electric.field.3)
  math elfield_mag = sqrt(vdot(efield,efield))

Or you can use the ResultOutput solver to save your results in vtu format, visualize them in ParaView and use the calculator there.

Or else you can use SaveData/SaveScalars to calculate your result in ElmerSolver directly and save it to a file.


HTH,

Matthias

[ftrillaudp]

Thanks,

Frederic

[ftrillaudp]

Hi mzenker,

I have tried to find a way to use SaveData ans SaveSaclars without success. How do I implement the magnetic energy calculation directly in Elmer sif file?, I am stuck there without any clues how to get the appropirate variable and so on.

Code: Select all

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

Simulation
  Max Output Level = 4
  Coordinate System = "Axi Symmetric"
  Coordinate Mapping(3) = 1 2 3
  Simulation Type = Steady state
  Steady State Max Iterations = 1
  Output Intervals = 1
  Timestepping Method = BDF
  BDF Order = 1
  Solver Input File = solenoid2D.sif
  Post File = solenoid2D.ep
End

Constants
  Gravity(4) = 0 -1 0 9.82
  Stefan Boltzmann = 5.67e-08
  Permeability of Vacuum = 1.257e-6
  Permittivity of Vacuum = 8.8542e-12
  Boltzmann Constant = 1.3807e-23
  Unit Charge = 1.602e-19
End

Body 1
  Target Bodies(1) = 10000
  Name = "Body 1"
  Equation = 1
  Material = 2
  Body Force = 1
End

Body 2
  Target Bodies(1) = 20000
  Name = "Body 2"
  Equation = 1
  Material = 1
End

Body 3
  Target Bodies(1) = 30000
  Name = "Body 3"
  Equation = 1
  Material = 1
End

Solver 1 
  Equation = Magnetic Vector Potential equation
  Variable = -dofs 1 Magnetic Vector Potential
  Procedure = "StatMagSolve" "StatMagSolver"
  Calculate Magnetic Flux = Logical True
  Calculate Magnetic Flux Abs = Logical True
  Calculate Joule Heating = True
  Exec Solver = Always
  Stabilize = True
  Bubbles = False
  Lumped Mass Matrix = False
  Optimize Bandwidth = True
  Steady State Convergence Tolerance = 1.0e-5
  Nonlinear System Convergence Tolerance = 1.0e-8
  Nonlinear System Max Iterations = 20
  Nonlinear System Newton After Iterations = 3
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 1
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStab
  Linear System Max Iterations = 500
  Linear System Convergence Tolerance = 1.0e-8
  Linear System Preconditioning = ILU0
  Linear System ILUT Tolerance = 1.0e-3
  Linear System Abort Not Converged = False
  Linear System Residual Output = 1
  Linear System Precondition Recompute = 1
End


Solver 2
  Exec Solver = after timestep"
  exec interval = 1
  Equation = "ResultOutput"
  Procedure = File "ResultOutputSolve" "ResultOutputSolver"
  Output File Name = "solenoid2D."
  Output Format = "vtu"
  Vtu Format = Logical True
End

Solver 3
 Exec Solver = After All
 Equation = SaveScalars
 Procedure = "SaveData" "SaveScalars"
 Filename = "magneticEnergy.dat"
End


Equation 1
  Name = "Magnetic Vector Potential equation"
  Active Solvers(1) = 1
  Static Magnetic Field Logical = Logical True
End

Body Force 1
  Name = "BodyForce 1"
  Current Density = 1000
End

Material 1
  Name = "Air (room temperature)"
  Heat expansion Coefficient = 3.43e-3
  Viscosity = 1.983e-5
  Heat Conductivity = 0.0257
  Relative Permittivity = 1.00059
  Sound speed = 343.0
  Viscosity = 1.983e-5
  Heat Capacity = 1005.0
  Density = 1.205
  Relative Permittivity = 1.00059
End

Material 2
  Name = "Copper (generic)"
  Poisson ratio = 0.34
  Heat expansion Coefficient = 16.5e-6
  Electric Conductivity = 59.59e6
  Youngs modulus = 115.0e9
  Heat Conductivity = 401.0
  Sound speed = 3810.0
  Heat Capacity = 385.0
  Mesh Poisson ratio = 0.34
  Density = 8960.0
  Poisson ratio = 0.34
  Youngs modulus = 115.0e9
End

Boundary Condition 1
 Target Boundaries = 40000
 Name = "BoundaryCondition 1"
 Magnetic Vector Potential = Real 0.0
End

[raback]

Hi

Look at SaveScalars manual. I guess your energy is \int B^2/2\mu dV. The "convective energy" looks a little bitt like this but you should define a material parameter inverse to permeability i.e. reluctivity to utilize that directly. Assuming you would have "magnetic field" as the field you would then set for SaveScalars.

Code: Select all

Variable 1 = "Magnetic Field"
Operator 1 = "convective energy"
Coefficient 1 = "Reluctivity"

Much more preferable would be to make a minor addition to the solver itself so that it would compute optimally the energy from the vector potential directly i.e. \int \curl A / 2\mu dV.

-Peter

[ftrillaudp]

Peter,

I have tried something similar:

Code: Select all

Solver 3
 Exec Solver = After All
 Equation = SaveScalars
 Procedure = "SaveData" "SaveScalars"
 Filename = "magneticEnergy.dat"
 Variable 1 = "Magnetic Field" 
! I tried: "magnetic flux density_abs" as well without success
 Operator 1 = "convective energy"
 Coefficient 1 = "Reluctivity"
End

But, I cannot find the appropriate variable for the computation. Here is the message that I get:

WARNING:: SaveData: Variable does not exist: magnetic field

I have not explored the option of changing the solver!

Best,

Frederic

[ftrillaudp]

Peter,

Sorry, I made a mistake in the name of the variable in my *.sif file. The following code produces a result which has not been cross-checked yet, but it runs. The variable is "magnetic field density_abs".

Thanks again,

Frederic

Code: Select all

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

Simulation
  Max Output Level = 4
  Coordinate System = "Axi Symmetric"
  Coordinate Mapping(3) = 1 2 3
  Simulation Type = Steady state
  Steady State Max Iterations = 1
  Output Intervals = 1
  Timestepping Method = BDF
  BDF Order = 1
  Solver Input File = solenoid2D.sif
  Post File = solenoid2D.ep
  Output File = solenoid2D.results
End

Constants
  Gravity(4) = 0 -1 0 9.82
  Stefan Boltzmann = 5.67e-08
  Permeability of Vacuum = 1.2566370614e-6
  Permittivity of Vacuum = 8.8542e-12
  Boltzmann Constant = 1.3807e-23
  Unit Charge = 1.602e-19
End

Body 1
  Target Bodies(1) = 10000
  Name = "Body 1"
  Equation = 1
  Material = 2
  Body Force = 1
End

Body 2
  Target Bodies(1) = 20000
  Name = "Body 2"
  Equation = 1
  Material = 1
End

Body 3
  Target Bodies(1) = 30000
  Name = "Body 3"
  Equation = 1
  Material = 1
End

Solver 1 
  Equation = Magnetic Vector Potential equation
  Variable = -dofs 1 Magnetic Vector Potential
  Procedure = "StatMagSolve" "StatMagSolver"
  Calculate Magnetic Flux = Logical True
  Calculate Magnetic Flux Abs = Logical True
  Calculate Joule Heating = True
  Exec Solver = Always
  Stabilize = True
  Bubbles = False
  Lumped Mass Matrix = False
  Optimize Bandwidth = True
  Steady State Convergence Tolerance = 1.0e-5
  Nonlinear System Convergence Tolerance = 1.0e-8
  Nonlinear System Max Iterations = 20
  Nonlinear System Newton After Iterations = 3
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 1
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStab
  Linear System Max Iterations = 500
  Linear System Convergence Tolerance = 1.0e-8
  Linear System Preconditioning = ILU0
  Linear System ILUT Tolerance = 1.0e-3
  Linear System Abort Not Converged = False
  Linear System Residual Output = 1
  Linear System Precondition Recompute = 1
End


Solver 2
  Exec Solver = after timestep"
  exec interval = 1
  Equation = "ResultOutput"
  Procedure = File "ResultOutputSolve" "ResultOutputSolver"
  Output File Name = "solenoid2D."
  Output Format = "vtu"
  Vtu Format = Logical True
End

Solver 3
 Exec Solver = After All
 Equation = SaveScalars
 Procedure = "SaveData" "SaveScalars"
 Filename = "magneticEnergy.dat"
 Variable 1 = "magnetic flux density_abs"
 Operator 1 = "convective energy"
 Coefficient 1 = "Reluctivity"
End

Equation 1
  Name = "Magnetic Vector Potential equation"
  Active Solvers(1) = 1
  Static Magnetic Field Logical = Logical True
End

Body Force 1
  Name = "BodyForce 1"
  Current Density = 1000
End

Material 1
  Name = "Air (room temperature)"
  Heat expansion Coefficient = 3.43e-3
  Viscosity = 1.983e-5
  Heat Conductivity = 0.0257
  Relative Permittivity = 1.00059
  Sound speed = 343.0
  Viscosity = 1.983e-5
  Heat Capacity = 1005.0
  Density = 1.205
  Reluctivity = Real 0.795774715e6
End

Material 2
  Name = "Copper (generic)"
  Poisson ratio = 0.34
  Heat expansion Coefficient = 16.5e-6
  Electric Conductivity = 59.59e6
  Youngs modulus = 115.0e9
  Heat Conductivity = 401.0
  Sound speed = 3810.0
  Heat Capacity = 385.0
  Mesh Poisson ratio = 0.34
  Density = 8960.0
  Poisson ratio = 0.34
  Youngs modulus = 115.0e9
  Reluctivity = Real 0.795774715e6
End

Boundary Condition 1
 Target Boundaries = 40000
 Name = "BoundaryCondition 1"
 Magnetic Vector Potential = Real 0.0
End

[raback]

Hi Frederic

Note that this approach has the optimal accuracy only when elements are of equal size and the reluctivity is continuous. The errors are not big but still not quite optimal... The reason is that part of the information is lost when the magnetic field density is averaged to a nodal quantity from the integration points.

-Peter

[Takala]

Good evening,

I would like to know if there is an example to show how the magnetic energy can be computed for a magnetostatic problem. I have simulated a solenoid in 2D axi-symmetry using the magnetostatic solver, I would like to compute the magnetic energy.

Best,

Frederic

Hi,

are you THE Frederic Trillaud who worked with the worlds first laser quenching device for NbTi strands under the supervision of THE Arnaud Devred?

If yes, guess who am I.

Cheers,

Eelis

[ftrillaudp]

Hi,

I am this person!


Frederic